Answer: A
Test:
1) n=3^(n-t)
Since n is a factor of t, we can express t as t=xn. x must be a positive integer (based on the original statement t and n are positive integers).
The value n-t will always be <= 0. This is because t will always be = or > n.
So, let's look at t>n. That means, n-t is a negative value (making the right side a fraction). Since n is a positive integer, it cannot equal a fraction.
Let's look at t=n. That means, n-t=0, making the right side of the equation = 1 (any number to the 0 power is = 1). So, can n (left side) = 1? Yes, when n=1 and t=1. So, this becomes the only solution.
In order for n=3^(n-t)to be true, n must = 1, and t must = 1. Is 1 a factor of 1? Yes.
2) t=3^n
This can be true when t=3, n=1. Yes, n is a factor.
Also, t=9, n=2. No, n is not a factor.
Stop. This solution fails.
So, the first statement allows us to determine that n is a factor of t.
Answer A
What is the official?
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
hard DS ,pls, help
Source: Beat The GMAT — Data Sufficiency |
IMO E
t = nK {K is any integer}
n = 3^(n-t), since n is an integer
for this n-t > = 0 this means n > = t
if n > t then n cant be a factor of t
if n = t then n is a factor of t .. 1 is insuff
2.) t = 3^n --> cant get anything out of this...insuff
1. + 2.
n = 3^(n-3n) --> n = 3^-2n
n is a positive integer -- therefore i cant get anything from 1. + 2.
--> E
t = nK {K is any integer}
n = 3^(n-t), since n is an integer
for this n-t > = 0 this means n > = t
if n > t then n cant be a factor of t
if n = t then n is a factor of t .. 1 is insuff
2.) t = 3^n --> cant get anything out of this...insuff
1. + 2.
n = 3^(n-3n) --> n = 3^-2n
n is a positive integer -- therefore i cant get anything from 1. + 2.
--> E
Ok..agreed 2 stmnts alone are not enuff.. but combining 2 stmnst you get sth like this
a,n=3^(n-t)
b,t=3^n
n = (3^n)/(3^t)
==> n = t/(3^t)
==> 3^t = t/n ... which is clearly an integer ..which in other words mean that n is factor of t .
Hence C IMO
a,n=3^(n-t)
b,t=3^n
n = (3^n)/(3^t)
==> n = t/(3^t)
==> 3^t = t/n ... which is clearly an integer ..which in other words mean that n is factor of t .
Hence C IMO
Statement 1 is also not sufficient ..take thsi examplBuckeyeT wrote:Answer: A
Test:
1) n=3^(n-t)
Since n is a factor of t, we can express t as t=xn. x must be a positive integer (based on the original statement t and n are positive integers).
The value n-t will always be <= 0. This is because t will always be = or > n.
So, let's look at t>n. That means, n-t is a negative value (making the right side a fraction). Since n is a positive integer, it cannot equal a fraction.
Let's look at t=n. That means, n-t=0, making the right side of the equation = 1 (any number to the 0 power is = 1). So, can n (left side) = 1? Yes, when n=1 and t=1. So, this becomes the only solution.
In order for n=3^(n-t)to be true, n must = 1, and t must = 1. Is 1 a factor of 1? Yes.
2) t=3^n
This can be true when t=3, n=1. Yes, n is a factor.
Also, t=9, n=2. No, n is not a factor.
Stop. This solution fails.
So, the first statement allows us to determine that n is a factor of t.
Answer A
What is the official?
e n = 3 and t = 2..
so put into ur 1st statement eqn, ==> 3 = 3^(3-2) = 3
But t = 2 is not divisible by n = 3..so not sufficient
thats the trick here 3^(n-t) = 3^n/3^trohan_vus wrote:Ok..agreed 2 stmnts alone are not enuff.. but combining 2 stmnst you get sth like this
a,n=3^(n-t)
b,t=3^n
n = (3^n)/(3^t)
==> n = t/(3^t)
==> 3^t = t/n ... which is clearly an integer ..which in other words mean that n is factor of t .
Hence C IMO
i wrote 3^(n-t) as 3^-2n and got confused...
great work rohan..
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
- GMAT Score:780
There's a problem with this question - where is it from? If we take both statements together, notice thatduongthang wrote:if n and t are positive intergers, is n a factor of t
a,n=3^(n-t)
b,t=3^n
n = 3^(n-t)
t = 3^n
and since n and t are positive integers, we must have that n < t (compare the powers on the right sides of the equations above; n-t must be smaller than n). But if n < t, then n-t < 0, and 3^(n-t) cannot be an integer -- the power would be negative. Since 3^(n-t) is equal to n, then n is not an integer, which contradicts what we're told in the question. So it's mathematically impossible for both statements to be true, and the question is nonsensical.
I think the question may have been mistranscribed. There's a GMATFocus question which reads:
If n and t are positive intergers, is n a factor of t
a,n=3^(n-2)
b,t=3^n
This is a question which can be answered; from Statement 1, we find that n = 3, but we have no information about t. From Statement 2, we have no way to determine if n is a factor of t. Taking the statements together, looking at the right side of each equation, n and t are both equal to powers of 3, but the exponent in the expression for n is smaller than that for t, so of course n is a factor of t (if we divide, t/n = 3^2 = 9).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
sorry friends
this question from 15test set and it is not writen clearly. so may be it is the question n=3^(n-2)
this question from 15test set and it is not writen clearly. so may be it is the question n=3^(n-2)
