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# Percentage Problem #4

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Manager
Joined: 25 Jan 2010
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Location: Calicut, India
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Percentage Problem #4 [#permalink]  22 Jul 2011, 12:13
00:00

Difficulty:

5% (low)

Question Stats:

50% (06:52) correct 50% (03:58) wrong based on 8 sessions
Alex, Ben, Charles and David are 4 friends. Alex purchases a machine for \$1000. He sells it to Ben at a certain gain percentage. Ben in turn sells it for \$1500 to Charles who in turn sells it to David. The gain percentages of Alex, Ben, Charles and David are in Arithmetic Progression. Had Ben sold the machine to David directly for the same rate which Charles sells the cycle, then he would have made a profit of 62.5%.

Q) What profit did Ben make on selling cycle to Charles? and What profit did Charles make on selling the cycle to David ?
A) 450 and 300
B) 250 and 600
C) 200 and 200
D) 300 and 450
E) 350 and 500
[Reveal] Spoiler: OA

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Manager
Joined: 28 May 2011
Posts: 197
Location: United States
GMAT 1: 720 Q49 V38
GPA: 3.6
WE: Project Management (Computer Software)
Followers: 2

Kudos [?]: 34 [0], given: 7

Re: Percentage Problem #4 [#permalink]  23 Jul 2011, 03:44
cleetus wrote:
Alex, Ben, Charles and David are 4 friends. Alex purchases a machine for \$1000. He sells it to Ben at a certain gain percentage. Ben in turn sells it for \$1500 to Charles who in turn sells it to David. The gain percentages of Alex, Ben, Charles and David are in Arithmetic Progression. Had Ben sold the machine to David directly for the same rate which Charles sells the cycle, then he would have made a profit of 62.5%.

Q) What profit did Ben make on selling cycle to Charles? and What profit did Charles make on selling the cycle to David ?
A) 450 and 300
B) 250 and 600
C) 200 and 200
D) 300 and 450
E) 350 and 500

I think there must be some typo in the question.

If we say in the cost of the machine to individuals :

A - 1000
B - 1000+x% (A earned x% profit)
C - 1500
D - (1000+x%) (1+ 62.5%) = 1500 - when Ben sell the cycle to David directly. and the cost to David still remains the same as it was when the he purchased the machine from Charles.

However the last equation doesn't seem to be right, because

1000 + x% > 1000 (assuming X > 0, because everybody earned profit)

and a profit of 62.5% on an amount greater than 1000 should always be greater than 1625 (not 1500).

Let me know if I have missed any thing present in the question.
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Manager
Joined: 31 May 2011
Posts: 95
Location: India
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
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Kudos [?]: 24 [1] , given: 4

Re: Percentage Problem #4 [#permalink]  23 Jul 2011, 05:16
1
KUDOS
cleetus wrote:
Alex, Ben, Charles and David are 4 friends. Alex purchases a machine for \$1000. He sells it to Ben at a certain gain percentage. Ben in turn sells it for \$1500 to Charles who in turn sells it to David. The gain percentages of Alex, Ben, Charles and David are in Arithmetic Progression. Had Ben sold the machine to David directly for the same rate which Charles sells the cycle, then he would have made a profit of 62.5%.

Q) What profit did Ben make on selling cycle to Charles? and What profit did Charles make on selling the cycle to David ?
A) 450 and 300
B) 250 and 600
C) 200 and 200
D) 300 and 450
E) 350 and 500

A => CP = 1000 ; SP = X
Profit% = [(X-1000)/1000]*100 --- say P(a)

B => CP = X ; SP = 1500
Profit% = [(1500-X)/X]*100 --- say P(b)

C => CP = 1500 ; SP = Y
Profit% = [(Y-1500)/1500]*100 --- say P(c)

Given profits are in AP hence: 2P(b) = P(a)+P(c) -- eq1

Again it also given when B sells directly to D at the same SP as C profit% 62.5%
hence: B -> D

[(Y-X)/X]*100 = 62.5
so we get 100Y = 162.5X -- Eq 2

Substituting the above value in eq 1 we get X = 1200 and Y = 1950

So profit amount from B ->C is 300 and from C ->D is 450.

Hence D
Senior Manager
Joined: 11 Apr 2011
Posts: 270
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Re: Percentage Problem #4 [#permalink]  23 Jul 2011, 12:24
What is the source of this question? Seems far beyond a typical gmat 700 level percent question...
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Manager
Joined: 25 Jan 2010
Posts: 114
Location: Calicut, India
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Re: Percentage Problem #4 [#permalink]  23 Jul 2011, 14:39
Mahtab wrote:
What is the source of this question? Seems far beyond a typical gmat 700 level percent question...

This is from a Indian MBA Entrance exam guide.
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Re: Percentage Problem #4   [#permalink] 23 Jul 2011, 14:39
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