Last visit was: 15 Sep 2024, 20:45 It is currently 15 Sep 2024, 20:45
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Is the integer n a multiple of 15?

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 27 Feb 2010
Posts: 54
Own Kudos [?]: 2220 [32]
Given Kudos: 14
Location: Denver
SVP
Joined: 12 Oct 2009
Status:<strong>Nothing comes easy: neither do I want.</strong>
Posts: 2279
Own Kudos [?]: 3694 [6]
Given Kudos: 235
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
General Discussion
Manager
Joined: 27 Feb 2010
Posts: 54
Own Kudos [?]: 2220 [0]
Given Kudos: 14
Location: Denver
SVP
Joined: 12 Oct 2009
Status:<strong>Nothing comes easy: neither do I want.</strong>
Posts: 2279
Own Kudos [?]: 3694 [0]
Given Kudos: 235
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: Is the integer n a multiple of 15? [#permalink]
zz0vlb
Gurpreetsingh Thanks. but n + 6 = 3m => n = 3m +6 should be n= 3m-6 => 3(m-2)

yes right, that's typo error. I have updated my post.
Intern
Joined: 05 Jan 2011
Posts: 45
Own Kudos [?]: 704 [0]
Given Kudos: 7
Re: Is the integer n a multiple of 15? (1) n is a multiple of 20 [#permalink]

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 ?
Math Expert
Joined: 02 Sep 2009
Posts: 95518
Own Kudos [?]: 658974 [3]
Given Kudos: 87262
Re: Is the integer n a multiple of 15? (1) n is a multiple of 20 [#permalink]
2
Kudos
1
Bookmarks
vishu1414

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 ?

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.

Hope it's clear.
Manager
Joined: 28 Feb 2012
Posts: 92
Own Kudos [?]: 190 [1]
Given Kudos: 17
GPA: 3.9
WE:Marketing (Other)
Re: Is the integer n a multiple of 15? [#permalink]
1
Bookmarks
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!
Intern
Joined: 17 Apr 2012
Posts: 12
Own Kudos [?]: 44 [0]
Given Kudos: 5
Location: United States
WE:Information Technology (Computer Software)
Re: Is the integer n a multiple of 15? [#permalink]
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.
Manager
Joined: 23 May 2013
Posts: 169
Own Kudos [?]: 412 [0]
Given Kudos: 42
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5
Is the integer n a multiple of 15? [#permalink]
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
Director
Joined: 26 Oct 2016
Posts: 506
Own Kudos [?]: 3424 [0]
Given Kudos: 877
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE:Education (Education)
Re: Is the integer n a multiple of 15? [#permalink]
"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
Director
Joined: 26 Oct 2016
Posts: 506
Own Kudos [?]: 3424 [1]
Given Kudos: 877
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE:Education (Education)
Re: Is the integer n a multiple of 15? [#permalink]
1
Kudos
"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
Senior Manager
Joined: 25 Aug 2020
Posts: 250
Own Kudos [?]: 163 [0]
Given Kudos: 216
Is the integer n a multiple of 15? [#permalink]
zz0vlb
Is the integer n a multiple of 15?

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

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.
Intern
Joined: 03 Sep 2023
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 1
Re: Is the integer n a multiple of 15? [#permalink]
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?
Math Expert
Joined: 02 Sep 2009
Posts: 95518
Own Kudos [?]: 658974 [1]
Given Kudos: 87262
Re: Is the integer n a multiple of 15? [#permalink]
1
Kudos
Finn_
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?

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. $$0! = 1! = 1$$.
Intern
Joined: 03 Sep 2023
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 1
Re: Is the integer n a multiple of 15? [#permalink]
Bunuel
Finn_
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?

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. $$0! = 1! = 1$$.

I completely overlooked that it would still work anyway. Thank you for the help! Seems so obvious now.
Re: Is the integer n a multiple of 15? [#permalink]
Moderator:
Math Expert
95518 posts