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Question 1 of 50

Instructions:
This section tests your ability to answer Problem Solving questions in the Quantitative part of the GRE. You are given a problem statement and some information relating to the context in which the problem is set. You should consider the numbers used in these problems to be real numbers, unless otherwise stated. All geometrical figures in this lab should be taken to be on a plane. You should take no more than 2 minutes per question.

If $\image001.png$ , which of the following options is true?

Opción múltiple

$\image002.png$ and $\image003.png$ >0

$\image002.png$ and $\image003.png$ <0

$\image004.png$ or $\image005.png$

$\image002.png$ ;#

$\image003.png$ <0

A)	This is the correct option. For the inequality to hold, either the denominator or the numerator must be negative, but not both.
B)	If both the denominator and numerator are negative, the fraction is positive and the inequality does not hold. This option is incorrect.
C)	If $\image004.png$ ,the numerator is 0 and the strict inequality does not hold. This option is incorrect.
D)	That $\image002.png$ is true does not make the inequality hold. We need to know if the denominator is positive or negative. We cannot answer the question. This option is incorrect.
E)	That $\image006.png$ <0 is true does not make the inequality hold. We need to know if the numerator is positive or negative. We cannot answer the question. This option is incorrect.

Question 2 of 50

If $\image007.png$ is any prime number, for which value of $\image015-X.png$ is $\image009.png$ ?

Opción múltiple

-1

$\image007.png$

	A)	If , then is which is not equal to . This option is incorrect.
	B)	This is the correct option. , therefore, .
	C)	With the equation becomes which is not equal to . This option is incorrect.
	D)	With the equation becomes which is not equal to . This option is incorrect.
	E)	With the equation becomes which is not equal to. This option is incorrect.

Question 3 of 50

A chord on a circle with a 26-foot diameter is 5 feet from the center at its closest point. How many feet long is the chord?

Opción múltiple

$\image021.png$

$\image022.png$

$\image023.png$

$\image024.png$ ;#

$\image025.png$

	A)	The shortest distance from a chord to the center of a circle forms a angle with the chord. Taking this line segment from the center to the chord, whose length we do not know, half the chord’s length and the point where the chord meets the circumference, we have a right-angled triangle. This triangle measureswhere is half the chord’s length. The ratio, for a right-angled triangle, is one of the Pythagorean triplets (i.e. 5:12:13). Using this information we know the total length of the chord is 24 feet. Alternatively, the length of half the chord may be calculated usingand solving for . This option is incorrect.
	B)	The shortest distance from a chord to the center of a circle forms a angle with the chord. Taking this line segment from the center to the chord, whose length we do not know, half the chord’s length and the point where the chord meets the circumference, we have a right-angled triangle. This triangle measureswhere is half the chord’s length. The ratio, for a right-angled triangle, is one of the Pythagorean triplets (i.e. 5:12:13). Using this information we know the total length of the chord is 24 feet. Alternatively, the length of half the chord may be calculated using and solving for . This option is incorrect.
	C)	The shortest distance from a chord to the center of a circle forms a angle with the chord. Taking this line segment from the center to the chord, whose length we do not know, half the chord’s length and the point where the chord meets the circumference, we have a right-angled triangle. This triangle measures where is half the chord’s length. The ratio, for a right-angled triangle, is one of the Pythagorean triplets (i.e. 5:12:13). Using this information we know the total length of the chord is 24 feet. Alternatively, the length of half the chord may be calculated usingand solving for .This option is incorrect.
	D)	This the correct opinion. The shortest distance from a chord to the center of a circle forms a angle with the chord. Taking this line segment from the center to the chord, whose length we do not know, half the chord’s length and the point where the chord meets the circumference, we have a right-angled triangle. This triangle measures whereis half the chord’s length. The ratio, for a right-angled triangle, is one of the Pythagorean triplets (i.e. 5:12:13). Using this information we know the total length of the chord is 24 feet. Alternatively, the length of half the chord may be calculated using and solving for .
	E)	The shortest distance from a chord to the center of a circle forms a angle with the chord. Taking this line segment from the center to the chord, whose length we do not know, half the chord’s length and the point where the chord meets the circumference, we have a right-angled triangle. This triangle measureswhere is half the chord’s length. The ratio, for a right-angled triangle, is one of the Pythagorean triplets (i.e. 5:12:13). Using this information we know the total length of the chord is 24 feet. Alternatively, the length of half the chord may be calculated using and solving for . This option is incorrect.

Question 4 of 50

In how many different ways can the position of Chief Executive Officer (CEO), Chief Technology Officer (CTO), and Chief Financial Officer (CFO) be selected from 10 candidates?

Opción múltiple

100

250 ;#

720

	A)	There are ten ways of choosing the first position. There are nine ways of choosing the second position because there are nine people left. There are eight ways of choosing the third position. Therefore, the number of ways we can choose people for these positions is . Alternatively, we are being asked for the possible combinations without replacement for 10 things in 3 places. The formula for this is $\image033.png$ . This option is incorrect.
	B)	There are ten ways of choosing the CEO. There are nine ways of choosing the CTO because there are nine people left. There are eight ways of choosing the CFO. Therefore, the number of ways we can choose people for these positions is . Alternatively, we are being asked for the possible combinations without replacement for 10 things in 3 places. The formula for this is $\image033.png$ . This option is incorrect.
	C)	There are ten ways of choosing the CEO. There are nine ways of choosing the CTO because there are nine people left. There are eight ways of choosing the CFO. Therefore, the number of ways we can choose people for these positions is . Alternatively, we are being asked for the possible combinations without replacement for 10 things in 3 places. The formula for this is $\image033.png$ . This option is incorrect.
	D)	There are ten ways of choosing the CEO. There are nine ways of choosing the CTO because there are nine people left. There are eight ways of choosing the CFO. Therefore, the number of ways we can choose people for these positions is . Alternatively, we are being asked for the possible combinations without replacement for 10 things in 3 places. The formula for this is $\image033.png$ . This option is incorrect.
	E)	This is the correct option. There are ten ways of choosing the CEO. There are nine ways of choosing the CTO because there are nine people left. There are eight ways of choosing the CFO. Therefore, the number of ways we can choose people for these positions is . Alternatively, we are being asked for the possible permutations of 10 things in 3 places. The formula for this is.

Question 5 of 50

Taking two different types of fruit at a time, how many different fruit blends can a juicer make using apples, bananas, oranges, strawberries, blueberries, kiwis, and mangoes?

Opción múltiple

654

840 ;#

1680

	A)	The problem is asking for the combinations of seven things in two places . This option is incorrect.
	B)	This is the correct option. The problem is asking for the combinations of seven things in two places .
	C)	The problem is asking for the combinations of seven things in two places . This option is incorrect.
	D)	The problem is asking for the combinations of seven things in two places . This option is incorrect.
	E)	The problem is asking for the combinations of seven things in two places . This option is incorrect.

Question 6 of 50

If there are 3 white balls and 3 blue balls, what is the probability of choosing the three blue balls without replacement?

Opción múltiple

D) ;#

	A)	This is the correct option. The probability that we choose a blue ball the first time is as there are three blue balls and six balls total. Following similar reasoning, the second blue-ball draw has a probability and the last one, a probability of . The probability of obtaining three blue balls consecutively is .
	B)	The probability that we choose a blue ball the first time is $\image040.png$ as there are three blue balls and six balls total. Following similar reasoning, the second blue-ball draw has a $\image040.png$ probability and the last one, a probability of $\image040.png$ . The probability of obtaining three blue balls consecutively is $\image041.png$ . This option is incorrect.
	C)	The probability that we choose a blue ball the first time is as there are three blue balls and six balls total. Following similar reasoning, the second blue-ball draw has a probability and the last one, a probability of . The probability of obtaining three blue balls consecutively is . This option is incorrect.
	D)	The probability that we choose a blue ball the first time is as there are three blue balls and six balls total. Following similar reasoning, the second blue-ball draw has a probability and the last one, a probability of . The probability of obtaining three blue balls consecutively is . This option is incorrect.
	E)	The probability that we choose a blue ball the first time is as there are three blue balls and six balls total. Following similar reasoning, the second blue-ball draw has a probability and the last one, a probability of . The probability of obtaining three blue balls consecutively is . This option is incorrect.

