Is the integer n a multiple of 15?

Question

(1) n is a multiple of 20
(2) n+6 is a multiple of 3.

gurpreetsingh · Answer

Statement 1: if n = 40 then answer is no, if n = 60 , answer is yes.
Thus not sufficient.

Statement 2: n+6 is a multiple of 3 => n + 6 = 3m => n = 3m -6

=> n = 3( m - 2) , now if 7 = 3, its true , if m = 4 not true.

thus not sufficient.

If you combine both , n is multiple of both 3 and 5(as multiple of 20)
=> n is multiple of 15.

Thus C

vishu1414 · Answer

I have one doubt for this question -Please help me to understand

1.n is a multiple of 20 ...I understand its not Sufficient

2.n+6 is a multiple of 3

considering n a multiple of 15 ,all possible multiples of 15 and +6 is always divisible by 3 ..So it should be sufficient ? 
Not sure why OA- C ?

Bunuel · Answer

It should be the other way around: any multiple of 15 plus 6 is a multiple of 3, but it's possible  n+6  to be a multiple of 3 so that  n  not to be a multiple of 15. Consider  n=3 .

Is the integer n a multiple of 15?

(1) n is a multiple of 20. If  n=20 , then the answer is NO but if  n=60 , then the answer is YES. Not sufficient. 
 From this statement though notice that  n  must be a multiple of 5.

(2) n+6 is a multiple of 3. If  n=3 , then the answer is NO but if  n=15 , then the answer is YES. Not sufficient. 
 From this statement though notice that  n  must be a multiple of 3, since  n+6=3q  -->  n=3(q-2) .

(1)+(2) From above we have that  n  is a multiple of both 5 and 3, thus it must be a multiple of 5*3=15. Sufficient.

Answer: C.

Hope it's clear.

ziko · Answer

1 statement tels us that there are at least 2*2*5 as prime factors in n, but we are not sure that 3*5 are among the prime factors - so insufficient.
2 statement indicates that n is a multiple of 3 so it could be 0, 3, 15 ... - not sufficient
1+2 statements, here we see that n is a number which has 2*2*5 and 3 in its primes, so it must be a multiple of 15!

nvijayprasanna · Answer

For a n to be multiple of 15, it has to be divisible its prime factors 3 and 5.

Statement 1 - n is multiple of 20 - divisible by prime factors 2 and 5. Not know about 3. Hence not sufficient. 
Statement 2 - n+6 multiple of 3 - meaning n is divisible by 3. Not know about 5. Hence not sufficient.

Combing both. n is divisible by 2, 3, 5. Hence n will be multiple of 15.

GSBae · Answer

The question asks whether n is a multiple of 15.

1)  n is a multiple of 20.  Clearly insufficient. However, notice that this means that 5,2,2 are prime factors of n. Thus, for n to be a multiple of 15, it also has to be a multiple of 3, to multiply with the 5 to get 15. We're looking to see if n is a multiple of 3.

2)  n+6 is a multiple of 3.   Notice this only says that n is a multiple of 3; if n+6 is a multiple of 3, then n+3 and n are also multiples of 3. On its own, it's insufficient, but it's precisely the information we were looking for from number 1.

Together, we have the information we need. Answer: C

anairamitch1804 · Answer

"Is the integer n a multiple of 15?" is really asking "Does n have both 3 and 5 as factors?" or alternately "Is n a multiple of both 3 and 5?"

Statement (1) tells you that n is a multiple of 20. You want to know if n has 3 and 5 as factors. Well, the 5 is taken care of, because 5 is a factor of 20. But what about the 3? It's not clear.

You can also illustrate this by picking numbers that fit the condition of St (1). Examples would be n = 20, 40, 60, 80, etc 
All of those have 5 as a factor, but not all of them have 3 as a factor. INSUFFICIENT.

