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M09-08
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16 Sep 2014, 00:39
16 Sep 2014, 00:39
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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
A. 2
B. 4
C. 5
D. 6
E. 9
Re M09-08
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16 Sep 2014, 00:39
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
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
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16 Dec 2014, 11:31
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
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
