vinviper1 wrote:Is the integer na multiple of 21?

1 n is a multipe of 14
2 n-12 is a multiple of 3



Answer is C


I am a bit confused as 1 means n is divisible by 2 AND 7. 21 is not divisible by 2. Am I missing something? Thanks much.

(1) n is a multple of 14. As you pointed out, we know for sure that n is a multiple of both 2 and 7. What we don't know is if n is also a multiple of 3.

For example, we could pick n=14. Is 14 a multiple of 21? NO

However, we could also pick n=42. Is 42 a multiple of 21? YES

We can get both a yes and a no answer, so (1) is insufficient.

(2) n-12 is a multiple of 3. Well, if n-12 is a multiple of 3, then n must also be a multiple of 3 (since 12 is a multiple of 3 all by itself). However, we don't know if n is also a multiple of 7.

So, we could pick n=15. Is 15 a muliple of 21? NO
We could also pick n=21. Is 21 a multiple of 21? YES

We can get both a yes and a no answer, so (2) is insufficient.

Combined, we know from (1) that n must be a multiple of 2 and 7. From (2) we know that n must be a multiple of 3.

Therefore, n must be a multiple of 2, 3 and 7. Since 2*3*7 = 42, n must be a multiple of 42. Since EVERY multiple of 42 is also a multiple of 21, we get a definite YES answer to the question.

Together the statements are sufficient, even though separately they're not: choose (c).

Thanks Stu!

I appreaciate all your help. Your complete explanations are quite informative!!

i am having some problems regarding the "multiple of" and "divisible by" i know that it is not the same thing,

for example:

is n a multiple of 24?

1) n is a multiple of 6
2) n is a multiple of 4

Answer is E

is n divisible by 24?

1) n is divisible by 6
2) n is divisible by 4

answer is C

now this may seem simple here but it becomes really confusing in the test, we need a clear and simple rule to memorise, any ideas ???

How can the OA be C

If you pick numbers which satisfy A and B condition, lets say

1. n =12 not div by 24
2. n = 24 div by 24
3. n = 36 not div by 24
4. n = 48 div by 24

so ans should be E

Sharbel wrote:
is n divisible by 24?

1) n is divisible by 6
2) n is divisible by 4

answer is C

now this may seem simple here but it becomes really confusing in the test, we need a clear and simple rule to memorise, any ideas ???