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

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Senior Manager
Joined: 22 Feb 2018
Posts: 428
If m and n are positive integers, what is the remainder when m is divi  [#permalink]

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01 Aug 2018, 05:08
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55% (hard)

Question Stats:

53% (01:26) correct 47% (01:12) wrong based on 80 sessions

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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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Joined: 28 Jun 2018
Posts: 154
Location: India
Concentration: Finance, Marketing
Schools: CUHK '21 (II)
GMAT 1: 650 Q49 V30
GPA: 4
If m and n are positive integers, what is the remainder when m is divi  [#permalink]

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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

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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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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
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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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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) $$n < 50$$
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   [#permalink] 07 Sep 2018, 04:03
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