Question 7 of 50

How many times would the number 2 be written when writing numbers from 1 to 10,000?

Opción múltiple

200

3,560

5,512

7,549 ;#

13,753

	A)	There are no number 2’s in 10,000 so we will count only the number of number 2’s from 1 to 9,999. There are $\image042.png$ ways to place one number in four places. Setting aside the place for the number 2 we have written, we need to count the different combinations we can make using the other possible numbers for each of the other places. We, hereby, obtain a total of $\image043.png$ times number 2 is written only once. Similarly, there are $\image044.png$ ways to place two numbers in four places. The number of times number 2 appears twice is $\image045.png$ . The number of times you can place three numbers in four places is $\image046.png$ . The number of times 2 appears three times is $\image047.png$ . There is one way to place four numbers in four places so, for this number (i.e. 2,222) number 2 appears 4 times. Adding each of these cases, we obtain the number of times number 2 is written in all numbers from 1 to 10,000. $\image048.png$ . This option is incorrect.
	B)	There are no number 2’s in 10,000 so we will count only the number of number 2’s from 1 to 9,999. There are $\image042.png$ ways to place one number in four places. Setting aside the place for the number 2 we have written, we need to count the different combinations we can make using the other possible numbers for each of the other places. We, hereby, obtain a total of $\image043.png$ times number 2 is written only once. Similarly, there are $\image044.png$ ways to place two numbers in four places. The number of times number 2 appears twice is $\image045.png$ . The number of times you can place three numbers in four places is $\image046.png$ . The number of times 2 appears three times is $\image047.png$ . There is one way to place four numbers in four places so, for this number (i.e. 2,222) number 2 appears 4 times. Adding each of these cases, we obtain the number of times number 2 is written in all numbers from 1 to 10,000. $\image048.png$ . This option is incorrect.
	C)	This is the correct option. There are no number 2’s in 10,000 so we will count only the number of number 2’s from 1 to 9,999. There are $\image042.png$ ways to place one number in four places. Setting aside the place for the number 2 we have written, we need to count the different combinations we can make using the other possible numbers for each of the other places. We, hereby, obtain a total of $\image043.png$ times number 2 is written only once. Similarly, there are $\image044.png$ ways to place two numbers in four places. The number of times number 2 appears twice is $\image045.png$ . The number of times you can place three numbers in four places is $\image046.png$ . The number of times 2 appears three times is $\image047.png$ . There is one way to place four numbers in four places so, for this number (i.e. 2,222) number 2 appears 4 times. Adding each of these cases, we obtain the number of times number 2 is written in all numbers from 1 to 10,000. $\image049.png$ .
	D)	There are no number 2’s in 10,000 so we will count only the number of number 2’s from 1 to 9,999. There are $\image042.png$ ways to place one number in four places. Setting aside the place for the number 2 we have written, we need to count the different combinations we can make using the other possible numbers for each of the other places. We, hereby, obtain a total of $\image043.png$ times number 2 is written only once. Similarly, there are $\image044.png$ ways to place two numbers in four places. The number of times number 2 appears twice is $\image045.png$ . The number of times you can place three numbers in four places is $\image046.png$ . The number of times 2 appears three times is $\image047.png$ . There is one way to place four numbers in four places so, for this number (i.e. 2,222) number 2 appears 4 times. Adding each of these cases, we obtain the number of times number 2 is written in all numbers from 1 to 10,000. $\image048.png$ . This option is incorrect.
	E)	There are no number 2’s in 10,000 so we will count only the number of number 2’s from 1 to 9,999. There are $\image042.png$ ways to place one number in four places. Setting aside the place for the number 2 we have written, we need to count the different combinations we can make using the other possible numbers for each of the other places. We, hereby, obtain a total of $\image043.png$ times number 2 is written only once. Similarly, there are $\image044.png$ ways to place two numbers in four places. The number of times number 2 appears twice is $\image045.png$ . The number of times you can place three numbers in four places is $\image046.png$ . The number of times 2 appears three times is $\image047.png$ . There is one way to place four numbers in four places so, for this number (i.e. 2,222) number 2 appears 4 times. Adding each of these cases, we obtain the number of times number 2 is written in all numbers from 1 to 10,000. $\image048.png$ . This option is incorrect.

Question 8 of 50

How many six-character computer passwords can be generated using the letters in the name Rafael without repetition or capital letter distinction?

Opción múltiple

A) 0;#

B) 2;#

C) 12;#

D) 360;#

E) 1,814,400

	A)	This is the correct option. The letter ‘a’ repeats so Rafael is not a valid password. To generate other passwords using the same letters, we would have to repeat letters.
	B)	The letter ‘a’ repeats so Rafael is not a valid password. To generate other passwords using the same letters, we would have to repeat letters. This option is incorrect.
	C)	The letter ‘a’ repeats so Rafael is not a valid password. To generate other passwords using the same letters, we would have to repeat letters. This option is incorrect.
	D)	The letter ‘a’ repeats so Rafael is not a valid password. To generate other passwords using the same letters, we would have to repeat letters. This option is incorrect.
	E)	The letter ‘a’ repeats so Rafael is not a valid password. To generate other passwords using the same letters, we would have to repeat letters. This option is incorrect.

Question 9 of 50

When two six-sided die numbered from 1-6 are tossed, is it more probable that the sum of the die equals 5 or 7?

Opción múltiple

It is equally probable.

It depends on which dice is thrown first. ;#

It cannot be known.

	A)	To add up to five, a pair of six-sided die can have the following combinations: (2,3), (3,2), (1,4), (4,1). To add up to seven the die could be in the following combinations: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3). We have more combinations for adding up to 7. This option is incorrect.
	B)	This is the correct option. To add up to five, a pair of six-sided die can have the following combinations: (2,3), (3,2), (1,4), (4,1). To add up to seven the die could be in the following combinations: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3). We have more combinations for adding up to 7.
	C)	To add up to five, a pair of six-sided die can have the following combinations: (2,3), (3,2), (1,4), (4,1). To add up to seven the die could be in the following combinations: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3). We have more combinations for adding up to 7. This option is incorrect.
	D)	To add up to five, a pair of six-sided die can have the following combinations: (2,3), (3,2), (1,4), (4,1). To add up to seven the die could be in the following combinations: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3). We have more combinations for adding up to 7. This option is incorrect.
	E)	To add up to five, a pair of six-sided die can have the following combinations: (2,3), (3,2), (1,4), (4,1). To add up to seven the die could be in the following combinations: (1,6), (6,1), (2,5), (5,2), (3,4), (4,3). We have more combinations for adding up to 7. This option is incorrect.

Question 10 of 50

A parallelogram for which three sides measure $\image050.png$ is inscribed in a circle. What is an expression for the area between the circle and the parallelogram?

