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Some GMAT Prep - PS Questions

by gig92 » Fri Nov 12, 2010 2:34 am
Hi, please find few questions in the file attached here. Each question is marked with a wrong and its answer. Could you please try to discuss/explain (how and whys) of these questions?

Each effort is highly appreciated.
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by beat_gmat_09 » Fri Nov 12, 2010 3:06 am
gig92 wrote:Hi, please find few questions in the file attached here. Each question is marked with a wrong and its answer. Could you please try to discuss/explain (how and whys) of these questions?

Each effort is highly appreciated.
1) PQ || OR , Angle RPQ=35; the circumference covered by both Angle PO and QR is same.
to get length arc PQ = 1/2 Circumference (1) - 2(circum of PO OR QR) (2)
length of arc PO = (angle subtended at center/360) * (2*pie*r)
angle subtended at center = 2*Angle subtended at a point on circumference = 2 * 35.
length of arc PO = (35/360) (2*pie*9) = 7/2(pie)
value of (2) = 2*(7/2) * (pie) = 7*pie.
value of (1) = pie * r = pie * 9.
Answer = (1)-(2) = 9*pie-7*pie = 2*pie.

3) x^4+y^4 = 100
x will be greatest when y is least or 0.
put y=0.
x^4 = 100.
x^2=10
x= approx 3.1
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by Rahul@gurome » Fri Nov 12, 2010 4:22 am
Question Number 1:

Image

Diameter OR = 18 => Radius = 9
Circumference of the circle = (2*Ï€*9) = 18Ï€
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*Ï€*9)/2 = 9Ï€

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 = 7Ï€/2

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

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

The correct answer is A.
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by Rahul@gurome » Fri Nov 12, 2010 4:35 am
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.
Last edited by Rahul@gurome on Fri Nov 12, 2010 9:25 pm, edited 1 time in total.
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by Rahul@gurome » Fri Nov 12, 2010 4:41 am
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.
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