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

[sachin_yadav]

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

[clock60]

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

[MAAJ]

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)!!!

[manpsingh87]

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

[rohu27]

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

[sachin_yadav]

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