hard DS ,pls, help

[tanviet]

if n and t are positive intergers, is n a factor of t

a,n=3^(n-t)
b,t=3^n

[BuckeyeT]

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?

[2010gmat]

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

[rohan_vus]

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

[rohan_vus]

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?

Statement 1 is also not sufficient ..take thsi exampl
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

[BuckeyeT]

Thanks! It appears I made the mistake of letting the "ask" creep in as an assumption.

[2010gmat]

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

thats the trick here 3^(n-t) = 3^n/3^t

i wrote 3^(n-t) as 3^-2n and got confused...

great work rohan..

[Ian Stewart]

if n and t are positive intergers, is n a factor of t

a,n=3^(n-t)
b,t=3^n

There's a problem with this question - where is it from? If we take both statements together, notice that

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).

[tanviet]

sorry friends

this question from 15test set and it is not writen clearly. so may be it is the question n=3^(n-2)