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

Question

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

chetan2u · Accepted Answer

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= \frac{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

GMATbuster92 · Answer

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

T1101 · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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