# 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 1Pump 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 is1 / 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 3Let 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 followsL = 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 4Let 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} + y^{2} + 2 x y = 289
x y is the product of the two numbers and is given. Hence x ^{2} + y^{2} + 2 (66) = 289
Which gives x ^{2} + y^{2} = 157
Hence the sum of the square of x and y is 157 ## Solution to Question 530% of the money spent on energy is given by30% * 30 = 9 ## Solution to Question 6Let x be the smallest of these numbers. x + 2 and x + 4 will the next two odd integers. Hencex + (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 7Let 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 8Let x the number. Hence20% x = 125 Solve for x (20 / 100) x = 125 x = 125 * 100 / 20 = 625 ## Solution to Question 9Let x be the original price. The price after the first reduction of 10% is given byx - 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 10The 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 |