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

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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, 01:03
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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
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Joined: 16 Aug 2015
Posts: 4716
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Re: 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, 23:46
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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] 20 Dec 2017, 23:46
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