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?

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4. S is a series of natural numbers. S₁ 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 S₂ = 5. What is the difference between the square of S₁₀₀ and the product of S₉₉ and S₁₀₁ if S₁ = S₂?
 

--------------------------

 
 
 5. A total of $2,030 was spent for a 30-day 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 night-rate call that costs the same as a 3-minute 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 seventh-grade 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. S₁ = S₂ = 5
therefore, S₃ = 5 + 5 = 10, S₄ = 10 + 5, S₅ = 25
S₂² - S₁S₃ = 25 - 10 x 5 = 25
S₃² - S₂S₄ = 100 - 5 x 15 = 25
S₄² - S₃S₅ = 225 - 250 = -25
 
Therefore, in general (Sn² - Sn = 1 S^n-1) = (-1) (n-1), 25
 
S₁₀₀² - S₁₀₁ S₉₉ = -25 But the difference means only the magnitude
 
Hence |S₁₀₀² – S₁₀₁ S₉₉| = |-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% =