positive integers - mulitple

[maria]

if a and b are positive integers, is 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 a factor of a.

Great thanks.

[punit.kaur.mba]

According to me, answer should be (B)

Explaination -

Any number (positive integer) can be expressed as a product of its prime factors alone.

Eg:- b= 24, a =12

b as product of primes = 2 x 2 x 2 x3

Prime factors of b are 2 & 3

Now a as product of primes

a= 2 x 2 x 3

Prime factors of a are 2 & 3

Stmt1:- Every prime factor of b is also a prime factor of a.

According to the above example every prime factor of b is a prime factor of a. but A is not multiple of b.Another case, if a was 48, Stmt1 is true, but a is a multiple of b.

Since Stmt1 does not give a definite answer, Stmt1 alone is insufficient to answer the question

choices narrowed to B,C,E

Stmt2:- Every factor of b is a factor of a
Eg:- b = 24 a =72

factors of b = 1,2,3,4,6,12,8,24
factors of a = 1,2,3,4,6,8,9,12,18,24,72

Every factor of b is a factor of a.

For any pair of a and b values satisfying Stmt2 will give the answer as a being a multiple of b, hence it gives a unique answer.

Stmt2 alone is sufficient and Stmt1 alone is not.

Ans is (B)

What is OA?

Someone correct me if I am wrong.

[rattanas]

The answer should be that all factors of b are all facors of a..but only the prime factors are not enough

[maria]

Dear punit.kaur.mba,

you are correct. OA is B.

It seems a long approach to get it. I am usually scared of problems related to integers and multiple like this. Can you pls show me how to get familiar?

Million thanks.

[punit.kaur.mba]

Hey Maria,

My explaination seems longer. But the concept is the same...

When problems like this come up, its always good to first go with the answer the problem suggests. For eg: try to take smaller exampels that satisfy what the question states


Then, instead of jumping to mark answer, Think critically and try to find a contradicting example (for instance the one where even though prime factors were same, a is not multiple of b).

that way you will get the right answer.

I am not sure how you attempted to solve this question. May be an instructors advice on how to sovle such questions could help you better ...

[netigen]

Ans is B

(B) every factor B includes B itself so it means B is a factor of A hence sufficient
(A) hold true for

a=21 (3 x 7)
b=63 (3 x 7 x 3)

or switch a and b

b=21 (3 x 7)
a=63 (3 x 7 x 3)


so insufficient