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If a, b and c are positive integers and c is odd, are both a and b div

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If a, b and c are positive integers and c is odd, are both a and b div [#permalink]

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New post 02 Sep 2014, 01:46
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If a, b and c are positive integers and c is odd, are both a and b divisible by c ?

(1) a + b is divisible by c.
(2) a - b is divisible by c.
[Reveal] Spoiler: OA

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Re: If a, b and c are positive integers and c is odd, are both a and b div [#permalink]

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If a, b and c are positive integers and c is odd, are both a and b divisible by c ?

(1) a + b is divisible by c. If a = b = c = 1, then the answer is YES but if a = 1, b = 2 and c = 3, then the answer is NO. Not sufficient.

(2) a - b is divisible by c. If a = b = c = 1, then the answer is YES but if a = b = 1, and c = 3, then the answer is NO. Not sufficient.

(1)+(2) From (1) a + b = cx and from (2) a - b = cy. Sum these two: 2a = c(x + y). This means that either c is a factor of a, or c is an odd factor of 2, so 1 (remember that we are told that c is odd). So, in either case a is divisible by c. Now, if a is divisible by c and a + b is divisible by c, then b must also be divisible by c. Sufficient.

Answer: C.
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Re: If a, b and c are positive integers and c is odd, are both a and b div [#permalink]

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New post 21 Oct 2017, 13:17
Bunuel wrote:
If a, b and c are positive integers and c is odd, are both a and b divisible by c ?

(1) a + b is divisible by c. If a = b = c = 1, then the answer is YES but if a = 1, b = 2 and c = 3, then the answer is NO. Not sufficient.

(2) a - b is divisible by c. If a = b = c = 1, then the answer is YES but if a = b = 1, and c = 3, then the answer is NO. Not sufficient.

(1)+(2) From (1) a + b = cx and from (2) a - b = cy. Sum these two: 2a = c(x + y). This means that either c is a factor of a, or c is an odd factor of 2, so 1 (remember that we are told that c is odd). So, in either case a is divisible by c. Now, if a is divisible by c and a + b is divisible by c, then b must also be divisible by c. Sufficient.

Answer: C.



Can you please highlight more about it? How 'c is an odd factor of 2'?

It is really unclear

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Re: If a, b and c are positive integers and c is odd, are both a and b div [#permalink]

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New post 01 Nov 2017, 01:23
2a = c(x + y)------------ Eq-1
and we know that c is an +ve odd integer .
c can be either 1 or any odd integer > 1.

if c=1 then obviously c divides both a and b as 1 is a factor of every integer
and if c is odd integer > 1. then acc. to eq- 1
2a = c(x + y)
c either is a factor of 2 or a
c must divide a as 2 isn't divisible by any odd integer>1
------------------------------------------
And if c divides a and a+b this implies that b is also an multiple of a .Hence in both cases i.e c=1 and c is odd integer > 1
c divides both A and B

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Re: If a, b and c are positive integers and c is odd, are both a and b div   [#permalink] 01 Nov 2017, 01:23
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