Some GMAT Prep - PS Questions

Question Number 1:



Diameter OR = 18 => Radius = 9
Circumference of the circle = (2*π*9) = 18π
Length of minor arc PQ = Circumference of the circle - Length of major arc PQ
Length of major arc PQ = Length of minor arc PO + Length of arc OR + Length of minor arc OQ
Length of arc OR = Circumference/2 = (2*π*9)/2 = 9π

Length of minor arc PO = Length of minor arc OQ

Angle ORP = 35°
Therefore, angle OCP = 2*35° = 70°

Length of minor arc PO = Length of arc that subtends an angle of 70° in the centre = (2*π*9)*70/360 = 7π/2
Therefore, Length of minor arc OQ = 7π/2

Length of major arc PQ = 7π/2 + 9π + 7π/2 = 16π

Length of minor arc PQ = Circumference of the circle - Length of major arc PQ = 18π - 16π = 2π

The correct answer is A.

Question Number 2:

Before being simplified, the instructions for computing income tax in country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?

• (A) 50 + I/200
  (B) 50 + 3I/100
  (C) 50 + I/40
  (D) 100 + I/50
  (E) 100 + 3I/100

The question defines the calculation of income tax as,

Income Tax = 2% of annual income + Average of 100 and 1% of annual income

If annual income = I,
Income tax = 2% of I + (100 + 1% of I)/2
= 0.02*I + (100 + 0.01*I)/2
= (100 + 0.04*I + 0.01*I)/2
= 50 + (0.05*I)/2
= 50 + (5*I/100)/2
= 50 + I/40

The correct answer is C.

Question Number 3:

If (x^4 + y^4) = 100, then the greatest possible value of x is between

• (A) 0 and 3
  (B) 3 and 6
  (C) 6 and 9
  (D) 9 and 12
  (E) 12 and 15

As no condition is given for the values of x and y, we can find the greatest possible value of x, just by setting y = 0.

For y = 0, x^4 = 100 => x^2 = 10 => x = √10 ≈ 3.16

The correct answer is B.