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## GRE Practice - Quantitative Reasoning - Set 21

1. The number 3/4 is approximately what percent of its reciprocal?
1. 48
2. 52
3. 56
4. 60
5. 63

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 =
1. 63
2. 91
3. 110
4. 117
5. 169

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?
1. 35
2. 42
3. 56
4. 63
5. 77

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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