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

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Re: Joanna bought only $0.15 stamps and $0.29 stamps. How many  [#permalink]

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New post 18 Jan 2017, 09:38
Quote:
So when we have equation of a type ax+by=cax+by=c and we know that xx and yy are non-negative integers, there can be multiple solutions possible for xx and yy (eg 5x+6y=605x+6y=60) OR just one combination (eg 15x+29y=44015x+29y=440). Hence in some cases ax+by=cax+by=c is NOT sufficient and in some cases it is sufficient.


Hi. How to figure out if ax+by=c has multiple or single solution of values?
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Re: Joanna bought only $0.15 stamps and $0.29 stamps. How many  [#permalink]

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New post 18 Jan 2017, 10:24
Ndkms wrote:
Can you please point to the rule that justifies the above statement?

I think we just need to do a trial and error here. In this case for example, there is only one unique set of integer values of x and y that satisfy 15x + 29y = 440
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Re: Joanna bought only $0.15 stamps and $0.29 stamps. How many  [#permalink]

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New post 23 Feb 2017, 04:45
PROMPT ANALYSIS
Let the number of $0.15 stamp be x and number of $0.29 stamp be y. Total value of stamp = 0.15x +0.29y.

Superset

X can be a nonnegative integer

Translation
In order to find the value of x we need:
1# exact value of x and y
2# two equations with x and y as variable to solve for x and y

Statement analysis
St 1: total value of stamp = 4.40 =0.15x +0.29y. One equation two variable. Since we know that x and y are positive integers. We can say 15x +29y =440: x =(440-29y)/15. The only integer that will satisfy will be x = 10 , y = 10, ANSWER. Hence option b, c, e eliminated.

St 2: x =y. Therefore the total will be 0.44x. We cannot calculate the value of x from this information. INSUFFICIENT.
Option A.
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Re: Joanna bought only $0.15 stamps and $0.29 stamps. How many  [#permalink]

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New post 02 Sep 2018, 20:27
Bunuel wrote:
udaymathapati 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.


Let \(x\) be the # of $0.15 stamps and \(y\) the # of $0.29 stamps. Note that \(x\) and \(y\) must be an integers. Q: \(x=?\)

(1) She bought $4.40 worth of stamps --> \(15x+29y=440\). Only one integer combination of \(x\) and \(y\) is possible to satisfy \(15x+29y=440\): \(x=10\) and \(y=10\). Sufficient.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps --> \(x=y\). Not sufficient.

Answer: A.

So when we have equation of a type \(ax+by=c\) and we know that \(x\) and \(y\) are non-negative integers, there can be multiple solutions possible for \(x\) and \(y\) (eg \(5x+6y=60\)) OR just one combination (eg \(15x+29y=440\)). Hence in some cases \(ax+by=c\) is NOT sufficient and in some cases it is sufficient.

For more on this type of questions check:
http://gmatclub.com/forum/eunice-sold-s ... 09602.html
http://gmatclub.com/forum/martha-bought ... 00204.html
http://gmatclub.com/forum/a-rental-car- ... 05682.html
http://gmatclub.com/forum/joe-bought-on ... 06212.html
http://gmatclub.com/forum/a-certain-fru ... 01966.html
http://gmatclub.com/forum/joanna-bought ... 01743.html
http://gmatclub.com/forum/at-an-amuseme ... 26814.html
http://gmatclub.com/forum/collections-c ... 81062.html

Hope it helps.


Is there the quickest way to solve statement 1(Diophantine eq)?
I spent 3 mins to solve this question correctly but I feel that it should not take more than 1.5mins to solve such questions.

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Re: Joanna bought only $0.15 stamps and $0.29 stamps. How many &nbs [#permalink] 02 Sep 2018, 20:27

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