Opción múltiple

$\image051.png$

$\image052.png$

$\image053.png$

$\image054.png$ ;#

$\image055.png$

	A)	If three of the sides of a parallelogram measure $\image050.png$ , then the parallelogram is necessarily a square. The diagonal of this a-sided square measures $\image053.png$ . The area for the circle is $\image056.png$ where $\image057.png$ is the diameter of the circle. The circle’s diameter coincides with the square’s diagonal, which allows us to express the circle’s area as $\image051.png$ . This same expression, when simplified, is $\image054.png$ . Then the area of the circle minus the area of the square is $\image058.png$ or $\image052.png$ . This option is incorrect.
	B)	This is the correct option. If three of the sides of a parallelogram measure $\image050.png$ , then the parallelogram is necessarily a square. The diagonal of this a-sided square measures $\image053.png$ . The area for the circle is $\image056.png$ where $\image057.png$ is the diameter of the circle. The circle’s diameter coincides with the square’s diagonal, which allows us to express the circle’s area as $\image051.png$ . This same expression, when simplified, is $\image054.png$ . Then the area of the circle minus the area of the square is $\image058.png$ or $\image052.png$ . This is the expression we are after.
	C)	If three of the sides of a parallelogram measure $\image050.png$ , then the parallelogram is necessarily a square. The diagonal of this a-sided square measures $\image053.png$ . The area for the circle is $\image056.png$ where $\image057.png$ is the diameter of the circle. The circle’s diameter coincides with the square’s diagonal, which allows us to express the circle’s area as $\image051.png$ . This same expression, when simplified, is $\image054.png$ . Then the area of the circle minus the area of the square is $\image058.png$ or $\image052.png$ . This option is incorrect.
	D)	If three of the sides of a parallelogram measure $\image050.png$ , then the parallelogram is necessarily a square. The diagonal of this a-sided square measures $\image053.png$ . The area for the circle is $\image056.png$ where $\image057.png$ is the diameter of the circle. The circle’s diameter coincides with the square’s diagonal, which allows us to express the circle’s area as $\image051.png$ . This same expression, when simplified, is $\image054.png$ . Then the area of the circle minus the area of the square is $\image058.png$ or $\image052.png$ . This option is incorrect.
	E)	If three of the sides of a parallelogram measure $\image050.png$ , then the parallelogram is necessarily a square. The diagonal of this a-sided square measures $\image053.png$ . The area for the circle is $\image056.png$ where $\image057.png$ is the diameter of the circle. The circle’s diameter coincides with the square’s diagonal, which allows us to express the circle’s area as $\image051.png$ . This same expression, when simplified, is $\image054.png$ . Then the area of the circle minus the area of the square is $\image058.png$ or $\image052.png$ . This option is incorrect.

Question 11 of 50

What is the area of a circular ring of grass whose inner diameter is $\image059.png$ , and external circumference is $\image060.png$ ?

Opción múltiple

$\image061.png$

$\image062.png$

$\image063.png$

$\image064.png$ ;#

$\image065.png$

	A)	The radius of the inner circle without grass is $\image066.png$ . The area of this circle is then $\image067.png$ . The circumference of a circle is $\image068.png$ . The outer circle has a radius of $\image069.png$ , and an area of $\image061.png$ . The area of the circular ring of grass is then $\image070.png$ or $\image064.png$ . This option is wrong.
	B)	The radius of the inner circle without grass is $\image066.png$ . The area of this circle is then $\image067.png$ . The circumference of a circle is $\image068.png$ . The outer circle has a radius of $\image069.png$ , and an area of $\image061.png$ . The area of the circular ring of grass is then $\image070.png$ or $\image064.png$ . This option is wrong.
	C)	The radius of the inner circle without grass is $\image066.png$ . The area of this circle is then $\image067.png$ . The circumference of a circle is $\image068.png$ . The outer circle has a radius of $\image069.png$ , and an area of $\image061.png$ . The area of the circular ring of grass is then $\image070.png$ or $\image064.png$ . This option is wrong.
	D)	This is the correct option. The radius of the inner circle without grass is $\image066.png$ . The area of this circle is then $\image067.png$ . The circumference of a circle is $\image068.png$ . The outer circle has a radius of $\image069.png$ , and an area of $\image061.png$ . The area of the circular ring of grass is then $\image070.png$ or $\image064.png$ .
	E)	The radius of the inner circle without grass is $\image066.png$ . The area of this circle is then $\image067.png$ . The circumference of a circle is $\image068.png$ . The outer circle has a radius of $\image069.png$ , and an area of $\image061.png$ . The area of the circular ring of grass is then $\image070.png$ or $\image064.png$ . This option is wrong.

Question 12 of 50

Which equation describes the line that forms a $\image071.png$ angle with the $\image072.png$ line?

Opción múltiple

A) $\image073.png$ ;#

B) $\image074.png$ ;#

C) $\image075.png$ ;#

D) $\image076.png$ ;#

E) $\image077.png$

	A)	The equation for a straight line is $\image078.png$ where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . If we take the displacement to be 0, we have a $\image081.png$ triangle that has a $\image082.png$ ratio relating its sides. We can then use the ratio to know a point other than (0,0) through which the line passes, (i.e. $\image083.png$ ). Substituting these points in $\image079.png$ we obtain $\image084.png$ . And substituting this result in $\image078.png$ , we obtain the equation $\image075.png$ . This is the equation for all lines forming a $\image071.png$ angle with $\image072.png$ . This answer is incorrect.
	B)	The equation for a straight line is $\image078.png$ where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . If we take the displacement to be 0, we have a $\image081.png$ triangle that has a $\image082.png$ ratio relating its sides. We can then use the ratio to know a point other than (0,0) through which the line passes, (i.e. $\image083.png$ ). Substituting these points in $\image079.png$ we obtain $\image084.png$ . And substituting this result in $\image078.png$ , we obtain the equation $\image075.png$ . This is the equation for all lines forming a $\image071.png$ angle with $\image072.png$ . This answer is incorrect.
	C)	This is the correct option. The equation for a straight line is $\image078.png$ where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . If we take the displacement to be 0, we have a $\image081.png$ triangle that has a $\image082.png$ ratio relating its sides. We can then use the ratio to know a point other than (0,0) through which the line passes, (i.e. $\image083.png$ ). Substituting these points in $\image079.png$ we obtain $\image084.png$ . And substituting this result in $\image078.png$ , we obtain the equation $\image075.png$ . This is the equation for all lines forming a $\image071.png$ angle with $\image072.png$ .
	D)	The equation for a straight line is $\image078.png$ where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . If we take the displacement to be 0, we have a $\image081.png$ triangle that has a $\image082.png$ ratio relating its sides. We can then use the ratio to know a point other than (0,0) through which the line passes, (i.e. $\image083.png$ ). Substituting these points in $\image079.png$ we obtain $\image084.png$ . And substituting this result in $\image078.png$ , we obtain the equation $\image075.png$ . This is the equation for all lines forming a $\image071.png$ angle with $\image072.png$ . This answer is incorrect.
	E)	The equation for a straight line is $\image078.png$ where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . If we take the displacement to be 0, we have a $\image081.png$ triangle that has a $\image082.png$ ratio relating its sides. We can then use the ratio to know a point other than (0,0) through which the line passes, (i.e. $\image083.png$ ). Substituting these points in $\image079.png$ we obtain $\image084.png$ . And substituting this result in $\image078.png$ , we obtain the equation $\image075.png$ . This is the equation for all lines forming a $\image071.png$ angle with $\image072.png$ . This answer is incorrect.

Question 13 of 50

What is the area of a square parking lot that measures $\image085.png$ diagonally?

Opción múltiple

$\image086.png$

$\image087.png$

$\image088.png$

$\image089.png$ ;#

$\image090.png$

	A)	This is the correct option. The diagonal of a square whose sides measure $\image030.png$ is $\image091.png$ . The side of the parking lot is $\image092.png$ . The area is $\image093.png$ .
	B)	The diagonal of a square whose sides measure $\image030.png$ is $\image091.png$ . The side of the parking lot is $\image092.png$ . The area is $\image093.png$ . This option is incorrect.
	C)	The diagonal of a square whose sides measure $\image030.png$ is $\image091.png$ . The side of the parking lot is $\image092.png$ . The area is $\image093.png$ . This option is incorrect.
	D)	The diagonal of a square whose sides measure $\image030.png$ is $\image091.png$ . The side of the parking lot is $\image092.png$ . The area is $\image093.png$ . This option is incorrect.
	E)	The diagonal of a square whose sides measure $\image030.png$ is $\image091.png$ . The side of the parking lot is $\image092.png$ . The area is $\image093.png$ . This option is incorrect.

