Is the sum of integers a and b divisible by 7 ?

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sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Wed Apr 06, 2011 11:02 am

Hi All,

Please help in following question on divisibility :-

Is the sum of integers a and b divisible by 7 ?

(1). a is not divisible by 7
(2). a - b is divisible by 7

Answer is C

Thanks & Regards
Sachin

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Wed Apr 06, 2011 12:44 pm

hi sachin yadav
i`ll try
is a+b-divisible by 7
(1)no info about b, insuff
(2)also insuff
a=9,b=2, 9-2=7-divisible by 7, but 9+2=11 is not
a=14,b=7, 14-7=7-divisible by 7, 14+7=21 aslo divisible by 7
together
a-b=7k where k is +ve integer
a=7k+b. and a is not divisible by 7, but 7k is divisible by 7, so it comes that b is not divisible by 7,
a+b=7k+b+b=7k+2b, this is divisible by 7 only if b is divisible by 7, but it is not.
so a+b is not divisible by 7
C looks right

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Wed Apr 06, 2011 6:20 pm

Is the sum of integers a and b divisible by 7?
The +/- of 2 multiples of n MUST be divisible by n (n = 7 in this case)
A multiple of n a +/- a non-multiple of n is not divisible by n
If you add two non-multiples of n, the result could be either a multiple of n or a non-multiple of n

(1) a is not divisible by 7
Does not tell us anything about b
Insufficient

(2) a - b is divisible by 7
They are both multiples of 7 -> (14 - 7)/7 = Integer
Or they are both non-multiples of 7 -> (8 - 1)/7 = Integer
The scenario where one is multiple and the other isn't, is not possible

Combining (1) and (2)
The scenario that applies is "a" and "b" are both non-multiples of 7, that when subtracted equals a multiple of 7.

Possible values of a and b:

8 / 1
9 / 2
10 / 3
11 / 4
12 / 5
13 / 6
etc...

If we sum either of these pairs the answer the result won't be divisible by 7. So pick (C)!!!

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Wed Apr 06, 2011 8:39 pm

sachin_yadav wrote:Hi All,

Please help in following question on divisibility :-

Is the sum of integers a and b divisible by 7 ?

(1). a is not divisible by 7
(2). a - b is divisible by 7

Answer is C

Thanks & Regards
Sachin

1) a is not divisible by 7, as here no information is given about b therefore its not sufficient to answer the question.!!
2) as a-b is divisible by 7 therefore a-b=7k; a=b+7k;, this is also not sufficient for example consider the following cases
case 1) a=8 b=1, a-b=7 a+b=9 not divisible by 7.
case 2) a=14 b=7, a-b=7 a+b=21 divisible by 7.

now combine 1 and 2
a =b+7k, as a is not divisible by 7 from 1, therefore b is also not divisible by 7 because if b becomes multiple of 7, then we have b=7m, now putting it in a=b+7k we have, a=7m+7k, a=7(m+k) i.e. a becomes multiple of 7 which violates condition 1 hence b is not a multiple of 7.

therefore a+b = b+7k+b, 2b+7k which is not divisible by 7 as b is not divisible by 7.

hence C

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rohu27: Legendary Member; Posts: 586; Joined: Tue Jan 19, 2010 4:38 amFollowed by: 5 members; Thanked: 31 times; GMAT Score:730

by rohu27 » Wed Apr 06, 2011 10:55 pm

The +/- of 2 multiples of n MUST be divisible by n (n = 7 in this case)
A multiple of n a +/- a non-multiple of n is not divisible by n
If you add two non-multiples of n, the result could be either a multiple of n or a non-multiple of n

Useful takeaway, thanks

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sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Thu Apr 07, 2011 6:47 pm

now combine 1 and 2
a =b+7k, as a is not divisible by 7 from 1, therefore b is also not divisible by 7 because if b becomes multiple of 7, then we have b=7m, now putting it in a=b+7k we have, a=7m+7k, a=7(m+k) i.e. a becomes multiple of 7 which violates condition 1 hence b is not a multiple of 7.

therefore a+b = b+7k+b, 2b+7k which is not divisible by 7 as b is not divisible by 7.

Thanks guys for helping.

Regards
Sachin

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