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# A coin bank contains only dimes and quarters. How many quarters are in

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Math Expert
Joined: 02 Sep 2009
Posts: 58414
A coin bank contains only dimes and quarters. How many quarters are in  [#permalink]

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02 Apr 2018, 21:47
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Difficulty:

25% (medium)

Question Stats:

88% (01:10) correct 12% (01:15) wrong based on 27 sessions

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A coin bank contains only dimes and quarters. How many quarters are in the coin bank? (dime = \$0.1, quarter = \$0.25)

(1) There are twice as many dimes as quarters in the coin bank.
(2) The total face value of the coins in the coin bank is \$9.90.

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Posts: 1140
Re: A coin bank contains only dimes and quarters. How many quarters are in  [#permalink]

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02 Apr 2018, 23:02
Bunuel wrote:
A coin bank contains only dimes and quarters. How many quarters are in the coin bank? (dime = \$0.1, quarter = \$0.25)

(1) There are twice as many dimes as quarters in the coin bank.
(2) The total face value of the coins in the coin bank is \$9.90.

We'll use numbers to eliminate contradictory statements.
This is an Alternative approach.

(1) If there are 2 dimes there is 1 quarter and if there are 4 dimes there are 2 quarters.
Insufficient.

(2) If we have 90 cents of dimes (9 dimes) then there are 9 dollars worth of quarters and if we he have \$1.9 of dimes (19 dimes) there are 8 dollars worth of quarters.
Insufficient.

Combined:
We now have two equations - d= 2q and 0.1d +0.25q=9.9. solving gives only one possible solution.
Sufficient.

(C) is our answer.
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GMAT 1: 640 Q50 V25
Re: A coin bank contains only dimes and quarters. How many quarters are in  [#permalink]

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03 Apr 2018, 02:13
let no of dimes be x and no of quarters be y
St 1: 2x=y
St2: 0.1x+0.25y=9.90
St1+St2, 0.6x=9.9
x=99/6=16.5
but x can't be in decimal
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A coin bank contains only dimes and quarters. How many quarters are in  [#permalink]

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03 Apr 2018, 02:19
NiharikaR wrote:
let no of dimes be x and no of quarters be y
St 1: 2x=y
St2: 0.1x+0.25y=9.90
St1+St2, 0.6x=9.9
x=99/6=16.5
but x can't be in decimal

Hi,

Your first equation should be x=2y and not y=2x.
Then combining them would give 0.45y=9.9
So y = 22 and x = 44.
Then you have \$4.4 worth of dimes and \$5.5 worth of quarters as required.

But note that none of this is necessary! Since you can't have 'illegal' answers on the GMAT, then if there exists only one solution it must be 'legal'.
In this case, it is enough to say that you have two distinct equations with two variables meaning that you can solve the question.
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A coin bank contains only dimes and quarters. How many quarters are in   [#permalink] 03 Apr 2018, 02:19
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# A coin bank contains only dimes and quarters. How many quarters are in

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