Question 14 of 50

What is the equation to describe a line passing through (-5,3) and is parallel to the x-axis?

Opción múltiple

A) ;#

B) $\image095.png$ ;#

C) $\image096.png$ $\image094.png$ ;#

D);# $\image097.png$

E) $\image098.png$

	A)	This is the correct option. The equation for a straight line is $\image078.png$ , where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . A line parallel to the $\image030.png$ -axis has the same value of $\image099.png$ for every $\image030.png$ and a slope equal to zero. The equation for such a line is $\image094.png$ , so that it passes through (-5,3), as the problem states.
	B)	The equation for a straight line is $\image078.png$ , where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . A line parallel to the $\image030.png$ -axis has the same value of $\image099.png$ for every $\image030.png$ and a slope equal to zero. The equation for such a line is $\image094.png$ , so that it passes through (-5,3), as the problem states. This option is incorrect.
	C)	The equation for a straight line is $\image078.png$ , where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . A line parallel to the $\image030.png$ -axis has the same value of $\image099.png$ for every $\image030.png$ , and a slope equal to zero. The equation for such a line is $\image094.png$ , so that it passes through (-5,3), as the problem states. This option is incorrect.
	D)	The equation for a straight line is $\image078.png$ , where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . A line parallel to the $\image030.png$ -axis has the same value of $\image099.png$ for every $\image030.png$ and a slope equal to zero. The equation for such a line is $\image094.png$ , so that it passes through (-5,3), as the problem states. This option is incorrect.
	E)	The equation for a straight line is $\image078.png$ , where $\image079.png$ is the slope and $\image080.png$ is its displacement from $\image072.png$ at $\image073.png$ . A line parallel to the $\image030.png$ -axis has the same value of $\image099.png$ for every $\image030.png$ and a slope equal to zero. The equation for such a line is $\image094.png$ , so that it passes through (-5,3), as the problem states. This option is incorrect.

Question 15 of 50

If a huge bird is spotted $\image071.png$ over the horizontal plane and 1 mile measured from the base of a certain building, how far is the bird from the observer?

Opción múltiple

1 mile

$\image100.png$ mile

2 miles

$\image101.png$ miles ;#

$\image102.png$ miles

	A)	The angle that the horizontal plane and the building make is a right angle. Given that another angle in the (observer, base, bird) triangle is $\image071.png$ the remaining angle must be a $\image103.png$ angle. This $\image081.png$ triangle has a $\image082.png$ ratio among its sides. The longest distance is the hypotenuse and it is the one we are looking for. The distance to the bird is 2 miles. This option is incorrect.
	B)	The angle that the horizontal plane and the building make is a right angle. Given that another angle in the (observer, base, bird) triangle is $\image071.png$ the remaining angle must be a $\image103.png$ angle. This $\image081.png$ triangle has a $\image082.png$ ratio among its sides. The longest distance is the hypotenuse and it is the one we are looking for. The distance to the bird is 2 miles. This option is incorrect.
	C)	This is the correct answer. The angle that the horizontal plane and the building make is a right angle. Given that another angle in the (observer, base, bird) triangle is $\image071.png$ the remaining angle must be a $\image103.png$ angle. This $\image081.png$ triangle has a $\image082.png$ ratio among its sides. The longest distance is the hypotenuse and it is the one we are looking for. The distance to the bird is 2 miles.
	D)	The angle that the horizontal plane and the building make is a right angle. Given that another angle in the (observer, base, bird) triangle is $\image071.png$ the remaining angle must be a $\image103.png$ angle. This $\image081.png$ triangle has a $\image082.png$ ratio among its sides. The longest distance is the hypotenuse and it is the one we are looking for. The distance to the bird is 2 miles. This option is incorrect.
	E)	The angle that the horizontal plane and the building make is a right angle. Given that another angle in the (observer, base, bird) triangle is $\image071.png$ the remaining angle must be a $\image103.png$ angle. This $\image081.png$ triangle has a $\image082.png$ ratio among its sides. The longest distance is the hypotenuse and it is the one we are looking for. The distance to the bird is 2 miles. This option is incorrect.

Question 16 of 50

A clock that consistently gains 12 seconds every 2 hours is set to read midday. What is the time the clock displays at noon 13 days later?

Opción múltiple

13h, 2m, 24s

14h, 0m, 56s

12h, 32m, 0s

13h, 12m, 48s ;#

12h, 31m, 12s

	A)	The amount in hours that 13 days spans is $\image104.png$ . The seconds the clock has gained in that time is $\image105.png$ which is $\image106.png$ minutes. One fifth of a minute is 12 seconds, so the time the clock will display is 31minutes and 12 seconds past noon. This option is incorrect.
	B)	The amount in hours that 13 days spans is $\image104.png$ . The seconds the clock has gained in that time is $\image105.png$ which is $\image106.png$ minutes. One fifth of a minute is 12 seconds, so the time the clock will display is 31minutes and 12 seconds past noon. This option is incorrect.
	C)	The amount in hours that 13 days spans is $\image104.png$ . The seconds the clock has gained in that time is $\image105.png$ which is $\image106.png$ minutes. One fifth of a minute is 12 seconds, so the time the clock will display is 31minutes and 12 seconds past noon. This option is incorrect.
	D)	The amount in hours that 13 days spans is $\image104.png$ . The seconds the clock has gained in that time is $\image105.png$ which is $\image106.png$ minutes. One fifth of a minute is 12 seconds, so the time the clock will display is 31minutes and 12 seconds past noon. This option is incorrect.
	E)	This is the correct option. The amount in hours that 13 days spans is $\image104.png$ . The seconds the clock has gained in that time is $\image105.png$ which is $\image106.png$ minutes. One fifth of a minute is 12 seconds, so the time the clock will display is 31minutes and 12 seconds past noon.

Question 17 of 50

A certain man takes a train to Chicago three times a week at regular intervals. A certain woman takes the same trip eight times every three weeks at regular intervals. How many times do these two passengers take the same train in a year?

Opción múltiple

10 times

12 times

17 times

25 times ;#

40 times

	A)	The man travels 3 times a week, or once every $\image107.png$ hours. The woman travels once every $\image108.png$ hours. They coincide the first time in a time that is the least common multiple of 56 and 63. The prime factors of 56 are $\image109.png$ . The ones for 63 are $\image110.png$ . The least common multiple is $\image111.png$ . They meet again after 504 hours or $\image112.png$ . This option is incorrect.
	B)	The man travels 3 times a week, or once every $\image107.png$ hours. The woman travels once every $\image108.png$ hours. They coincide the first time in a time that is the least common multiple of 56 and 63. The prime factors of 56 are $\image109.png$ . The ones for 63 are $\image110.png$ . The least common multiple is $\image111.png$ . They meet again after 504 hours or $\image112.png$ . This option is incorrect.
	C)	This is the correct option. The man travels 3 times a week, or once every $\image107.png$ hours. The woman travels once every $\image108.png$ hours. They coincide the first time in a time that is the least common multiple of 56 and 63. The prime factors of 56 are $\image109.png$ . The ones for 63 are $\image110.png$ . The least common multiple is $\image111.png$ . They meet again after 504 hours or $\image112.png$ .
	D)	The man travels 3 times a week, or once every $\image107.png$ hours. The woman travels once every $\image108.png$ hours. They coincide the first time in a time that is the least common multiple of 56 and 63. The prime factors of 56 are $\image109.png$ . The ones for 63 are $\image110.png$ . The least common multiple is $\image111.png$ . They meet again after 504 hours or $\image112.png$ . This option is incorrect.
	E)	The man travels 3 times a week, or once every $\image107.png$ hours. The woman travels once every $\image108.png$ hours. They coincide the first time in a time that is the least common multiple of 56 and 63. The prime factors of 56 are $\image109.png$ . The ones for 63 are $\image110.png$ . The least common multiple is $\image111.png$ . They meet again after 504 hours or $\image112.png$ . This option is incorrect.

