If m and n are positive integers such that m > n, what is the remainder when m^2 - n^2 is divided by 21?
(1) The remainder when (m + n) is divided by 7 is 1.
(2) The remainder when (m - n) is divided by 3 is 1.
OA E
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If m and n are positive integers such that m > n, what is
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m^2 - n^2 = (m+n) (m-n)
(m+n) (m-n) / 21 = ?
from 1, (m+n)= 7q +1, incomplete info since we dont have any other info about 3 (factor of 21 = 7*3). hence not sufficient.
from 2, (m-n) = 3p + 1 , incomplete info since we dont have any other info about 7 (factor of 21 = 7*3). hence not sufficient.
Combining 1 and 2
(m+n) (m-n) / 21
= (7q +1) (3p +1)
= 21qp + 7q + 3p + 1
When the above polynomial is divided by 21, 21qp gives a remainder of 0, but we no nothing about other terms.
hence we cant find the remainder.
Hence E.
(m+n) (m-n) / 21 = ?
from 1, (m+n)= 7q +1, incomplete info since we dont have any other info about 3 (factor of 21 = 7*3). hence not sufficient.
from 2, (m-n) = 3p + 1 , incomplete info since we dont have any other info about 7 (factor of 21 = 7*3). hence not sufficient.
Combining 1 and 2
(m+n) (m-n) / 21
= (7q +1) (3p +1)
= 21qp + 7q + 3p + 1
When the above polynomial is divided by 21, 21qp gives a remainder of 0, but we no nothing about other terms.
hence we cant find the remainder.
Hence E.
