Free GRE Numeric Entry Questions with Explanations
Sample 1

Solutions and detailed explanations to GRE numeric questions and problems in sample 1

Solution to Question 1

Pump A can fill the tank in 4 hours, therefore the quarter of the tank is filled in one hour, hence the rate of pump A in filling the tank is
1 / 4
If T is the number of hours for pump B to fill the tank, then its rate is
1 / T
When working together for 3 hours both pumps are working at their rates to fill 1 tank. Hence
3(1 / 4) + 3(1 / T) = 1
The term 3(1 / 4) in the above equation is due to pump A working at its rate for 3 hours. The term 3(1 / T) is due to pump B and the "1" on the right of the equation corresponds to 1 tank. We now solve the above equation for T
3(1 / T) = 1 - 3 / 4
3(1 / T) = 1 / 4
1 / T = 1 / 12
T = 12 hours

Solution to Question 2

"y = 45 when x = 3" is used to find the constant k by substituting y and x by their values in the equation y = k / x.
45 = k / 3
Solve for k
k = 3 * 45 = 135
We now use the same equation with known value of k to find x when y = 180 as follows
180 = 135 / x
Solve for x
x = 135 / 180 = 3 / 4

Solution to Question 3

Let L, W and P be the length, width and perimeter of the rectangle. Hence "a rectangle has a length that is one third of its perimeter" is translated as follows
L = P / 3 = 150 / 3 = 50
The perimeter P is given by the formula
P = 2L + 2W
Substitute P by 150 and L by 50 and solve for W
150 = 2 * 50 + 2 W
W = 25
The area A of the rectangle is given by
A = L W = 50 * 25 = 1250

Solution to Question 4


Let x and y be the two numbers. "The square of the sum of two numbers is 289" is translated as follows
(x + y)2 = 289
Expand the left side of the above equation
x2 + y2 + 2 x y = 289
x y is the product of the two numbers and is given. Hence
x2 + y2 + 2 (66) = 289
Which gives
x2 + y2 = 157
Hence the sum of the square of x and y is 157

Solution to Question 5

30% of the money spent on energy is given by
30% * 30 = 9

Solution to Question 6

Let x be the smallest of these numbers. x + 2 and x + 4 will the next two odd integers. Hence
x + (x + 2) + (x + 4) = 249
Solve for x the above equation.
3x + 2 + 4 = 249
3x = 243
x = 81
The largest of these numbers is x + 4 and its value is
x + 4 = 81 + 4 = 85

Solution to Question 7


Let x and y be the two numbers. Hence
x + y = 3.6 and x - y = 1.2
Solve the above system of equations by adding the left sides and right sides of the two equations
(x + y) + (x - y) = 3.6 + 1.2
2x = 4.8
x = 2.4
Use equation x + y = 3.6 to find y
y = 3.6 - 2.4 = 1.2
The largest of these numbers is 2.4

Solution to Question 8

Let x the number. Hence
20% x = 125
Solve for x
(20 / 100) x = 125
x = 125 * 100 / 20 = 625

Solution to Question 9

Let x be the original price. The price after the first reduction of 10% is given by
x - 10% x = x - (10/100)x = x - 0.1x
The price after the second reduction of 15% is given by
(x - 0.1x) - 15% (x - 0.1x) = x - 0.1x - (15/100)(x - 0.1x)
= x - 0.1x - 0.15(x - 0.1x)
= x - 0.1x - 0.15x + 0.015x
= 0.765x
The final price is 22 dollars. Hence
0.765x = 22
Solve for x
x = 28.7581
Rounded to the nearest cent, the original price x is equal to
28.76 dollars

Solution to Question 10

The average of 1/2, 1/4, 2/3 and x is given by
(1/2 + 1/4 + 2/3 + x) / 4
and is equal to 3/4. Hence
(1/2 + 1/4 + 2/3 + x) / 4 = 3 / 4
Solve for x. First multiply both sides of the equation by 4 ans simplify
(1/2 + 1/4 + 2/3 + x) = 3 x = 3 - (1/2 + 1/4 + 2/3)
Set all fractions to common denominator
x = 36/12 - (6/12 + 3/12 + 8/12) = 36/12 - 17/12
x = 19/12

More Math Practice Tests
Free GRE Quantitative for Practice
Free Practice for GAMT Math tests
Free Compass Math tests Practice
Free Practice for SAT, ACT Math tests
Free AP Calculus Questions (AB and BC) with Answers