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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
Joined: 16 Aug 2015
Posts: 4716
GPA: 3.82
Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and [#permalink]

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20 Dec 2017, 01:03
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Difficulty:

35% (medium)

Question Stats:

70% (01:10) correct 30% (01:29) wrong based on 40 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4716
GPA: 3.82
Re: Suppose you have a collection of 1 cent, 5 cent, 10 cent, 25 cent, and [#permalink]

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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.

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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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