IMPROVE YOUR GRE SCORE

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 = 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.

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)

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 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

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

QUANTITY A

2^x+y

QUANTITY B

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

Answer: A