# 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
x
2 + y2 + 2 x y = 289
x y is the product of the two numbers and is given. Hence
x
2 + y2 + 2 (66) = 289
Which gives
x
2 + 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
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