# Free GRE Solutions and Explanations to Sample 1

Solutions and detailed explanations to questions and problems similar to the questions in the GRE test. sample 1

## Solution to Question 1

The number of miles covered using 1 gallon is given by
(130 / 4) = 32.5 miles/gallon
Using 6.5 gallons, the car will cover
6.7 * 32.5 = 217.75 miles

## Solution to Question 2

Shown below is the graph of ||x|-4| by steps. First top left is the V-shaped graph of |x|, then below is the graph of |x|-4 which is the graph of |x| shifted 4 units down. Top right is the graph of ||x| - 4| which is the graph of |x|-4 where the part of the graph below the x axis is reflected on the x axis to make it positive or zero. Finally the graph of ||x| - 4| and that of y = 2 shows that there are 4 points of intersection. .

## Solution to Question 3

Convert all given quantities into decimal numbers
A) 125% = 125/100 = 1.25
B) 1.25 = 1.25
C) 1 + 1/3 = 1.333...
D) 4/3 = 1.333...
E) 0.0015/0.001 = 1.5/1 = 1.5
The largest of all given quantities is 0.0015/0.001

## Solution to Question 4

First calculate |- 10 - 19|
|- 10 - 19| = |-29| = 29
Substitute |- 10 - 19| by 29 in the given expression and calculate
| |- 10 - 19| - 20 | = |29 - 20| = |9| = 9

## Solution to Question 5

Since division by 0 is not allowed in mathematics, the given expression is undefined for any value that makes its denominator equal to 0. The denominator of the given expression is equal to 0 if
x + 2 =0 or x = - 2
The given expression is undefined if x = -2

## Solution to Question 6

We first expand the given expression using the identity (x - y)(x + y) = x2 - x2 and then simplify
(√5 - √7)(√5 + √7) = (√5)2 - (√7)2 = 5 - 7 = - 2

## Solution to Question 7

The size of angle BAC is equal to 46� since it is a vertical angle to the given angle of size 46�. We now use the fact that the sum of all angles in a triangle is equal to 180�.
size of angle ABC + size of angle ACB + 46� = 180�
Since AB and AC have equal lengths, triangle ABC is isosceles and therefore angles ABC and ACB are equal in size. Hence
2 (size of angle ABC) + 46� = 180�
size of angle ABC = (180 - 46) / 2 = 67�

## Solution to Question 8

The sum of all three angles in a triangle is equal to 180�. Hence
(4x + 4y) + (x + 3y) + (x + 2y) = 180
Group like terms
6x + 9y = 180
Substitute y by 10 in the equation and solve for x.
6x + 9(10) = 180
6x = 180 - 90 = 90
x = 15

## Solution to Question 9

Let L, W and H be the length, width and height of the rectangular solid. The volume V is given by
V = L W H
When L, W and H are increased by 25%, they become
L = L + 25%L = L(1 + 25/100) = L(1 + 0.25) = 1.25 L
W = 1.25 W
H = 1.25 H
The volume V2 after the increase is given by
V2 = (1.25 L) (1.25 W) (1.25 H) = 1.253 L W H
Find the percentage P of increase of the volume as follows
P = (V2 - V) / V = (1.253 L W H - L W H) / L W H =
L W H (1.253 - 1) / L W H
= 1.253 - 1 = 0.95 (rounded to the nearest hundredth)
= 95%

## Solution to Question 10

The prime numbers between 20 and 40 are
23, 29, 31 and 37
Their average is equal to
(23 + 29 + 31 + 37) / 4 = 30

## More References and Links to Maths Practice Tests

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