Is the integer n a multiple of 15 ? (1) n is a multiple of 20 (2) n

Question

Is the integer n a multiple of 15 ?

(1) n is a multiple of 20

(2) n + 6 is a multiple of 3

passionatevibes · Accepted Answer

Start with statement 1. It is not sufficient because for a number to be a multiple for 15, it should be divisible by both 3 and 5. Clearly, 20 does not have 3 as a factor. Hence, statement 1 is not sufficient.

Statement 2 says that n+6 is a multiple of three. If you break it down, it is basically saying that n is a multiple of 3. But that we don't know whether n is a multiple of 5 or not. Hence, this is not sufficient.

If you combine both 1 and 2, you can conclude that n has both 5 (from statement 1)and 3 (from statement 2) as factors. Hence, C is the answer.

fluke · Answer

Q: Is n a multiple of 15?

This can be solved by prime factors.

Question can be rephrased as; are at least both 3 and 5 prime factors of n

3 and 5 are factors of 15. If n also contains at least both 3 and 5 as factors, it must be divided by 15.

1. n is a multiple of 20.
Prime factors of 20 are 2*2*5

This tells us that n is definitely a multiple of 5. But, there is no 3 among its factors. We must have at least both 3 and 5 as factors for n to be a definite multiple of 15.

We also can't definitely tell that n is not a multiple of 15.

e.g. 
n=40- Multiple of 20. NOT a Multiple of 15.
n=60- Multiple of 20. Also a multiple of 15.

So, the prime factors 2*2*5 tell us that n is NOT definitely a multiple of 15. It may or may not be a multiple of 15. NOT SUFFICIENT.

2. (n+6) is a multiple of 3.

6 is a muliple of 3, so n must also be a multiple of 3.

if (a+b) is a muliple of x and b is a multiple of x, then "a" must be a multiple of x
if (a-b) is a muliple of x and b is a multiple of x, then "a" must be a multiple of x
conversely also true,
if "a" is a multiple of x and "b" is a multiple of x,
then (a+b) must be a multiple of x
also; (a-b) must be a mutiple of x

So, we know n is definitely a multiple of 3. i.e. 3 is a factor of n. But, n is not necessarily a multiple of 15.

For "n" to be a multiple of 15, it must have at least both 3 and 5 as factors.

e.g.

6- multiple of 3. Not a multiple of 15.
30- multiple of 3. Also a multiple of 15.
NOT SUFFICIENT.

Using both statements;
We know 5 and 3 are both factors of n. Thus, n must be a multiple of 15.

SUFFICIENT.

Ans: C

Bunuel · Answer

Is the integer n a mulltiple of 15 ?

(1) n is a multiple of 20 --> now, if  n=0  then the answer will be YES but if  n=20  then the answer will be NO. Not sufficient.

But from this statement we can derive that as  n  is a multiple of 20 then it's a multiple of 5.

2) n + 6 is a multiple of 3 --> again, if  n=0  then the answer will be YES but if  n=3  then the answer will be NO. Not sufficient.

But from this statement we can derive that  n  is a multiple of 3 ( n+6=3q  -->  n=3(q-2) , for some integer  q :).

(1)+(2)  n  is a multiple of both 5 and 3 thus it must be a multiple of 3*5=15. Sufficient.

Answer: C.

Wayxi · Answer

Thanks a lot guys. Really put it into perspective. I was a little confused with how to use the second statement but how fluke broke it down makes sense. I remember the property that mgmat gave. When a is a multiple of x and b is a mutiple of x. a + b will be a multiple of x.

GMATinsight · Answer

For n to be a multiple of 15, n must be a multiple of 3 and also a multiple of 5

Statement 1 : n is a multiple of 20 
This statement confirm that n is a multiple of 5 but doesn't confirm whether n is a multiple of 3 or not hence
NOT SUFFICIENT

Statement 2 : n+6 is a multiple of 3 
This statement confirm that n is a multiple of 3 but doesn't confirm whether n is a multiple of 5 or not hence
NOT SUFFICIENT

Combining the two statements  
n is a multiple of 3 and 5 both hence
SUFFICIENT

Answer: Option C

Franciscomgs · Answer

If n=40

Statement 1: true, because 40 is a multiple of 20
Statement 2: true, because 40 + 6 = 46, which is a multiple of 3
 However n is not a multiple of 15.

If n=60

Statement 1: true, because 60 is a multiple of 20
Statement 2: true, because 60 + 6 = 66, which is a multiple of 3
 In this case n is a multiple of 15.

So, I fail to understand why answer C is correct, when from the example above we can observe that the statements put together can yield different results for N which are and are not multiples of 15.
In my view E should be the correct choice.
Can someone please explain what is wrong in my reasoning?
Thanks in advance!

Bunuel · Answer

46 is not a multiple of 3.

AmritaSarkar89 · Answer

I was bit confused about the sign in statement 2. It can pass as division as well. 
Just wondering can we face such confusing signs on the GMAT

PituxaBR · Answer

My understaning is that when you combine (1) and (2) and do a LCM of it LCM(20,3) you will get 2*2*5 and 3 --> 2*2*5*3 = 60.

N will multiple of 15 since it is multiple of 60 or you can see that 60 prime factorization contains 3 and 5.

ScottTargetTestPrep · Answer

Question Stem Analysis:

We need to determine whether n is a multiple of 15. Notice that if n is a multiple of 3 and 5, then n is also a multiple of LCM(3, 5) = 15.

Statement One Alone:

\Rightarrow  n is a multiple of 20

Since n is a multiple of 20, n is a multiple of 5. However, without knowing whether n is also a multiple of 3, we cannot determine whether n is a multiple of 15. For instance, if n = 20, n is not a multiple of 15. If n = 60, n is a multiple of 15. Since there are more than one possible answers, statement one alone is not sufficient.

Eliminate answer choices A and D.

Statement Two Alone:

\Rightarrow  n + 6 is a multiple of 3

Since n + 6 is a multiple of 3, we can write n + 6 = 3k for some integer k. Then, we can write n = 3k - 6 = 3(k - 2). We see that n is a multiple of 3. However, without knowing whether n is also a multiple of 5, we cannot determine whether n is a multiple of 15. For instance, if n = 3, n is not a multiple of 15. If n = 15, n is a multiple of 15. Since there are more than one possible answers, statement two alone is not sufficient.

Eliminate answer choice B.

Statement One and Two Together:

From statement one, we know n is a multiple of 5. From statement two, we know n is a multiple of 3. Since n is a multiple of both 3 and 5, n is a multiple of 15. Statements one and two together are sufficient.

Answer: C

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Is the integer n a multiple of 15 ? (1) n is a multiple of 20 (2) n

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