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

- 48
- 52
- 56
- 60
- 63

Answer: C

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%

- What is the value of x in the figure above?

Answer: 110

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

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

- 63
- 91
- 110
- 117
- 169

Answer: E

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.

- 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?

- 35
- 42
- 56
- 63
- 77

Answer: D

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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