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Joanna bought only $0.15 stamps and$0.29 stamps. How many

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Joanna bought only $0.15 stamps and$0.29 stamps. How many [#permalink]  24 Feb 2008, 17:15
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Joanna bought only $0.15 stamps and$0.29 stamps. How many $0.15 stamps did she buy? (1) She bought$4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps and$0.29 stamps.

OA is A

We can get an equation from choice 1 as
15x + 29Y = 440,
but how do we determine if the above equation has only one solution.
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Re: DS - Stamps [#permalink]  24 Feb 2008, 18:53
A

In the equation 15x + 29y =440, in order to end the sum with "0" in units, 29y should have 5 or 0 in units.
so I picked 5, 10 and 15 for y. Only y=10 leaves enough money divisble by 15. So the values must be 10 and 10.
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Re: DS - Stamps [#permalink]  27 Feb 2008, 07:44
sam76 wrote:
Joanna bought only $0.15 stamps and$0.29 stamps. How many $0.15 stamps did she buy? (1) She bought$4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps and$0.29 stamps.

OA is A

We can get an equation from choice 1 as
15x + 29Y = 440,
but how do we determine if the above equation has only one solution.

You have train yourself to test these problems. This is a GMAT trap for C. Red flags should go up b/c we arrive at C way to easily, in about 10 seconds or less u could get this answer. You should reanalyze.

S2: 15x+29y --> 15x+29x --> No help here.

S1: 15x+29y=440. You def recognize that 29 is a prime and in order to have 15x+29y = 440 evenly, we are going to have very limited choice(s). Hint hint.

Also recognize that the result of 440-29y must be divisble by 15. So we again narrow the choices here. Only 5, 10, 15, * 29 could meet our criteria b/c this would produce a 5 or 0 in the units digit of 440-29y.

Try 5. 29*5=145 440-145= 295. 295/15 is not an integer.

29*10=290. 440-290=150. This works b/c 150/15=10

29*15 = 435 too big.

Thus only 10 works. A is the answer

Again. Always be wary of problems in which you arrive at the answer all too quickly.

Also notice that S2 is true in this case 29(10)+15(10)=440. x=y
Re: DS - Stamps   [#permalink] 27 Feb 2008, 07:44
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