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M09-08

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Bunuel
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M09-08 [#permalink] New post   16 Sep 2014, 00:39
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84% (01:09) correct 16% (01:26) wrong based on 105 sessions
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If \(x\) and \(y\) are positive integers such that \(\frac{x}{y}= 2.625\), which of the following could be the remainder when \(x\) is divided by \(y\)?

A. 2
B. 4
C. 5
D. 6
E. 9
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C
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Bunuel
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Re M09-08 [#permalink] New post   16 Sep 2014, 00:39
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Official Solution:

If \(x\) and \(y\) are positive integers such that \(\frac{x}{y}= 2.625\), which of the following could be the remainder when \(x\) is divided by \(y\)?

A. 2
B. 4
C. 5
D. 6
E. 9


\(x\) divided by \(y\) yielding the remainder \(r\) can always be expressed as: \(\frac{x}{y}=q+\frac{r}{y}\) (which is the same as \(x=qy+r\)), where \(q\) is the quotient and \(r\) is the remainder.

\(\frac{x}{y}=2.625=2\frac{5}{8}=2+\frac{5}{8}\), so according to the above, \(\frac{r}{y}=\frac{5}{8}\), which means that \(r\) must be a multiple of 5. Only option C offers an answer that is a multiple of 5.


Answer: C
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Re: M09-08 [#permalink] New post   16 Dec 2014, 11:31
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If x and y are positive integers such that \frac{x}{y}= 2.625, which of the following could be the remainder when x is divided by y?

Sol:
frac{x}{y}= 2.625
The formula to calculate remainder if X/Y = a.bcd is to multiply denominator of LHS to post decima l part of RHS

Rem = y * 0.625
= y * 625/1000
= y * 5/8
which is multiple of 5 and only option which is multiple of 5 in the options is 5.
So 5 is the answer
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Re: M09-08 [#permalink] New post   16 Dec 2014, 11:32
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If x and y are positive integers such that \frac{x}{y}= 2.625, which of the following could be the remainder when x is divided by y?

Sol:
frac{x}{y}= 2.625
The formula to calculate remainder if X/Y = a.bcd is to multiply denominator of LHS to post decima l part of RHS

Rem = y * 0.625
= y * 625/1000
= y * 5/8
which is multiple of 5 and only option which is multiple of 5 in the options is 5.
So 5 is the answer
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pratiksingh023
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Re: M09-08 [#permalink] New post   23 May 2018, 23:23
Can i mark 5 as the answer choice considering that 0.625 will be a multiple of 5 only since it is ending with 5?
Thanks
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Re: M09-08 [#permalink] New post   24 May 2018, 01:21
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pratiksingh023 wrote:
Can i mark 5 as the answer choice considering that 0.625 will be a multiple of 5 only since it is ending with 5?
Thanks


No. If it were 2.15 instead of 2.625, then we'd get \(\frac{x}{y}=2.15=2\frac{3}{20}=2+\frac{3}{20}\), and in this case r would need to be a multiple of 3, not necessarily a multiple of 5.
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Re: M09-08 [#permalink] New post   09 Jul 2019, 15:01
This post by VeritasKarishma explains it perfectly.
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Re: M09-08 [#permalink] New post   22 Jul 2023, 03:18
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M09-08 [#permalink]
22 Jul 2023, 03:18
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