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GRE Practice - Quantitative Reasoning - Set 21

  1. The number 3/4 is approximately what percent of its reciprocal?

The reciprocal of 3/4 is 4/3
So, the question is: 3/4 is what percent of 4/3
(3/4)/(4/3) x 100 = 9/16 x 100 = 56.25% ≈56%

  1. What is the value of x in the figure above?

Using the Pythagoras theorem on ΔPQT: QT = 10
Using the Pythagoras theorem on ΔRQS: QS = 10
Thus, ΔRQS is isosceles with QT = QS
x+35+35= 180. x = 110

  1. If |x + 3| = 10 and |y +2| = 11, the maximum value of xy =

Let’s first find the solutions for x and y.

(x + 3) = 10 or (x + 3) = −10
x = 7 OR x = −13

(y + 2) = 11 or (y + 2) = −11
y = 9 OR y = −13
The maximum value for xy will be (−13)( −13) = 169.

  1. At a certain company, the ratio of supervisors to managers is 7:4. If 8 of the supervisors become managers, the new ratio will be 5:4. How many supervisors are currently at the company?

Let the number of supervisors be 7x, therefore the number of managers is 4x
If 8 of the supervisors become managers:
Number of supervisors: 7x – 8
Number of managers: 4x + 8
(𝟕𝒙 − 𝟖) / (𝟒𝒙 + 𝟖) = 5/4
28x – 32 = 20x + 40
8x = 72
x = 9
Number of supervisors = 9 x 7 = 63

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