Last visit was: 24 Jul 2024, 12:39 It is currently 24 Jul 2024, 12:39
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.

# If n and t are positive integers, is n a factor of t ?

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 10 Oct 2005
Posts: 83
Own Kudos [?]: 494 [130]
Given Kudos: 0
Location: Hollywood
Math Expert
Joined: 02 Sep 2009
Posts: 94609
Own Kudos [?]: 643614 [17]
Given Kudos: 86737
Math Expert
Joined: 02 Sep 2009
Posts: 94609
Own Kudos [?]: 643614 [11]
Given Kudos: 86737
General Discussion
Manager
Joined: 22 Apr 2011
Posts: 103
Own Kudos [?]: 609 [0]
Given Kudos: 18
Concentration: Accounting
Q47  V28 GMAT 2: 570  Q40  V29
GPA: 3.44
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
hello Bunuel, How'd you figure it out in statement 1 that n=3. i do comprehend that n must be 3 but i cant figure it out by doing algebra.

GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11797 [4]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
2
Kudos
2
Bookmarks
Hi All,

This question can be solved with a combination of arithmetic and TESTing VALUES.

We're told that N and T are POSITIVE INTEGERS. We're asked if N is a factor of T. This is a YES/NO question.

Fact 1: N = 3^(N−2)

Since this Fact tells us NOTHING about T, it's clearly insufficient. We can find the value of N without too much trouble though since we already know that it's a positive integer. With a little "brute force", we can find that N = 3 is the solution.
Fact 1 is INSUFFICIENT

Fact 2: T = 3^N

IF....
N = 1
T = 3
1 IS a factor of 3 so the answer to the question is YES

IF....
N = 2
T = 9
2 is NOT a factor of 9 so the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
N = 3
T = 3^N = 3^3 = 27
3 IS a factor of 27 so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich
Manager
Joined: 07 Apr 2015
Posts: 127
Own Kudos [?]: 192 [0]
Given Kudos: 185
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t

However this does not help me in any way... Where am i going wrong?
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6031
Own Kudos [?]: 13826 [0]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
noTh1ng wrote:
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t

However this does not help me in any way... Where am i going wrong?

The highlighted steps are out of Sink

$$a^{(b^c)}$$ is NOT equal to $$a^b*a^c$$

Whereas, $$(a^b)^c$$ = $$a^b*a^c$$

i.e. $$3^{(3^{(n-2)})}$$ is NOT same as $$3^{3n} * 1/3^6$$
Manager
Joined: 07 Apr 2015
Posts: 127
Own Kudos [?]: 192 [0]
Given Kudos: 185
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
GMATinsight wrote:
noTh1ng wrote:
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t

However this does not help me in any way... Where am i going wrong?

The highlighted steps are out of Sink

$$a^{(b^c)}$$ is NOT equal to $$a^b*a^c$$

Whereas, $$(a^b)^c$$ = $$a^b*a^c$$

i.e. $$3^{(3^{(n-2)})}$$ is NOT same as $$3^{3n} * 1/3^6$$

Thank you, so the only way would be to plug in values for n for $$3^{(3^{(n-2)})}$$ ?

Or is there any way to rewrite this?
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6031
Own Kudos [?]: 13826 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
1
Kudos
noTh1ng wrote:
GMATinsight wrote:
noTh1ng wrote:
Quick Algebra question for Statement 1&2 combined:

If I plug in n = 3^(n-2) into t = 3^n I get:
n = 3^(3^(n-2))

when I rewrite it I eventually come to 3^3n * 1/3^6 = t

However this does not help me in any way... Where am i going wrong?

The highlighted steps are out of Sink

$$a^{(b^c)}$$ is NOT equal to $$a^b*a^c$$

Whereas, $$(a^b)^c$$ = $$a^b*a^c$$

i.e. $$3^{(3^{(n-2)})}$$ is NOT same as $$3^{3n} * 1/3^6$$

Thank you, so the only way would be to plug in values for n for $$3^{(3^{(n-2)})}$$ ?

Or is there any way to rewrite this?

There are three ways

1) Plug-in the Values from Options
2) Take Logarithm on both sides and then solve further
3) Change the method and follow the methods given in other explanations

Third seems the Best to me

I hope it Helps!
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19191
Own Kudos [?]: 22716 [7]
Given Kudos: 286
Location: United States (CA)
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
6
Kudos
1
Bookmarks
TOUGH GUY wrote:
If n and t are positive integers, is n a factor of t ?

(1) n = 3^(n-2)
(2) t = 3^n

We need to determine whether t/n = integer

Statement One Alone:

n = 3^(n - 2)

Since we do not have any information regarding t, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

t = 3^n

We can substitute some numbers for n. For example, if n = 1, then t = 3^1 = 3 and 1 is a factor of 3. However, if n = 2, then t = 3^2 = 9 but 2 is not a factor of 9. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we can substitute 3^(n - 2) for n and 3^n for t in our question: t/n = integer ?

(3^n)/3^(n - 2) = integer ?

Since we are dividing similar bases, we can subtract the exponents and keep the base. Then we have:

3^(n - n + 2) = integer ?

3^2 = integer ?

9 = integer ?

Since 9 IS an integer. We have answered “yes” to the question.

Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [0]
Given Kudos: 432
Location: United States
If n and t are positive integers, is n a factor of t ? [#permalink]
If n and t are positive integers, is n a factor of t ?

(1) $$n = 3^{n-2}$$

By plugging in numbers we see that only n = 3 works. However, we have no information on t. Insufficient.

(2) $$t = 3^n$$
$$t = 3^n$$
$$3 = 3^1$$-- Yes
$$9 = 3^2$$-- No
$$27 = 3^3$$ -- Yes

We can't determine this without knowing what n is. Insufficient.

(1&2) This tells us that 27 = 3^3. Therefore, n is a factor of t. Sufficient.

Intern
Joined: 01 Mar 2020
Posts: 26
Own Kudos [?]: 4 [0]
Given Kudos: 65
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
Hi Bunuel chetan2u VeritasKarishma GMATBusters nick1816

Is the following solution correct?

(1) and (2) independently are not sufficient.

Combining,
For n to be a factor of t, t/n should give us an integer.

Given, n = 3^n-2 = 3^n/3^2 and t = 3^n

On dividing, t/n we get 3^2, which is an integer. Hence n is a factor of t. (C) sufficient.

RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11485
Own Kudos [?]: 34583 [1]
Given Kudos: 325
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
1
Kudos
Laksh47 wrote:
Hi Bunuel chetan2u VeritasKarishma GMATBusters nick1816

Is the following solution correct?

(1) and (2) independently are not sufficient.

Combining,
For n to be a factor of t, t/n should give us an integer.

Given, n = 3^n-2 = 3^n/3^2 and t = 3^n

On dividing, t/n we get 3^2, which is an integer. Hence n is a factor of t. (C) sufficient.

Yes, you are absolutely correct.
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5312
Own Kudos [?]: 4250 [0]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
Asked: If n and t are positive integers, is n a factor of t ?

(1) $$n = 3^{n-2}$$
n = 3
NOT SUFFICIENT

(2) $$t = 3^n$$
There are multiple solutions for n & t
NOT SUFFICIENT

(1) + (2)
(1) $$n = 3^{n-2}$$
(2) $$t = 3^n$$
n = 3
t = 9
n=3 is a factor of t=9
SUFFICIENT

IMO C
Non-Human User
Joined: 09 Sep 2013
Posts: 34074
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If n and t are positive integers, is n a factor of t ? [#permalink]
Moderator:
Math Expert
94609 posts