Statement (2) says n+6 is a multiple of 3. The tricky thing here is to realize that 6 is a multiple of 3, and thus if n+6 is a multiple of 3, n itself must also be a multiple of 3.

Again, you can test numbers to verify this. n could equal 0, 3, 6, 9, etc. All those values of n are already multiples of 3.

So St (2) really just says "n is a multiple of 3."

Unfortunately, we don't know about the 5, so we can't say if n is a multiple of 15. INSUFFICIENT.

Together, (1) tells us n has 5 as a factor and (2) tells us n has 3 as a factor. Therefore, since n has both 5 and 3 as factors, it must also have 3*5 = 15 as a factor. SUFFICIENT

Ans: C

anairamitch1804 · Answer

"Is the integer n a multiple of 15?" is really asking "Does n have both 3 and 5 as factors?" or alternately "Is n a multiple of both 3 and 5?"

Statement (1) tells you that n is a multiple of 20. You want to know if n has 3 and 5 as factors. Well, the 5 is taken care of, because 5 is a factor of 20. But what about the 3? It's not clear.

You can also illustrate this by picking numbers that fit the condition of St (1). Examples would be n = 20, 40, 60, 80, etc 
All of those have 5 as a factor, but not all of them have 3 as a factor. INSUFFICIENT.

Statement (2) says n+6 is a multiple of 3. The tricky thing here is to realize that 6 is a multiple of 3, and thus if n+6 is a multiple of 3, n itself must also be a multiple of 3.

Again, you can test numbers to verify this. n could equal 0, 3, 6, 9, etc. All those values of n are already multiples of 3.

So St (2) really just says "n is a multiple of 3."

Unfortunately, we don't know about the 5, so we can't say if n is a multiple of 15. INSUFFICIENT.

Together, (1) tells us n has 5 as a factor and (2) tells us n has 3 as a factor. Therefore, since n has both 5 and 3 as factors, it must also have 3*5 = 15 as a factor. SUFFICIENT

Ans: C

BLTN · Answer

Does N is multiple of 3*5 = 15 ?

From 1st statement:
  \frac{n}{20}  =  \frac{n}{4*5} 
Hence N must be multiple of 5, but we need additional factor 3 as well.

From 2nd statement:
  \frac{n+6}{3}  =  \frac{n}{3}  +  \frac{6}{3} 
Thus N is multiple of 3 yet we need additional factor 5 as well.

1st + 2nd statements give us necessitated factors 3 & 5.

Finn_ · Answer

Bunuel  - I'm confused as to why the 2nd prompt is guaranteed to give us a factor of 3.

Given: n+6 = 3 * some integer

What if n + 6 = 6? Wouldn't that give us n=0 and thus we're missing the factor of 3 we need to answer the question?

Bunuel · Answer

ZERO:

1. Zero is an  INTEGER .

2. Zero is an  EVEN  integer. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. Zero is  neither positive nor negative  (the only one of this kind).

4. Zero is  divisible by EVERY integer except 0 itself  ( \frac{x}{0} = 0 , so 0 is a divisible by every number, x).

5. Zero is a  multiple of EVERY integer  ( x*0 = 0 , so 0 is a multiple of any number, x).

6. Zero is  NOT a prime number  (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed:  anything/0 is undefined .

8. Any non-zero number  to the power of 0 equals 1  ( x^0 = 1 )

9.  0^0  case is  NOT tested on the GMAT .

10. If the exponent n is positive (n > 0),  0^n = 0 .

11. If the exponent n is negative (n < 0),  0^n  is undefined, because  0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0} , which is undefined.  You CANNOT take 0 to the negative power .

12.  0! = 1! = 1 .

Finn_ · Answer

I completely overlooked that it would still work anyway. Thank you for the help! Seems so obvious now.

Broc · Answer

My favorite explanation, thank you for breaking it down in addition to solving it. When you rephrased it as "what they're really asking you..." is when it clicked for me. Thank you!

Is the integer n a multiple of 15?

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