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Some GMAT Prep - PS Questions

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gig92: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Fri Jul 23, 2010 2:22 amFollowed by: 1 member; Thanked: 2 times

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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Source: Beat The GMAT — Problem Solving | Fri Nov 12, 2010 2:34 am

beat_gmat_09: Master | Next Rank: 500 Posts; Posts: 437; Joined: Sat Nov 22, 2008 5:06 amFollowed by: 1 member; Location: India; Thanked: 50 times; GMAT Score:580

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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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Nov 12, 2010 4:22 am

Question Number 1:

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 = 35Â°
Therefore, angle OCP = 2*35Â° = 70Â°

Length of minor arc PO = Length of arc that subtends an angle of 70Â° in the centre = (2*Ï€*9)*70/360 = 7Ï€/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.

Rahul Lakhani
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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

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.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

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 = âˆš10 â‰ˆ 3.16

The correct answer is B.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
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