Question 18 of 50

If a gas tank is 3/8th full and reaches ½ its capacity when 25 liters are added it, what is the tank’s full capacity?

Opción múltiple

38 liters

50 liters

96 liters

200 liters ;#

400 liters

	A)	Taking the tank’s capacity to be $\image030.png$ , the full tank capacity is obtained by solving $\image113.png$ for $\image030.png$ . $\image114.png$ or $\image115.png$ or $\image116.png$ .This option is incorrect.
	B)	Taking the tank’s capacity to be $\image030.png$ , the full tank capacity is obtained by solving $\image113.png$ for $\image030.png$ . $\image114.png$ or $\image115.png$ or $\image116.png$ .This option is incorrect.
	C)	Taking the tank’s capacity to be $\image030.png$ , the full tank capacity is obtained by solving $\image113.png$ for $\image030.png$ . $\image114.png$ or $\image115.png$ or $\image116.png$ .This option is incorrect.
	D)	This is the correct option. Taking the tank’s capacity to be $\image030.png$ , the full tank capacity is obtained by solving $\image113.png$ for $\image030.png$ . $\image114.png$ or $\image115.png$ or $\image116.png$ .
	E)	Taking the tank’s capacity to be $\image030.png$ , the full tank capacity is obtained by solving $\image113.png$ for $\image030.png$ . $\image114.png$ or $\image115.png$ or $\image116.png$ .This option is incorrect.

Question 19 of 50

What is the number in the units-position of $\image117.png$ ?

Opción múltiple

10 ;#

	A)	This is the correct answer. Whenever a number has a 5 in the units position, all the powers of such number will have 5 in the units position.
	B)	Whenever a number has a 5 in the units position, all the powers of such number will have 5 in the units position. This option is incorrect.
	C)	Whenever a number has a 5 in the units position, all the powers of such number will have 5 in the units position. Besides, you can only place one digit in the units position. This option is incorrect.
	D)	Whenever a number has a 5 in the units position, all the powers of such number will have 5 in the units position. Besides, you can only place one digit in the units position. This option is incorrect.
	E)	Whenever a number has a 5 in the units position, all the powers of such number will have 5 in the units position. This option is incorrect.

Question 20 of 50

A certain stadium sells tickets at 4/5th the normal price for 1/8th of its seating capacity. If the remaining 117,649 tickets are sold full price for $125 and the stadium fills to capacity, how much money is the stadium administration not receiving due to the discount?

Opción múltiple

$117,649

$310,140

$336,140

$400,125 ;#

$420,175

	A)	If $\image030.png$ is the stadium capacity we know $\image118.png$ , and we are looking for the number of tickets that is $\image119.png$ . Solving the first equation for $\image030.png$ and substituting the result in $\image119.png$ we have the number of tickets sold at half price $\image120.png$ . $\image121.png$ , so $25 dollars are lost in each of these tickets. The total loss is $\image122.png$ . This option is incorrect.
	B)	If $\image030.png$ is the stadium capacity we know $\image118.png$ , and we are looking for the number of tickets that is $\image119.png$ . Solving the first equation for $\image030.png$ and substituting the result in $\image119.png$ we have the number of tickets sold at half price $\image120.png$ . $\image121.png$ , so $25 dollars are lost in each of these tickets. The total loss is $\image122.png$ . This option is incorrect.
	C)	If $\image030.png$ is the stadium capacity we know $\image118.png$ , and we are looking for the number of tickets that is $\image119.png$ . Solving the first equation for $\image030.png$ and substituting the result in $\image119.png$ we have the number of tickets sold at half price $\image120.png$ . $\image121.png$ , so $25 dollars are lost in each of these tickets. The total loss is $\image122.png$ . This option is incorrect.
	D)	If $\image030.png$ is the stadium capacity we know $\image118.png$ , and we are looking for the number of tickets that is $\image119.png$ . Solving the first equation for $\image030.png$ and substituting the result in $\image119.png$ we have the number of tickets sold at half price $\image120.png$ . $\image121.png$ , so $25 dollars are lost in each of these tickets. The total loss is $\image122.png$ . This option is incorrect.
	E)	This is the correct option. If $\image030.png$ is the stadium capacity we know $\image118.png$ , and we are looking for the number of tickets that is $\image119.png$ . Solving the first equation for $\image030.png$ and substituting the result in $\image119.png$ we have the number of tickets sold at half price $\image120.png$ . $\image121.png$ , so $25 dollars are lost in each of these tickets. The total loss is $\image122.png$ .

Question 21 of 50

What is the value of $\image123.png$ ?

Opción múltiple

$\image124.png$

$\image125.png$

$\image126.png$

$\image127.png$ ;#

$\image128.png$

	A)	This is the correct option. $\image123.png$ = $\image129.png$ = $\image124.png$ . We simplified each fraction, and then each denominator cancels the numerator of the following fraction starting with 5 as a denominator. We are left with the first numerator and the last denominator.
	B)	$\image130.png$ = $\image129.png$ = $\image124.png$ . We simplified each fraction, and then each denominator cancels the numerator of the following fraction starting with 5 as a denominator. We are left with the first numerator and the last denominator. This option is incorrect.
	C)	$\image130.png$ = $\image129.png$ = $\image124.png$ . We simplified each fraction, and then each denominator cancels the numerator of the following fraction starting with 5 as a denominator. We are left with the first numerator and the last denominator. This option is incorrect.
	D)	$\image131.png$ = $\image129.png$ = $\image124.png$ . We simplified each fraction, and then each denominator cancels the numerator of the following fraction starting with 5 as a denominator. We are left with the first numerator and the last denominator. This option is incorrect.
	E)	$\image131.png$ = $\image129.png$ = $\image124.png$ . We simplified each fraction, and then each denominator cancels the numerator of the following fraction starting with 5 as a denominator. We are left with the first numerator and the last denominator. This option is incorrect.

Question 22 of 50

A certain music CD is $12 dollars at its regular price. If the music store has a promotional 12% discount on the label and an additional 10% off all music CD’s, what is the equivalent discount for that CD.

Opción múltiple

9.504%

15.6%

20.8%

25% ;#

79.2%

	A)	The original price is $12. With a 12% discount the price is $\image132.png$ . With an additional 10% off the price is $\image133.png$ . This is equivalent to $\image134.png$ or 79.2% of the original price. Therefore, the equivalent discount is 100-79.2=20.8 percent. This option is incorrect.
	B)	The original price is $12. With a 12% discount the price is $\image132.png$ . With an additional 10% off the price is $\image133.png$ . This is equivalent to $\image134.png$ or 79.2% of the original price. Therefore, the equivalent discount is 100-79.2=20.8 percent. This option is incorrect.
	C)	This is the correct option. The original price is $12. With a 12% discount the price is $\image132.png$ . With an additional 10% off the price is $\image133.png$ . This is equivalent to $\image134.png$ or 79.2% of the original price. Therefore, the equivalent discount is 100-79.2=20.8 percent.
	D)	The original price is $12. With a 12% discount the price is $\image132.png$ . With an additional 10% off the price is $\image133.png$ . This is equivalent to $\image134.png$ or 79.2% of the original price. Therefore, the equivalent discount is 100-79.2=20.8 percent. This option is incorrect.
	E)	The original price is $12. With a 12% discount the price is $\image132.png$ . With an additional 10% off the price is $\image133.png$ . This is equivalent to $\image134.png$ or 79.2% of the original price. Therefore, the equivalent discount is 100-79.2=20.8 percent. This option is incorrect.

