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- a and b are integers

(-2)^{a}(4)^{b}= 64

a

b

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

Answer: D

Ignore the signs to start with

(-2)^{a}(4)^{b} = 2^{6}

(-2)^{a}(2)^{2b} = 2^{6}

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.

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

f(g(-2)

g(f(-2)

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

Answer: B

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

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

- 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?

- 3
- 6
- 8
- 9
- 3√3

Answer: C

The sector has a central angle of 90^{0} so it represents ¼ of the circle.

Area of sector = ¼ π r^{2}

Area of isosceles right triangle AOB = ½ x r x r = ½ r^{2}

Area of shaded region = Area of sector – area of ΔAOB = r^{2}( π/4 – ½)

Area of shaded region = ¼ r^{2}( π – 2)

But, area of shaded region = 9(π – 2), ¼ r^{2}= 9 or r = 6

- If 2
^{x+3y}= 512, where x and y are positive integers

2^{x+y}

16

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

Answer: A

2^{x+3y} = 2^{9}, 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, 2^{x+y} = 2^{7} OR 2^{5}

Quantity A is either 128 or 32; in either case it’s greater than 16

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