If 'a' and 'b' are positive integers, ia 'a' a multiple of

Question

If 'a' and 'b' are positive integers, ia 'a' a multiple of 'b'?
1) Every prime factor of 'b' is also a prime factor of 'a'
2) Every factor of 'b' is also factor of 'a'

Try it please

LM · Answer

is 'a' a multiple of 'b'? is same as asking is a divisible by b

is a/b ?

For a to be divisible by b, every factor of "b" should also be factor of "a".

Take for example; a=26 = 1*2*13

b = 13 = 1*13

Every factor of b is also factor of a

Note also the every prime factor of b is prime factor of a.

Thus each statement on it's own is sufficient.

therfore the answer is "D".

Please tell the OA?

Himalayan · Answer

I go with D though I am little confused with factors and prime factors.

1: if b = 15, a has to be a multiple of 15 to have every prime factors of b also to be prime factors of a. suppose b= 10, a = 30. b's prime factors (2 and 5) are also prime factors (2, 3 and 5) of a (30).

2: it is more clear that if every factor of b is factors of a, then a is a multiple of b. if b = 10, a = 20 or 30 or 40 or 50 so on.

So D.

Dek · Answer

B.

S1. If b= 12
a=6

prime factors of b=12 = 3,2,2
prime factorsof a=6=3,2

As I see it, all prime factors of b are prime factors of a. But it doesnt need to be divisible.

S2. Same reasoning as above

Caas · Answer

I will post the OA later as I should get OE in a while by mail.

I have one question regarding condition 2.
Let's say a=12 and b=8
12 is not a multiple of 8. Factors of 8: 2,4
2 and 4 are also factors of 12.
If we imply this logic then (2) is not suff. BUT should we consider also 8 a factor of 8????

Caas · Answer

Dek, it seems you are right.....

Andr359 · Answer

At first I chose D, but actually A is insuff, as b´s factors could be to a higher power than a´s (think b=2^7*3^5 vs a=2^3*3^4).

If 'a' and 'b' are positive integers, ia 'a' a multiple of

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