multiples

[taneja.niks]

If K is a multiple of 11,is KL a multiple of 154?

1) L has all the same factors as 42.
2) K is divisible by 21

please give the answer and explanation for this

[albatross86]

K is a multiple of 11. So K = 11n, where n is a positive integer.

Is KL a multiple of 154? .... 154 = 11 * 14 = 11 * 7 * 2

Thus for an answer of yes we would need the product KL to contain all 3 primes - 11, 7 and 2.

STATEMENT 1:

L has all the same factors as 42. This is a flowery way of saying that L is a multiple of 42.

42 = 2 * 7 * 3

So L = 2 * 7 * 3 * m .... where m is a positive integer.


=> K * L = 11* n * 2* 7*3*m => we have all 3 primes 11, 7 and 2 in this --- SUFFICIENT


STATEMENT 2:

K is divisible by 21.

21 = 7 * 3

This means K must contain atleast one each of 7 and 3 in order that it is divisible by 21.

-> K = 11 * 7 * 3 * p ... where p is some positive integer.

But we do not know anything about L. So we cannot be sure if we are going to get that 2 we want to or not.

INSUFFICIENT

Pick A.