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DS r+s

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DS r+s

by harsh.champ » Wed Feb 17, 2010 5:42 am
If r and s are integers, is r + s divisible by 3?
(1) s is divisible by 3.
(2) r is divisible by 3.
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by Osirus@VeritasPrep » Wed Feb 17, 2010 7:12 am
This is a number properties problem.

(1) insufficient: When an integer is divisible by a number then adding that number to an integer that isn't divisible by that number can result in a number divisible by N or a number not divisible by N (chapter 1 Manhattan GMAT Number Properties)

(2) insufficient: we don't know anything about s

(1) and (2) sufficient: When you add two numbers that are divisible by N, then the result is a number that is also divisible by N. Choose C
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by shashank.ism » Wed Feb 17, 2010 7:47 am
harsh.champ wrote:If r and s are integers, is r + s divisible by 3?
(1) s is divisible by 3.
(2) r is divisible by 3.
St. 1: s=3k but we don't know about r
St. 2: r=3p but we don't know about s
combined: r+s = 3(k+p)/3 = k+p divisible[spoiler] Ans C
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by harsh.champ » Thu Feb 18, 2010 12:53 am
The OA is C.
Important Note:-In case of 2 no.s being divisible by some no. say N,their addition,subtraction and multiplication by the no. N is also possible.Only in case of division ,we cannot surely say whether the no. will be divisible by N.

Suppose we take 6 and 9.Both are divisible by 3.
1)Addition:-6+9 = 15 divisible by 3
2)Subtraction:- 6 - 9 = -3 divisible by 3
3)Multiplication:- 6 x 9 = 54 divisible by 3
4)Division:- 9/6 = 1.5 not divisible by 3

I hope the above example makes it clear. :)
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