If m and n are positive integers such that m > n, what is

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Dec 05, 2019 7:14 pm

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

Source: Manhattan Prep

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 05, 2019 7:14 pm

nitink: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Thu Oct 11, 2018 9:10 am

by nitink » Fri Dec 06, 2019 2:50 am

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.

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