Question 23 of 50

If a worker’s salary increases from 15,012 to 15,598 dollars, what is the approximate percent increase in his salary?

Opción múltiple

2.5%

3.9%

4.2% ;#

	A)	The percent increase is $\image135.png$ . This option is incorrect.
	B)	The percent increase is $\image135.png$ . This option is incorrect.
	C)	This is the correct option. The percent increase is $\image135.png$ .
	D)	The percent increase is $\image135.png$ . This option is incorrect.
	E)	The percent increase is $\image135.png$ . This option is incorrect.

Question 24 of 50

A certain gold mine deposit has a mineral composition that is 0.0003% gold. The extraction process is 83% effective at retrieving gold from that mineral composition. How many tons, of this mineral composition, need to be processed to get 25 grams of gold?

Opción múltiple

.263

.57

1.008

10.04 ;#

23.501

	A)	If you process 1 ton=1000kg of material whose mineral composition is 0.0003% gold, you have 1000(0.000003)= 0.003kg. or 3gr. of gold per ton in the mine’s deposit. This gives an amount of 3(.83)= 2.49gr. after recovery. To get 25grams you need to process $\image136.png$ tons of the mineral composition. This option is incorrect.
	B)	If you process 1 ton=1000kg of material whose mineral composition is 0.0003% gold, you have 1000(0.000003)= 0.003kg. or 3gr. of gold per ton in the mine’s deposit. This gives an amount of 3(.83)= 2.49gr. after recovery. To get 25grams you need to process $\image136.png$ tons of the mineral composition. This option is incorrect.
	C)	If you process 1 ton=1000kg of material whose mineral composition is 0.0003% gold, you have 1000(0.000003)= 0.003kg. or 3gr. of gold per ton in the mine’s deposit. This gives an amount of 3(.83)= 2.49gr. after recovery. To get 25grams you need to process $\image136.png$ tons of the mineral composition. This option is incorrect.
	D)	This is the correct option. If you process 1 ton=1000kg of material whose mineral composition is 0.0003% gold, you have 1000(0.000003)= 0.003kg. or 3gr. of gold per ton in the mine’s deposit. This gives an amount of 3(.83)= 2.49gr. after recovery. To get 25grams you need to process $\image136.png$ tons of the mineral composition.
	E)	If you process 1 ton=1000kg of material whose mineral composition is 0.0003% gold, you have 1000(0.000003)= 0.003kg. or 3gr. of gold per ton in the mine’s deposit. This gives an amount of 3(.83)= 2.49gr. after recovery. To get 25grams you need to process $\image136.png$ tons of the mineral composition. This option is incorrect.

Question 25 of 50

Swimming at 2/3rds maximum speed, a person covers 2.8km in 50 minutes. What distance would this person cover in 2 days swimming at ½ the maximum speed?

Opción múltiple

93.5km

80.64km

120.96km

161.28km ;#

241.92km

	A)	The swimmer swims at $\image137.png$ km/hr when swimming at 2/3 maximum speed. The maximum swimming speed is $\image138.png$ or $\image139.png$ km/hr. Swimming at half this speed, the swimmer would swim $\image140.png$ km. This option is incorrect.
	B)	The swimmer swims at $\image137.png$ km/hr when swimming at 2/3 maximum speed. The maximum swimming speed is $\image138.png$ or $\image139.png$ km/hr. Swimming at half this speed, the swimmer would swim $\image140.png$ km. This option is incorrect.
	C)	This is the correct option. The swimmer swims at $\image137.png$ km/hr when swimming at 2/3 maximum speed. The maximum swimming speed is $\image138.png$ or $\image139.png$ km/hr. Swimming at half this speed, the swimmer would swim $\image140.png$ km.
	D)	The swimmer swims at $\image137.png$ km/hr when swimming at 2/3 maximum speed. The maximum swimming speed is $\image138.png$ or $\image139.png$ km/hr. Swimming at half this speed, the swimmer would swim $\image140.png$ km. This option is incorrect.
	E)	The swimmer swims at $\image137.png$ km/hr when swimming at 2/3 maximum speed. The maximum swimming speed is $\image138.png$ or $\image139.png$ km/hr. Swimming at half this speed, the swimmer would swim $\image140.png$ km. This option is incorrect.

Question 26 of 50

Instructions

This section tests your ability to answer Quantitative Comparison questions in the Quantitative part of the GRE. You are given a problem statement and some information relating to the context in which the problem is set. You will be given two quantities, one in column A and the other in column B. You are to consider the relative amounts the two quantities represent given the problem, and choose one of the provided answer choices. The answer choices in this section are:

A, if the quantity in column A is greater than the one in column B.

B, if the quantity in column B is the greater one.

C, if both quantities are equal.

D, is the information provided in the problem statement and in the columns is not sufficient to determine the relation between the quantities.

You should consider the numbers used in these problems to be real numbers, unless otherwise stated. All geometrical figures, i.e. triangles, in this lab should be considered to lie in a plane. You should never select E as the answer choice as only options A-D are valid in this section of the GRE. You should take no more than 2 minutes per question.

is an integer, and.
Column A	Column B
of	of

Opción múltiple

A) The quantity in column A is greater than that in column B.;#
B) The quantity in column B is greater than that in column A.;#
C) Both quantities in column A and B are equal.;#
D) The information provided in both columns and the problem statement is insufficient to determine the relation between the quantities.;#
E) This option is incorrect.


	A)	If we take, we get. of. Now, taking the same value forand the quantity in column B we haveand. Column B is greater than column A. This option is incorrect.
	B)	This is the correct option. If we take, we get. of. Now, taking the same value forand the quantity in column B we haveand. Column B is greater than column A.
	C)	If we take, we get. of. Now, taking the same value forand the quantity in column B we haveand. Column B is greater than column A. This option is incorrect.
	D)	If we take, we get. of. Now, taking the same value forand the quantity in column B we haveand. Column B is greater than column A. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 27 of 50

Ifand, then.
Column A	Column B

Opción múltiple


	A)	Solveforand. Forwe get, and for,. Stating the equation forin the same form, we can see that for all positive values . Therefore, column B is greater than column A. This option is incorrect.
	B)	This is the correct option. Solveforand. Forwe get, and for,. Stating the equation forin the same form, we can see that for all positive values . Therefore, column B is greater than column A.
	C)	Solveforand. Forwe get, and for,. Stating the equation forin the same form, we can see that for all positive values . Therefore, column B is greater than column A. This option is incorrect.
	D)	Solveforand. Forwe get, and for,. Stating the equation forin the same form, we can see that for all positive values . Therefore, column B is greater than column A. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 28 of 50

A girl spends 20% of her allowance money on candies. She then spends $5 on food, and she still has 20% of her allowance left.
Column A	Column B
$2	What is left of her allowance

Opción múltiple


	A)	This is the correct option. If she spent 20% on candies and she still has 20%, then $5=60%, whereis her total allowance. Solving for we get het allowance to be . What is left of her allowance is. Comparing the two quantities, we have that.
	B)	If she spent 20% on candies and she still has 20%, then $5=60%, whereis her total allowance. Solving for we get het allowance to be . What is left of her allowance is. Comparing the two quantities, we have that. This option is incorrect.
	C)	If she spent 20% on candies and she still has 20%, then $5=60%, whereis her total allowance. Solving for we get het allowance to be . What is left of her allowance is. Comparing the two quantities, we have that. This option is incorrect.
	D)	If she spent 20% on candies and she still has 20%, then $5=60%, whereis her total allowance. Solving for we get het allowance to be . What is left of her allowance is. Comparing the two quantities, we have that. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 29 of 50

Column A	Column B

Opción múltiple

A) The quantity in column A is greater than that in column B. ;#
B) The quantity in column B is greater than that in column A. ;#
C) Both quantities in column A and B are equal. ;#
D) The information provided in both columns and the problem statement is insufficient to determine the relation between the quantities. ;#
E) This option is incorrect.


