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28 Jul 2023, 08:00
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C
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Difficulty:
85%
(hard)
Question Stats:
47% (02:10) correct
53%
(02:10)
wrong
based on 164
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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.
(1) m - n is divisible by 42.
(2) m*n is divisible by 35.
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28 Jul 2023, 08:06
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Bunuel
(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.
28 Jul 2023, 08:22
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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
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
Bunuel
