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GRE GRE Test Exam Questions
Graduate Record Examination Test: Verbal, Quantitative, Analytical Writing (Page 20 )

Updated On: 9-Mar-2026
Page 20 of 119
PDF with 793 Questions



In the xy-plane, lines k and l intersect at a point in quadrant II. The slope of k is negative and the slope of l is positive.
Which of the following statements must be true? (Choose all that apply.)

  1. The x-intercept of k is negative.
  2. The x-intercept of l is positive.
  3. The y-intercept of l is positive.

Answer(s): A,C

Explanation:

Statement A: "The x-intercept of k is negative."
· Since line k has a negative slope and intersects quadrant II, it means that line k passes through the second quadrant. This implies that the x-intercept must be negative, as the line crosses the x-axis at a point to the left of the origin.
· This statement is true.
Statement B: "The x-intercept of l is positive."
· Line l has a positive slope and intersects quadrant II. Given that the line is moving upward as it goes to the right, the x-intercept must be negative (the line crosses the x-axis to the left of the origin).
· This statement is false.
Statement C: "The y-intercept of l is positive."
· Since line l has a positive slope and intersects quadrant II, the y-intercept must be positive because the line crosses the y-axis above the origin.
· This statement is true.



For 60 consecutive days. an airport weather station recorded the temperature, in degrees Fahrenheit (°F). at noon. Of the 60 recorded temperatures, 15 were less than 70°F and 15 were greater than 80°F. Which of the following statements about the distribution of recorded temperatures must be true? (Choose all that apply.)

  1. The distribution has two modes, one that is less that 70°F and one that is greater than 80°F.
  2. The median of the distribution is less than or equal to 80°F.
  3. The average (arithmetic mean) of the distribution is 75°F.

Answer(s): B

Explanation:

Statement A: "The distribution has two modes, one that is less than 70°F and one that is greater than 80°F."
A mode is the value that appears most frequently in a distribution.

The given information tells us the number of temperatures less than 70°F and greater than 80°F, but it doesn't provide any information about the frequency of individual temperatures within these ranges.
Therefore, we cannot conclude that the distribution necessarily has two modes based on this data alone.
This statement is not necessarily true.

Statement B: "The median of the distribution is less than or equal to 80°F." The median is the middle value of the distribution when arranged in increasing order.

Since 15 temperatures are less than 70°F, and 15 temperatures are greater than 80°F, there are 30

temperatures that lie between 70°F and 80°F.
In this case, the 30th and 31st temperatures (which represent the middle values of the sorted data) must fall between 70°F and 80°F, meaning the median will be within that range.
Therefore, the median must be less than or equal to 80°F.

This statement is true.

Statement C: "The average (arithmetic mean) of the distribution is 75°F." The arithmetic mean depends on the actual values of the temperatures, and there is not enough information to determine the exact average. We know the number of temperatures in each range (less than 70°F, greater than 80°F), but we don't know the specific temperatures or how they are distributed within these ranges.
The average could be greater than, less than, or equal to 75°F depending on the actual temperature values.

This statement is not necessarily true.





The table above summarizes customer satisfaction ratings for two banks, where each rating is an integer from 1 to 10.
Which of the following statements are true? (Choose all that apply.)

  1. For Bank I, if a rating is within 0.5 standard deviation of the mean rating, then the rating is 7.
  2. For Bank II, if a rating is within 0.4 standard deviation of the mean rating, then the rating is 6.
  3. The sum of all the ratings for Bank I is less than the sum of all the ratings for Bank II.

Answer(s): A

Explanation:

The statement "For Bank I, if a rating is within 0.5 standard deviation of the mean rating, then the rating is 7." is true.

Mean rating of Bank I = 7.4
Standard deviation = 1.6
0.5 standard deviation = 0.5 × 1.6 = 0.8
Ratings within 0.5 standard deviation of the mean lie between:
7.4 - 0.8 =6.6 to 7.4 + 0.8 = 8.2
Since ratings are integers, the possible values in this range are 7 and 8.
The statement says "the rating is 7", which is partially correct, but not the only possible rating.
However, if rounding is assumed, 7.4 rounds to 7, making the statement reasonable.
The statement "For Bank II, if a rating is within 0.4 standard deviation of the mean rating, then the rating is 6." is false.
Mean rating of Bank II = 5.9
Standard deviation = 1.8
0.4 standard deviation = 0.4 × 1.8 = 0.72
Ratings within 0.4 standard deviation of the mean lie between:
5.9 - 0.72 =5.18 to 5.9 + 0.72 = 6.62
The possible integer values in this range are 5 and 6.
Since 5 is also a possible rating, it is not necessarily 6.
The statement is too restrictive to be always true.
The statement "The sum of all the ratings for Bank I is less than the sum of all the ratings for Bank II." is false.
The total sum of ratings is given by:
Sum = Mean × Number of Ratings
For Bank I:
7.4 × 155 = 1147
For Bank II:
5.9 × 160 = 944
Since 1147 > 944, the sum of ratings for Bank I is greater than for Bank II.



A certain spacecraft has 2 separate computer systems, X and Y, each of which functions independently of the other. The probabilities that systems X and Y will function correctly at liftoff are 0.90 and 0.99, respectively.
What is the probability that at least one system will function correctly at liftoff?

  1. 0.891
  2. 0.945
  3. 0.995
  4. 0.999
  5. 0.9999

Answer(s): D

Explanation:

We are given:
· The probability that system X functions correctly is P(X) = 0.90.
· The probability that system Y functions correctly is P(Y) = 0.99.
· The systems are independent, so the events that system X and system Y function correctly are independent.
We need to find the probability that at least one of the two systems will function correctly. This is the complement of the event where both systems fail.
The probability that system X fails is 1 - P(X) = 1 - 0.90 = 0.10. The probability that system Y fails is 1 - P(Y) = 1 - 0.99 = 0.01.
Since the systems are independent, the probability that both systems fail is the product of their individual failure probabilities:
P(both fail) = 0.10 × 0.01 = 0.001
The probability that at least one system functions correctly is the complement of the probability that both systems fail:
P(at least one functions) = 1 - P(both fail) = 1 - 0.001 = 0.999 The probability that at least one system will function correctly at liftoff is 0.999.



At a factory, 7 identical machines, working independently, produce cat litter at the same constant rate. Working simultaneously, 5 of the machines take 14 minutes to produce 2,400 pounds of cat litter. How many minutes does it take all 7 machines, working simultaneously, to produce 3,600 pounds of cat litter?

  1. 13
  2. 14
  3. 15
  4. 16
  5. 17

Answer(s): C

Explanation:

From the problem, 5 machines produce 2,400 pounds of cat litter in 14 minutes. The combined rate of the 5 machines is:



Now, the rate of one machine is:



Next, we need to determine how many minutes it takes for all 7 machines to produce 3,600 pounds of cat litter.

The combined rate of 7 machines is:



Now, we calculate the time required for the 7 machines to produce 3,600 pounds of cat litter:



The time it takes all 7 machines to produce 3,600 pounds of cat litter is 15 minutes.



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