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).
