N = 2^j3^k, where j and k are positive integers. What is N?

Question

N = 2^j3^k , where j and k are positive integers. What is N?

(1) 2 is a divisor of N, but 4 is not.

(2) N is a divisor of 36, but not of 24.

DHRJ0032 · Answer

1) only possible values of j are 0 and 1 for the given condition. But j is a positive integer.so j=1 but k could be any positive integer..
NOT SUFFICIENT.

2)36=2²x3²
 24=3x2³
For a num to be a multiple of 24 it shud be a multiple of 2³ i.e 8. 
So with the given condition j could be 1 or 2 
But k could be anything from k>2
Again..
NOT SUFFIICIENT

on combining,
j=1 
and 
k could only be 2.

C is the answer

Posted from my mobile device

TestPrepUnlimited · Answer

Statement 1:

Since 4 is not a factor, we have  j < 2 . Since 2 is a factor, we have  j \geq 1 . Thus j = 1. We still need to know k so insufficient.

Statement 2:

The factors of 36 are 1*36=2*18=3*12=4*9=6*6. Among these 36, 18, and 9 are not divisors of 24. Insufficient.

Combined:

We know N has a multiple of 2 but not 4. Among 36, 18, and 9, only 18 satisfies this. Sufficient.

Ans: C

youcouldsailaway · Answer

1st condition: 2 is a divisor of N, but 4 is not.

This statement tells us that  j<2  because,  2^2 = 4  and 4 is not a factor of N. Since 2 is a factor of N, it follows that  j\leq{1} . Combining the first and second part, and noting that j is a positive number, we get that  j = 1 . However, since we no have information about k, st. 1 is not sufficient.

2nd condition: N is a divisor of 36, but not of 24.

36= 2^2 * 3^2
24 = 2^3 * 3^1

This statement tell us that k will need to be at least 2 or above in order for N to be a factor of 36. Another way to look at it: If  k=0 , then j can be any +ve number but we already know that j & k are +ve; thus  k = 0  is out. If  k = 1 , then j can be any value but to be a factor of 36 but not 24; we have to exclude 6 and 12 from possible values of N. Thus, this only leaves those factors which has k with values of 2 or above. But as this st. doesn't give us any information about j, st. 2 is not sufficient.

Combining the two statement,  j = 1, k\geq{2} , thus N can be  2 * 3^2  = 18, which is also a factor of 36.

Thus, the two statements combined are helpful but neither st. alone is sufficient. (C)

N = 2^j3^k, where j and k are positive integers. What is N?

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GMAT Data Sufficiency (DS) Questions

N = 2^j3^k, where j and k are positive integers. What is N?

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