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GMAT CLUB OLYMPICS: If x and y are positive integers and

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Bunuel
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GMAT CLUB OLYMPICS: If x and y are positive integers and [#permalink] New post   25 Aug 2021, 08:00
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If x and y are positive integers and \((5\frac{3}{x})*(y\frac{1}{2})=19\), where \(5\frac{3}{x}\) and \(y\frac{1}{2}\) are mixed fractions, then what is the values of x + y?

A. 3
B. 5
C. 7
D. 10
E. 11


 


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D
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Bunuel
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Re: GMAT CLUB OLYMPICS: If x and y are positive integers and [#permalink] New post   22 Nov 2021, 04:02
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Official Solution:

If \(x\) and \(y\) are positive integers and \((5\frac{3}{x})*(y\frac{1}{2})=19\), where \(5\frac{3}{x}\) and \(y\frac{1}{2}\) are mixed fractions, then what is the values of \(x + y\)?

A. \(3\)
B. \(5\)
C. \(7\)
D. \(10\)
E. \(11\)


\((5\frac{3}{x})*(y\frac{1}{2})=19\)

\((\frac{5x+3}{x})*(\frac{2y+1}{2})=19\)

\((5x+3)(2y+1)=38x\)

From, \((5\frac{3}{x})*(y\frac{1}{2})=19\) it follows that \(y\) must be less than 4 (\(5.something*4.something=20.something\)). So, \(y\) can be 3, 2, or 1.

If \(y=3\), then from \((5x+3)(2y+1)=38x\), \(x=7\), and \(x+y=10\).

If \(y=2\), then from \((5x+3)(2y+1)=38x\), \(x=\frac{15}{13}\neq integer\). Not possible since \(x\) must be integer.

If \(y=1\), then from \((5x+3)(2y+1)=38x\), \(x=\frac{9}{23}\neq integer\). Not possible since \(x\) must be integer.


Answer: D
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Re: GMAT CLUB OLYMPICS: If x and y are positive integers and [#permalink] New post   25 Aug 2021, 08:18
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IMO D

Since the final product is 19, y must be 3
[As 5*3 < 19 < 5*4]

Thus we are left with solving for x:

[(5x+3)/3]*7/2=19
Solving for x, we get x=7
Therefore x+y=7+3=10 ANS
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Re: GMAT CLUB OLYMPICS: If x and y are positive integers and [#permalink] New post   25 Aug 2021, 08:29
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Hello everyone

The correct answer is 10 (D)

Here is my solution
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Re: GMAT CLUB OLYMPICS: If x and y are positive integers and [#permalink] New post   09 May 2022, 11:28
I have a slightly different approach to this one. I also came up with the answer to be D. Please see the attached picture for my logics. Sorry, the writing is not very good.
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Re: GMAT CLUB OLYMPICS: If x and y are positive integers and [#permalink] New post   05 Jun 2023, 03:11
Hello from the GMAT Club BumpBot!

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Re: GMAT CLUB OLYMPICS: If x and y are positive integers and [#permalink]
05 Jun 2023, 03:11
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