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GRE Practice - Quantitative Reasoning - Set 26

  1. The lengths of two sides of a right triangle are x/2 and x/3. If one of these sides is the hypotenuse, what is the length of the third side of the triangle?
  1. √7x/12
  2. √13x/12
  3. √7x/6
  4. √5x/6
  5. √13x/6

The hypotenuse is the longest side so it must be x/2
By Pythagoras’ Theorem, if the third side is s, then (x/2)2 = (x/3)2 + s2
(x2/4) – (x2/9) = s2
s2 = 5x2/36
s= √5x/6

  1. 9 – x2 = 37 + 11x

QUANTITY A

x

QUANTITY B

-x

  1. Quantity A is greater
  2. Quantity B is greater
  3. The two quantities are equal
  4. The relationship cannot be determined from the information given

Set the quadratic equal to zero: x2 + 11x + 28 = 0.
We factorize it: (x + 4)(x + 7) = 0.
There are two solutions:
EITHER (x + 3) = 0 and x = –3
OR (x + 4) = 0 and x = –4
Since both solutions are negative, x < 0 and –x > 0.

  1. What is the difference between the areas of a square with perimeter P and a square with perimeter 2P?
  1. P2/16
  2. P2/4
  3. P2/8
  4. 3P2/16
  5. 3P2/4

A square with perimeter P has sides of length P/4 Area = P2/16
A square with perimeter 2P has sides of length P/2 Area = P2/4
Difference: P2/4 – P2/16 = 3P2/16

  1. Betty is 10 years older than Jenny. In 3 years, Betty will be double Jenny’s age. How old will Betty be in 5 years?

Betty is 10 years older than Jenny: b = j + 10
In 3 years, Betty will be double Jenny’s age: b + 3 = 2(j + 3)
But, j = b – 10
So, b + 3 = 2(b – 10 + 3)
b + 3 = 2b – 14
17 = b
In 5 years, Betty will be 22.

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