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Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and [#permalink]

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New post 20 Dec 2017, 02:03
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Difficulty:

  35% (medium)

Question Stats:

73% (01:16) correct 27% (01:29) wrong based on 51 sessions

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[GMAT math practice question]

Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and 50 cent coins. If you make 50 cents with these coins, which of the following could be the total number of coins used?

I. 41
II. 31
III. 26

A. I only
B. II only
C. III only
D. I & III
E. II & III
[Reveal] Spoiler: OA

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Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5288
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and [#permalink]

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New post 21 Dec 2017, 00:46
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Let \(a, b, c, d\) and \(e\) be the numbers of 1 cent, 5 cent, 10 cent, 25 cent and 50 cent coins, respectively.
Then \(a + 5b + 10c + 25d + 50d = 50.\)

The possible numbers of each coin are as follows:
(a,b,c,d,e) = (50,0,0,0,0) : 50 coins
(a,b,c,d,e) = (45,1,0,0,0) : 46 coins
(a,b,c,d,e) = (40,2,0,0,0) : 42 coins
(a,b,c,d,e) = (40,0,1,0,0) : 41 coins
(a,b,c,d,e) = (35,1,1,0,0) : 37 coins
(a,b,c,d,e) = (30,2,1,0,0) : 33 coins
(a,b,c,d,e) = (30,0,2,0,0) : 32 coins
(a,b,c,d,e) = (25,1,2,0,0) : 28 coins
(a,b,c,d,e) = (25,0,0,1,0) : 26 coins

Only 41 and 26 are in this list.
Therefore, the answer is D.

Answer: D
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Re: Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and   [#permalink] 21 Dec 2017, 00:46
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Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and

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