GRE Math : GRE Quantitative Reasoning
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Example Questions
Example Question #561 : Gre Quantitative Reasoning
What is the average of 
Average is the sum of all the terms divided by the number of terms. So:
Example Question #562 : Gre Quantitative Reasoning
If the average test score of three students is 70, which of the following could a fourth student receive such that the average of all four scores is greater than 73 and less than 75?
The sum of the scores of the first three students whose average was 70 is 
If the average needs to be between 73 and 75 then:
Solving for
Only 83 falls in that range.
Example Question #35 : Statistics
Jane had an arithmetic mean of 84 on the first four math tests she took this year. By the time she'd taken six tests, her arithmetic mean was 86. Assuming that 100 is the maximum number of points possible per test, what is the lowest score that Jane could have possibly received on her fifth test?
To achieve an average of 84 on the first four tests, Jane would have to have received a total of 
Example Question #36 : Statistics
Which statement is true assuming that a represents the range, b represents the mean, c represents the median, and d represents the mode.
which sequence is correct for the number set: 8, 3, 11, 12, 3, 4, 6, 15, 1 ?
The answer is 
First organize the number set 1, 3, 3, 4, 6, 8, 11, 12, 15
a = range = 14
b = mean = 7
c = median = 6
d = mode = 3
so the order is mode<median<mean<range
or d < c < b < a.
Example Question #37 : Statistics
Which statement is true assuming that a represents the range, b represents the mean, c represents the median, and d represents the mode.
Which sequence is correct for the number set: 51, 8, 51, 17, 102, 31, 20
c < b < d < a
c < a < d < b
b < d < c < a
a < b < d < c
d < c < a < b
c < b < d < a
The answer is c < b < d < a.
When we arrange the number set we see: 8, 17, 20, 31, 51, 51, 102
a = range = 94
b = mean = 40
c = median = 31
d = mode = 51
median < mean < mode < range so c < b < d < a
Example Question #38 : Statistics
Jim got scores of 84, 78, 92, and 89 on the first four exams in his math class. What must he get on the fifth exam to have an average score of 88 for all five exams?
95
91
99
97
93
97
Write out the average formula, with x representing the fifth score, and filling in 88 as the average score we want.
Then isolate and solve for x.
Example Question #31 : Arithmetic Mean
If the average of 
40
90
70
150
80
80
If the average of 
Likewise, if the average of b and c is 110, then their sum must be 220.
Example Question #39 : Statistics
The average of 10 test scores is 120 and the average of 30 additional scores is 100.
Quantity A: The weighted average of these scores
Quantity B: 105
The relationship cannot be determined from the information given
Quantity B is greater
Quantity A is greater
The two quantities are equal
The two quantities are equal
The sum of the first ten scores is 1,200 and the sum of the next 30 scores is 3,000. To take the weighted average of all scores, divide the sum of all scores (4,200) by the total number of scores (40), which would equal 105.
Example Question #41 : Statistics
A plane flies from San Francisco to New York City at 600 miles per hour and returns along the same route at 400 miles per hour. What is the average flying speed for the entire route (in miles per hour)?
First, pick a distance, preferably one that is divisible by 400 and 600. As an example, we will use 1,200. If the distance is 1,200, then it took 2 hours to get to New York City and 3 hours to get back to San Francisco. So, the plane traveled 2,400 miles in 5 hours. The average speed is simply 2,400 miles divided by 5 hours, which is 480 miles per hour.
Example Question #563 : Gre Quantitative Reasoning
Column A: The median of the set
Column B: The mean of the set
Columns A and B are equal.
Column A is greater.
Column B is greater.
Cannot be determined.
Column B is greater.
The median is the middle number of the data set. If there is an even number of quantities in the data set, take the average of the middle two numbers.
Here, there are 8 numbers, so (18 + 20)/2 = 19.
The mean, or average, is the sum of the integers divided by number of integers in the set: (20 + 35 + 7 + 12 + 73 + 12 + 18 + 31) / 8 = 26
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