# 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 1The 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 2Shown 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 3Convert 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 4First 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 5Since 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 ifx + 2 =0 or x = - 2 The given expression is undefined if x = -2 ## Solution to Question 6We first expand the given expression using the identity (x - y)(x + y) = x^{2} - x^{2} and then simplify
(√5 - √7)(√5 + √7) = (√5) ^{2} - (√7)^{2} = 5 - 7 = - 2
## Solution to Question 7The 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 8The 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 9Let L, W and H be the length, width and height of the rectangular solid. The volume V is given byV = 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) = 1.25 ^{3} L W H
Find the percentage P of increase of the volume as follows P = (V2 - V) / V = (1.25 ^{3} L W H - L W H) / L W H =
L W H (1.25 ^{3} - 1) / L W H
= 1.25 ^{3} - 1 = 0.95 (rounded to the nearest hundredth)
= 95% ## Solution to Question 10The prime numbers between 20 and 40 are23, 29, 31 and 37 Their average is equal to (23 + 29 + 31 + 37) / 4 = 30 ## More References and Links to Maths Practice TestsFree GRE Quantitative for PracticeFree Practice for GAMT Maths tests Free Compass Maths tests Practice Free Practice for SAT, ACT Maths tests Free AP Calculus Questions (AB and BC) with Answers |