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# What is the number of 10 cents coins in the piggy bank?

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Manager
Status: The journey is always more beautiful than the destination
Affiliations: Computer Science
Joined: 24 Apr 2017
Posts: 53
Location: India
Concentration: Statistics, Strategy
GMAT 1: 570 Q40 V28
GPA: 3.14
What is the number of 10 cents coins in the piggy bank?  [#permalink]

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Updated on: 09 Apr 2018, 00:18
2
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:40) correct 31% (01:23) wrong based on 82 sessions

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What is the number of 10 cents coins in the piggy bank?

(1) A total of 69 coins are there in the denomination of 25 cents, 50 cents, 10 cents and 1 cent coins.
(2) The number of 25 cents, 50 cents and 1 cents coins are in the ratio 18 : 7 : 12.

source:time4education

_________________

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Originally posted by Nixondutta on 08 Apr 2018, 22:41.
Last edited by Bunuel on 09 Apr 2018, 00:18, edited 1 time in total.
Edited the question.
Manager
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Concentration: General Management, Marketing
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Re: What is the number of 10 cents coins in the piggy bank?  [#permalink]

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08 Apr 2018, 22:53
1
Nixondutta wrote:
What is the number of 10 cents coins in the piggy bank?
source:time4education

(1) A total of 69 coins are there in the denomination of 25 cents, 50 cents, 10 cents and 1 cent coins.
(2) The number of 25 cents, 50 cents and 1 cents coins are in the ratio 18 : 7 : 12.

Let 25 cents=a,
50 cents=b,10 cents =c,1 cents=d

from1 :a+b+c+d=69

not sufficient.

from2 :a:b:d=18 : 7 : 12

not sufficient.

combining both
18x+7x+12x+c=69

for x=1 ,unique value of c is possible.

Hence C
Intern
Joined: 23 Jun 2017
Posts: 9
GMAT 1: 610 Q43 V31
Re: What is the number of 10 cents coins in the piggy bank?  [#permalink]

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30 Apr 2018, 04:13
How does x=1 satisfy the equation? If x=1, then there are multiple answers for 10 cent coins and 1 cent coins. Please explain
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Re: What is the number of 10 cents coins in the piggy bank?  [#permalink]

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01 May 2018, 13:07
The way I looked at it is that the ratio of 18:7:12 cannot be reduced any further. Since all coins must be whole coins (we cannot presumably have fractional coins in our total) we must have at LEAST that ratio worth of coins, and for any total number of coins, the amount of 25,50, and 1 cent coins has to be a multiple of our ratio.

Since 18+7+12 = 37, then we must have at least 37 coins in the jar plus an unknown number of 10 cent pieces. We could also have 74, or 111, or any other multiple of 37 worth of 25,50, and 1 cent coins, but the total of those three denominations must be a multiple of 37 to maintain our ratio.

If we know there are 69 coins in the jar, we can easily see that 2X37=74 would be too many coins. Thus the total number is 18+7+12=37 for our 25, 50, and 1s, and the remainder must be 10 cents
Re: What is the number of 10 cents coins in the piggy bank? &nbs [#permalink] 01 May 2018, 13:07
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