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GRE Practice - Quantitative Reasoning - Set 23

  1. a and b are integers
    (-2)a(4)b = 64

QUANTITY A

a

QUANTITY B

b
  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

Ignore the signs to start with
(-2)a(4)b = 26
(-2)a(2)2b = 26
a + 2b = 6
Possibilities are a=0 and b = 3 or a=2 and b=2 or a = 4 and b = 1
There are 3 cases and a is lesser than, equal to, and greater than in each case respectively.

  1. For all numbers x where x ≠ 0, if f(x) =1/x and g(x) = 1/(1 + x)

QUANTITY A

f(g(-2)

QUANTITY B

g(f(-2)
  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

f(g(-2))= f(1/(1-2)) = f(-1) = -1
g(f(-2)) = g(1/-2)=g(-1/2) = 1/(1-1/2) = 2

  1. If O is the centre of the circle and the area of the shaded region is 9(π – 2), what is the radius of the circle?
QR23

The sector has a central angle of 900 so it represents ¼ of the circle.
Area of sector = ¼ π r2
Area of isosceles right triangle AOB = ½ x r x r = ½ r2
Area of shaded region = Area of sector – area of ΔAOB = r2( π/4 – ½)
Area of shaded region = ¼ r2( π – 2)
But, area of shaded region = 9(π – 2), ¼ r2= 9 or r = 6

  1. If 2x+3y = 512, where x and y are positive integers

QUANTITY A

2x+y

QUANTITY B

16
  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

2x+3y = 29, so x+ 3y = 9
Now, x and y are positive integers
So the possibilities are x = 6 and y = 1 OR x = 3 and y = 2
So, 2x+y = 27 OR 25
Quantity A is either 128 or 32; in either case it’s greater than 16

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