New GRE Math questions Practice
1. The ratio of days worked to days not worked for a certain employee was 8 to
7 in June. If the employee worked 5 more days in July than in June, then what
per cent of the total number of days in July were days that the employee
worked?
Give your answer to the nearest percent.
%
2.
n 
1 
2 
3 
4 
5 
6 
7 
8 
… 
r 
1 
2 
2 
3 
2 
4 
2 
4 
… 
In the table above, the numbers in the row labeled n form the sequence of
positive integers and each number in the row labeled r is the number of
different positive divisors of the corresponding integer n. What is the value
of r that corresponds to the integer 36?
r = 
3. A manager has to write performance appraisals for all of her staff. She has
written 20% of the total number of appraisals. After she writes 2 more, she
will still have 75% of the total number of them to write. How many appraisals
will she still have to write?

4. S is a series of natural numbers. S_{1} represents the 'i' th number
of the series. S_{i} (for i > 2) is equal to the sum of S_{i – 1 }and
S_{i – 2 . }Also S_{2} = 5. What is the difference between the square of S_{100} and the product of S_{99} and S_{101} if S_{1}
= S_{2}?

5. A total of $2,030 was spent for a 30day vacation. If transportation
expenses were $230, lodging was $750, and exactly $20 was spent per day for
meals and tips, what was the average (arithmetic mean) amount per day that was
spent on other expenses?
 dollars
6. A pentagonal prism is to be painted. No two Adjacent faces are painted. In
how many ways can the prism be painted?

7. COST OF A TELEPHONE CALL AT DAY AND NIGHT RATES

Cost for First Minute 
Cost for Each Additional Minute 
Day rate 
$ 0.50 
$ 0.34 
Night Rate 
$ 0.20 
$ 0.14 
According to the table above, a nightrate call that costs the same as a
3minute day rate call would last a total of how many minutes?
 minutes
8. The calorie content of five fruits is measured. The sum of calorie content
of three fruits taken at a time are 150, 160, 120, 180, 140, 150, 170, 130, 160
and 140. What is the average calorie content of a fruit?
 calories
9. If a total of x identical disks can be arranged in 8 stacks of equal height
or in 12 stacks of equal height, what is the least possible value of x?
x = 
10. Forty percent of Mr. Johnson’s seventhgrade class are boys. If on a
certain day 10 per cent of the boys and 20 per cent of the girls are absent,
what proportion of Mr. Johnson’s class is absent?
Give your answer as a fraction.
/
Answer Key:
Question 
Correct Answer 
1 
68 
2 
9 
3 
30 
4 
25 
5 
15 
6 
13 
7 
8 
8 
50 
9 
24 
10 
4 / 25 
Detailed Explanations
1. There are 30 days in June.
working: nonworking days = 8:7 = 16 days : 14 days.
In July = 3: days. He worked 16 + 5 = 21 days.
% of working days =
2. 1 is divisible by only 1 T = 1
2 is divisible by 1 and 2 T = 2
3 is divisible by 1 and 3 T = 2
36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, 36, T = 9.
3. Let total no. of staff be ‘x’,
therefore
x = 40
Appraisal still to be written =
4. S_{1} = S_{2 }= 5
therefore, S_{3} = 5 + 5 = 10, S_{4} = 10 + 5, S_{5} =
25
S_{2}^{2}  S_{1}S_{3} = 25  10 x 5 = 25
S_{3}^{2}  S_{2}S_{4} = 100  5 x 15 = 25
S_{4}^{2}  S_{3}S_{5} = 225  250 = 25
Therefore, in general (Sn^{2}  Sn = 1 S^{n1}) = (1) (n1),
25
S_{100}^{2}  S_{101} S_{99} = 25 But the
difference means only the magnitude
Hence S_{100}^{2} – S_{101} S_{99} = 25
5. Transportation expenses $ 230
Lodging $750
Meals and tips @ $20 per day $600
Total $1580
Therefore other expenses = 2030  1580 = $450
Therefore average daily other expenses = 450/30 = $15
6. If only one face is painted then there are seven ways of painting the
prism.
Two faces can be painted as follows:
The base and top are painted (1 way)
Two vertical faces (not adjacent) can be painted in 5 ways.
Hence total number of ways = 7 + 1 + 5 = 13
7. A 3 minute day call costs 50 + (2 x 34) cents = $1.18
At night the first minute is $0.20 and the next n minutes cost $1.18
 $0.20 = $0.98
rate per minute after the first minute is $0.14
n = .98 divided by .14 = 7
Total number of minutes = 1 + 7 = 8
8. The sum of calories contents of fruits taken 3 at a time = 1500
Now average calories content for 3 fruits taken at a time =
Average calories content of a fruit =
Alternatively, the sum of five fruits taken 3 at a time = 1500
When total amount of 1500 is considered, it will have 10 x 3 = 30 fruits.
But there are only 5 different kinds of fruits.
Thus, each of the 5 fruit is counted = 6 times.
To find sum of five fruits, we have to divided total amount by 6,
which is = .
Now, to find average of each of five fruit, we get = 50.
9. The least possible value of x is the LCM of 8 and 12 , which is 24.
10. Let x be total no. of students in the class
Then, boys = .4x absent boys = .1 x .4x = 0.4x
Girls = .6x absent girls = .2 x .6x = 0.12x
Total of absent students = 0.16x
16% of the class is absent. 16% =