common divisor

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gmataug08: Master | Next Rank: 500 Posts; Posts: 105; Joined: Sat May 17, 2008 8:12 pm; Thanked: 6 times

by gmataug08 » Fri Nov 28, 2008 9:18 am

Two different numbers when divided by the same divisor left remainders of 11 and 21 respectively. When the numbers' sum was divided by the same divisor, the remainder was 4. What was the divisor?

a)36
b)28
c)12
d) 9
e) none

OA : b

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Source: Beat The GMAT — Problem Solving | Fri Nov 28, 2008 9:18 am

austin: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Oct 23, 2008 9:12 amFollowed by: 1 member; Location: India; Thanked: 9 times

by austin » Fri Nov 28, 2008 9:33 am

When two different numbers (x,y) are divided by a number (d) and the remainders are r1 and r2, then when (x+y) is divided by d, the remainder is r1+r2.

If r1+r2 > d, resulting remainder r = r1 + r2 -d.

In this case, sum of remainders = 11+ 21 = 32.

When the numbers' sum was divided by the same divisor, the remainder was 4.

Since the remainder is 4, the number should be 32 - 4 = 28

eg. 5/12 - remainder 5; 8/12 - remainder 8; (5+8)/12 - remainder 13

r1+r2 > d (12). Therefore, resulting remainder = 13 -12 = 1

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