Around the World in 80 Questions (Day 10): If m and n are positive

Question

If m and n are positive integers, what is the reminder when m*n is divided by 49 ?

(1) m - n is divisible by 42.
(2) m*n is divisible by 35.

nivivacious · Answer

(1) m - n is divisible by 42. 
This statement alone doesn't provide enough information to determine the remainder when m*n is divided by 49. 
We don't know the values of m and n, so we can't determine their product.

(2) m*n is divisible by 35. This statement alone also doesn't provide enough information. Even though we know that m*n is divisible by 35, we don't know the exact value of m*n, so we can't determine the remainder when it's divided by 49.

However, if we combine both statements, we can determine the remainder. If m*n is divisible by 35 and m - n is divisible by 42, then m*n must be a multiple of the least common multiple of 35 and 42, which is 210. Since 210 is divisible by 49 with a remainder of 14, the remainder when m*n is divided by 49 is 14.
Therefore C.

Archit3110 · Answer

given that m& n are +ve integers
target what is remainder when m*n is divided by 49
#1
m - n is divisible by 42.
(43,1) ; ( 50-8) ; (55-13)
remainder values are different
insufficient
#2
m*n is divisible by 35.
m*n has to be a factor of 35
35,1 ; 35,2 ; 70,1 ; 105,1 ; 140,1

again remainder values are different
insufficient
from 1 &2
m,n has to be a factor of 35 such that least value is 
70,28 ; 105,63 ; 140,98
all these pair values are factors of 7 and the remainder here when m*n is divided by 7^2 will be 0
sufficient
  option C

missionmba2025 · Answer

(1) m - n is divisible by 42.

A) m = n = 42*49

what is the reminder when m*n is divided by 49 ? - The remainder = 0

B) m = 43, n = 1

what is the reminder when m*n is divided by 49 ? - The remainder = 43

Not sufficient.

(2) m*n is divisible by 35.

A) m = n = 35*49

what is the reminder when m*n is divided by 49 ? - The remainder = 0

B) m = 7, n = 5

what is the reminder when m*n is divided by 49 ? - The remainder = 35

Not sufficient.

Combined

m * n is divisible by 35, so either m or n has 7 as its prime factor
Combined with
m - n is divisible by 42, so both m and n must have 7 as its prime factor.

Hence, m * n will have two seven in its prime factorized form ; m*n will be divisible by 49.

Sufficient.

IMO C

PK1 · Answer

If m and n are positive integers, what is the reminder when m*n is divided by 49 ?

(1) m - n is divisible by 42.
(2) m*n is divisible by 35.

Case I: m-n is divisible by 42
so if m =43 and n=1 , m*n is not divisible by 49
however if m =49 and n =7, m-n becomes 42 and is divisible by 42
so we do not get unique answer from the same
Hence this option is not sufficient

Case II: m*n is divisible by 35
which means m can be 35 , n can 1....in this case mn is not divided by 49
or m can be 7 and n can be 5,....... in this case mn is not divided by 49
or m can be 35 and n can be 7.....in this case mn is divided by 49
so again we do not get unique answer from the same
Hence this option is not sufficient

Combining both,
m*n is divisible by 35 means it is divisible 7 and 5 so either one of the two would be a multiple of 5 and other a multiple of 7 or limiting condition m=35 and n=1 but that does not satifsy m-n=42
m-n=42 which means both differ by 42 units which is a multiple of 7
so combining m*n we get conclusive answer that mn is divisible by 49

C is the answer

Around the World in 80 Questions (Day 10): If m and n are positive

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