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If m and n are positive integers, what is the remainder when m is divi

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If m and n are positive integers, what is the remainder when m is divi  [#permalink]

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New post 01 Aug 2018, 05:08
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If \(m\) and \(n\) are positive integers, what is the remainder when \(m\) is divided by \(n\)?

(1) \(\frac{m}{n} = 12.64\)
(2) \(n < 50\)

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If m and n are positive integers, what is the remainder when m is divi  [#permalink]

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New post 01 Aug 2018, 05:44
Good question

statement 1 : m/n = 12.64 ,

we know m & n both are integers , therefore 12.64 * n = m (integer value)
if we convert 12.64 into fraction we get = 1264/100 = 316/25
so n can be any multiple of 25,
n= 25,50,75, 100.......
therefore m = 316 , 632, 948 , 1264.....
remainder = 16 , 32 , 48....... ---> Insufficient

Statement 2 : n<50
we cannot determine value of m ----> Insufficient


statement 1 & 2 together , we get n=25 and m= 316 ----> Sufficient

answer is C
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Re: If m and n are positive integers, what is the remainder when m is divi  [#permalink]

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New post 07 Sep 2018, 03:47
Same approach as GMATbuster92, just think that S(1) is easier to solve with smaller numbers.

S(1) we know that \(\frac{m}{n}\)=12.64

Which can be translated into \(\frac{m}{n}\)=\(\frac{64}{100}\) --> \(\frac{16}{25}\)

From this we know that m is a multiple of 16, and n is a multiple of 25... So the remainder can take several values depending on the value of n.

\(\frac{16}{25}\) R=16
\(\frac{32}{50}\) R=32
\(\frac{38}{75}\) R=38

INSUFFICIENT

S(2) Clearly insufficient, since it only provides information about n.
INSUFFICIENT

S(1)+S(2)= If n<50 then only case possible \(\frac{16}{25}\) R=16
Correct Answer: C
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Re: If m and n are positive integers, what is the remainder when m is divi  [#permalink]

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New post 07 Sep 2018, 04:03
1
If \(m\) and \(n\) are positive integers, what is the remainder when \(m\) is divided by \(n\)?

(1) \(\frac{m}{n} = 12.64\)
So m=12.64*n=(12+0.64)*n=12n+0.64n
So 0.64n is the remainder ...0.64n=\(\frac{64}{100}\)*n=\(\frac{16n}{25}\),
So n has to be a multiple of 25 and accordingly the remainder will also change..
If n=25, remainder=16*25/25=16
If n=25*2=50, remainder=16*2=32..
Insufficient

(2) \(n < 50\)
Nothing about m
Insufficient

Combined
n<50, so only one possibility is 25..
Remainder=16
Sufficient

C
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Re: If m and n are positive integers, what is the remainder when m is divi &nbs [#permalink] 07 Sep 2018, 04:03
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