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I apologize if this was posted already. But here goes: On

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Senior Manager
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I apologize if this was posted already. But here goes: On [#permalink] New post 07 Sep 2009, 20:28
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I apologize if this was posted already. But here goes:

On one of the OG questions, I got the equation 29x+15y=440 for one of the statements. The coefficients are ticket prices in cents and the variables are amount bought per ticket price. Anyway, this type of equation without the whole number constraint of tickets bought would be insufficient. But since it's a whole number constraint it turns out that it can only be valid when x=10 and y=10. I actually figured it out after minutes upon minutes of racking my brain. The way I figured it out is I realized that 440-15y would be a multiple of 5, so I substituted all numbers of x that would give me a multiple of 5 that would be less than or equal to 440 and would be valid if y is an integer. Unfortunately, with a whole number constraint there isn't always just one valid combo for the 2 variables. For example, if the equation were 50x+100y=300. Then there can be either 2 tickets at 50 cents a piece and 2 tickets at $1 OR 4 tickets at 50 cents a piece and 1 ticket at $1 (not to mention if it's possible for no tickets bought at one of the 2 amounts). Is there somehow a faster way of figuring out whether only one set of x and y satisfy the equation? Would there only be 1 answer for x and y whenever the coefficients have no prime factors in common (such as 15 and 29)?

Thanks for your help.
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Re: Whole number constraint [#permalink] New post 08 Sep 2009, 02:12
which OG question is it?

I think it depends on what the question says. for example x and y MUST be integers or not?
have a look here it could help you understand the theory behind this kind of equation.
the bezout's identity
http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity
Senior Manager
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Joined: 19 Jul 2009
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GMAT 1: 690 Q44 V41
GPA: 3.75
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Re: Whole number constraint [#permalink] New post 08 Sep 2009, 20:16
madeinafrica wrote:
which OG question is it?

I think it depends on what the question says. for example x and y MUST be integers or not?
have a look here it could help you understand the theory behind this kind of equation.
the bezout's identity
http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity


Thanks. It's question #123 in the data sufficiency chapter (P283).

Here it is exactly:

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.
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Re: Whole number constraint [#permalink] New post 08 Sep 2009, 20:54
Tough but good one. Is OA A?
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Re: Whole number constraint [#permalink] New post 08 Sep 2009, 21:13
Aleehsgonji wrote:
Tough but good one. Is OA A?


What do you mean OA?

And yes, the answer is A. That's because of the whole number constraint that I mentioned. Only X=10 and Y=10, fits that equation. Now I'm just hoping someone will help me recognize these and solve quickly. Specifically talking about a whole number constraint. Or is this problem specific?
Re: Whole number constraint   [#permalink] 08 Sep 2009, 21:13
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