	A)	For negative values, the quantity closest to zero is the greatest. The greater the denominator, the smaller the fraction. Column B is smaller, so column B is closer to zero. Column B is the greater quantity for negative values of x. For positive values, the opposite happens. We, therefore, do not have enough information to determine the relation between the columns. This option is incorrect.
	B)	For negative values, the quantity closest to zero is the greatest. The greater the denominator, the smaller the fraction. Column B is smaller, so column B is closer to zero. Column B is the greater quantity for negative values of x. For positive values, the opposite happens. We, therefore, do not have enough information to determine the relation between the columns. This option is incorrect.
	C)	For negative values, the quantity closest to zero is the greatest. The greater the denominator, the smaller the fraction. Column B is smaller, so column B is closer to zero. Column B is the greater quantity for negative values of x. For positive values, the opposite happens. We, therefore, do not have enough information to determine the relation between the columns. This option is incorrect.
	D)	This is the correct option. For negative values, the quantity closest to zero is the greatest. The greater the denominator, the smaller the fraction. Column B is smaller, so column B is closer to zero. Column B is the greater quantity for negative values of x. For positive values, the opposite happens. We, therefore, do not have enough information to determine the relation between the columns.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 30 of 50

is a multiple of 5 and 6.
Column A	Column B

Opción múltiple


	A)	The relation between the columns cannot be determined becausecould take either positive or negative values and the relation is different for each case. This option is incorrect.
	B)	The relation between the columns cannot be determined becausecould take either positive or negative values and the relation is different for each case. This option is incorrect.
	C)	The relation between the columns cannot be determined becausecould take either positive or negative values and the relation is different for each case. This option is incorrect.
	D)	This is the correct option. The relation between the columns cannot be determined becausecould take either positive or negative values and the relation is different for each case.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 31 of 50

Figure A is an n-sided polygon inscribed in circle B.
Column A	Column B
The circumference of circle B	The perimeter of the polygon

Opción múltiple


	A)	This is the correct option. The perimeter of any polygon inscribed in a circle will be less than the circumference of that circle.
	B)	The perimeter of any polygon inscribed in a circle will be less than the circumference of that circle. This option is incorrect.
	C)	The perimeter of any polygon inscribed in a circle will be less than the circumference of that circle. This option is incorrect.
	D)	The perimeter of any polygon inscribed in a circle will be less than the circumference of that circle. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 32 of 50

A triangle has sides,,and.
Column A	Column B
The area of the triangle	3

Opción múltiple


	A)	The area of triangle ABC is zero because line segments+=. This is, the “triangle” is a straight line and it has no area. . This option is incorrect.
	B)	This is the correct option. The area of triangle ABC is zero because line segments+=. This is, the “triangle” is a straight line and it has no area.
	C)	The area of triangle ABC is zero because line segments+=. This is, the “triangle” is a straight line and it has no area. . This option is incorrect.
	D)	The area of triangle ABC is zero because line segments+=. This is, the “triangle” is a straight line and it has no area. . This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 33 of 50

A certain n-sided polygon and circle share the center point P.
Column A	Column B
The perimeter of the circumscribed polygon	The perimeter of the inscribed polygon

Opción múltiple


	A)	This is the correct option. That a polygon is circumscribed means the circle is inside the polygon, which would make the perimeter of the polygon greater than that of the circle. An inscribed polygon is a polygon inside a circle sharing the points that belong to its vertices with the circle. The perimeter of the polygon is smaller than that of the circle.
	B)	That a polygon is circumscribed means the circle is inside the polygon, which would make the perimeter of the polygon greater than that of the circle. An inscribed polygon is a polygon inside a circle sharing the points that belong to its vertices with the circle. The perimeter of the polygon is smaller than that of the circle. This option is incorrect.
	C)	That a polygon is circumscribed means the circle is inside the polygon, which would make the perimeter of the polygon greater than that of the circle. An inscribed polygon is a polygon inside a circle sharing the points that belong to its vertices with the circle. The perimeter of the polygon is smaller than that of the circle. This option is incorrect.
	D)	That a polygon is circumscribed means the circle is inside the polygon, which would make the perimeter of the polygon greater than that of the circle. An inscribed polygon is a polygon inside a circle sharing the points that belong to its vertices with the circle. The perimeter of the polygon is smaller than that of the circle. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 34 of 50

Two six-sided dice are tossed.
Column A	Column B
The probability that the sum is 5	The probability that the sum is 6

Opción múltiple


	A)	There are four ways we can get the sum to be five i.e. (1,4), (4,1), (2,3), and (3,2). There are 5 ways for the sum to be six i.e. (1,5), (5,1), (2,4), (4,2), and (3,3). Therefore, the probability for the sum to be six is greater than that for the sum to be five. This option is incorrect.
	B)	This is the correct option. There are four ways we can get the sum to be five i.e. (1,4), (4,1), (2,3), and (3,2). There are 5 ways for the sum to be six i.e. (1,5), (5,1), (2,4), (4,2), and (3,3). Therefore, the probability for the sum to be six is greater than that for the sum to be five.
	C)	There are four ways we can get the sum to be five i.e. (1,4), (4,1), (2,3), and (3,2). There are 5 ways for the sum to be six i.e. (1,5), (5,1), (2,4), (4,2), and (3,3). Therefore, the probability for the sum to be six is greater than that for the sum to be five. This option is incorrect.
	D)	There are four ways we can get the sum to be five i.e. (1,4), (4,1), (2,3), and (3,2). There are 5 ways for the sum to be six i.e. (1,5), (5,1), (2,4), (4,2), and (3,3). Therefore, the probability for the sum to be six is greater than that for the sum to be five. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 35 of 50

Column A	Column B

Opción múltiple


	A)	This is the correct option. We know and . The middle value between 144 and 169 is 156.5, so >.
	B)	We know and . The middle value between 144 and 169 is 156.5, so >. This option is incorrect.
	C)	We know and . The middle value between 144 and 169 is 156.5, so >. This option is incorrect.
	D)	We know and . The middle value between 144 and 169 is 156.5, so >. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 36 of 50

Column A	Column B

Opción múltiple

	A)	This is the correct option. The equation in column A yields 9+6=15. Column B yields 36/10=3.6.
	B)	The equation in column A yields 9+6=15. Column B yields 36/10=3.6. This option is incorrect.
	C)	The equation in column A yields 9+6=15. Column B yields 36/10=3.6. This option is incorrect.
	D)	The equation in column A yields 9+6=15. Column B yields 36/10=3.6. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 37 of 50

Column A	Column B

Opción múltiple


	A)	This is the correct option. We knowand , so. We also knowand, so column A is greater.
	B)	We knowand , so. We also knowand, so column A is greater. This option is incorrect.
	C)	We knowand , so. We also knowand, so column A is greater. This option is incorrect.
	D)	We knowand , so. We also knowand, so column A is greater. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 38 of 50

Column A	Column B
	8

Opción múltiple

A) The quantity in column A is greater than that in column B.;#

B) The quantity in column B is greater than that in column A.;#

C) Both quantities in column A and B are equal.;#

D) The information provided in both columns and the problem statement is insufficient to determine the relation between the quantities.;#

E) This option is incorrect.

A) 2√2(√8) = 2(√(2*8)) = 2(√16) = 2(4) = 8. The quantities in both columns are equal. This option is incorrect. ;#

B) 2√2(√8) = 2(√(2*8)) = 2(√16) = 2(4) = 8. The quantities in both columns are equal.. This option is incorrect. ;#

C) This is the correct option. 2√2(√8) = 2(√(2*8)) = 2(√16) = 2(4) = 8. The quantities in both columns are equal. ;#

D) 2√2(√8) = 2(√(2*8)) = 2(√16) = 2(4) = 8. The quantities in both columns are equal. This option is incorrect. ;#

E) You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 39 of 50

Column A	Column B
	2

Opción múltiple


	A)	. The quantities in both columns are equal. This option is incorrect.
	B)	. The quantities in both columns are equal. This option is incorrect.
	C)	This is the correct option.. The quantities in both columns are equal.
	D)	. The quantities in both columns are equal. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 40 of 50


Column A	Column B

Opción múltiple


	A)	If we divide by 4 we get. We then have the relation. Therefore>. This option is incorrect.
	B)	This is the correct option. If we divide by 4 we get. We then have the relation. Therefore>.
	C)	If we divide by 4 we get. We then have the relation. Therefore>. This option is incorrect.
	D)	If we divide by 4 we get. We then have the relation. Therefore>. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 41 of 50

Column A	Column B

Opción múltiple


	A)	, so column A is. , so column B is. . This option is incorrect.
	B)	This is the correct option., so column A is. , so column B is. .
	C)	, so column A is. , so column B is. . This option is incorrect.
	D)	, so column A is. , so column B is. . This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 42 of 50


Column A	Column B

Opción múltiple


	A)	Solvingforwe getorwhich can be factorized as. This equation renders valuesandof which onlysatisfies the original equation. The values in the columns are, therefore, equal. This option is incorrect.
	B)	Solvingforwe getorwhich can be factorized as. This equation renders valuesandof which onlysatisfies the original equation. The values in the columns are, therefore, equal. This option is incorrect.
	C)	This is the correct option. Solvingforwe getorwhich can be factorized as. This equation renders valuesandof which onlysatisfies the original equation. The values in the columns are, therefore, equal.
	D)	Solvingforwe getorwhich can be factorized as. This equation renders valuesandof which onlysatisfies the original equation. The values in the columns are, therefore, equal. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 43 of 50


Column A	Column B

Opción múltiple


	A)	This is the correct option. Multiplying both sides of the original equation bywe getor. , so the quantity in column A is greater than that in column B.
	B)	Multiplying both sides of the original equation bywe getor. , so the quantity in column A is greater than that in column B. This option is incorrect.
	C)	Multiplying both sides of the original equation bywe getor. , so the quantity in column A is greater than that in column B. This option is incorrect.
	D)	Multiplying both sides of the original equation bywe getor. , so the quantity in column A is greater than that in column B. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 44 of 50

Column A	Column B

Opción múltiple


	A)	This is the correct option. The quantity in column A can be expressed as, which is greater than.
	B)	The quantity in column A can be expressed as, which is greater than. This option is incorrect.
	C)	The quantity in column A can be expressed as, which is greater than. This option is incorrect.
	D)	The quantity in column A can be expressed as, which is greater than. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 45 of 50


Column A	Column B
68

Opción múltiple


	A)	If we multiplyby 3 we get. 68<69. This option is incorrect.
	B)	This is the correct option. If we multiplyby 3 we get. 68<69.
	C)	If we multiplyby 3 we get. 68<69. This option is incorrect.
	D)	If we multiplyby 3 we get. 68<69. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 46 of 50

andare integers andand.
Column A	Column B

Opción múltiple

A) The quantity in column A is greater than that in column B. ;#
B) The quantity in column B is greater than that in column A. ;#
C) Both quantities in column A and B are equal. ;#
D) The information provided in both columns and the problem statement is insufficient to determine the relation between the quantities. ;#
E) This option is incorrect.

	A)	The range of valuescan take (6,7), and the range of possible values for(8,9,10,11) Allows us to determine for all their possible values. Furthermore, the statement is false for all the possible combinations. This option is incorrect.
	(B)	This is the best answer. The range of valuescan take (6,7), and the range of possible values for (8,9,10,11) Allows us to determine for all their possible values. Furthermore, the statement is false for all the possible combinations.
	(C)	The range of values can take (6,7), and the range of possible values for (8,9,10,11) Allows us to determine for all their possible values. Furthermore, the statement is false for all the possible combinations. This option states that the relation betweenand is one of equality. This option is incorrect.
	(D)	The range of valuescan take (6,7), and the range of possible values for (8,9,10,11) Allows us to determine for all their possible values. Furthermore, the statement is false for all the possible combinations. This option states that the relation betweenand cannot be determined. This option is incorrect.
	(E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 47 of 50


Column A	Column B

Opción múltiple

A) The quantity in column A is greater than that in column B. ;#
B) The quantity in column B is greater than that in column A. ;#
C) Both quantities in column A and B are equal. ;#
D) The information provided in both columns and the problem statement is insufficient to determine the relation between the quantities. ;#
E) This option is incorrect.


	A)	This is the correct option. The ratiocan be obtained from the original equation. The inverse ratiois the inverse fraction. Therefore, >.
	B)	The ratiocan be obtained from the original equation. The inverse ratiois the inverse fraction. Therefore, >. This option is incorrect.
	C)	The ratiocan be obtained from the original equation. The inverse ratiois the inverse fraction. Therefore, >. This option is incorrect.
	D)	The ratiocan be obtained from the original equation. The inverse ratiois the inverse fraction. Therefore, >. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 48 of 50

and
Column A	Column B

Opción múltiple

A) The quantity in column A is greater than that in column B. ;#
B) The quantity in column B is greater than that in column A. ;#
C) Both quantities in column A and B are equal. ;#
D) The information provided in both columns and the problem statement is insufficient to determine the relation between the quantities. ;#
E) This option is incorrect.


	A)	From the first equationand from the second one. We end up comparingto. From this comparison we get<. This option is incorrect.
	B)	This is the correct option. From the first equationand from the second one. We end up comparingto. From this comparison we get<.
	C)	From the first equationand from the second one. We end up comparingto. From this comparison we get<. This option is incorrect.
	D)	From the first equationand from the second one. We end up comparingto. From this comparison we get<. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 49 of 50

The diagonal of a rectangular box is , its dimensions are 3 by 4 by 5.
Column A	Column B
The ratio of diagonal to height	The side to height ratio

Opción múltiple


	A)	This is the correct option. Regardless of which dimension we take to be the height and which the side, the first ratio is greater because it is the greatest dimension in the box and it is in the numerator. i.e. If height is 3 and side is 4,. If height is 5 and side 4,then…
	B)	Regardless of which dimension we take to be the height and which the side, the first ratio is greater because it is the greatest dimension in the box and it is in the numerator. i.e. If height is 3 and side is 4,. If height is 5 and side 4,then…This option is incorrect.
	C)	Regardless of which dimension we take to be the height and which the side, the first ratio is greater because it is the greatest dimension in the box and it is in the numerator. i.e. If height is 3 and side is 4,. If height is 5 and side 4,then…This option is incorrect.
	D)	Regardless of which dimension we take to be the height and which the side, the first ratio is greater because it is the greatest dimension in the box and it is in the numerator. i.e. If height is 3 and side is 4,. If height is 5 and side 4,then…This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

Question 50 of 50

Column A	Column B

Opción múltiple


	A)	We can eliminatebecause it appears on both columns. If we order the remaining fractions we can ballpark to the answer<. Otherwise, add the fractions to obtaincompared to. This option is incorrect.
	B)	This is the correct option. We can eliminatebecause it appears on both columns. If we order the remaining fractions we can ballpark to the answer<. Otherwise, add the fractions to obtaincompared to.
	C)	We can eliminatebecause it appears on both columns. If we order the remaining fractions we can ballpark to the answer<. Otherwise, add the fractions to obtaincompared to. This option is incorrect.
	D)	We can eliminatebecause it appears on both columns. If we order the remaining fractions we can ballpark to the answer<. Otherwise, add the fractions to obtaincompared to. This option is incorrect.
	E)	You should never select E as the answer choice as only options A-D are valid in this section of the GRE.

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