A number is called “terminating in base N” if that number can be expre

Question

A number is called “terminating in base N” if that number can be expressed as A/N^B for some integers A and B. What is the smallest positive integer N for which 5/24 is terminating in base N?

A. 1
B. 2
C. 6
D. 8
E. 24

Diwakar003 · Answer

A/N^B=5/24

N^B=(24 * A)/5

24=2^3*3

Now since R.H.S has 3 and 2 L.H.S must also have a 3 and 2. Plugging lowest such no from the options(6) we get;

6^B = (2^3 * 3) * A / 5

Now A can be 3^2 * 5 (Choosing in such a way to make RHS an integral power of LHS)

(3*2)^B = (2^3 * 3) * (3^2 * 5) / 5

(3*2)^B = 3^3 * 2^3 = (3*2)^3

Hence option C.

Cheers!

JeffTargetTestPrep · Answer

To solve this problem, we need to first find the smallest integer k such that 24k is a power of N.

Since 24 = 2^3 x 3, k must be 3^2 so that 24k = (2^3 x 3) x (3^2) = 2^3 x 3^3 = 6^3.

Thus we see that N = 6. (Note: 5/24 = (5 x 3^2)/(24 x 3^2) = 45/6^3 which is in A/N^B format.)

Answer: C

BrentGMATPrepNow · Answer

We must find a fraction that's EQUIVALENT to 5/24 so that the EQUIVALENT fraction can be written in the form A/(N^B)

24 = (2)(2)(2)(3)
So, the denominator of the EQUIVALENT fraction must have at least three 2's
Notice that if we take 24 = (2)(2)(2)(3) and multiply both sides by  9 , we get: 24( 9 ) = (2)(2)(2)(3)( 9 )
Rewrite as: 216 = (2)(2)(2)(3)( 3 )( 3 )
Rewrite as: 216 =    
Rewrite as: 216 =  ³
Rewrite as: 216 = 6³

This means we can take: 5/24
And multiply top and bottom by  9  to get the EQUIVALENT fraction: 45/216
Now rewrite the denominator as follows: 45/6³
In other words, 5/24 = 45/216 = 45/6³
Since 45/ 6 ³ is written in the form A/( N ^B), we can see that  N = 6

Answer: C

Cheers, 
Brent

Shobhit7 · Answer

Denominator 24 must be manipulated to N^B format such that N has minimum value.
Factorizing 24 = 2^3 * 3^1

For 24^1: N= 24, B= 1
For 2^4*3^2= 144: N= 12, B=2
For 2^3*3^3= 6^3: N=6, B=3
For 2^4*3^4= 6^4: N=6, B=4
and so on.

So, Max N is 24 and Min N is 6.
Ans C

AnthonyRitz · Answer

Careful with the maximum. The fraction can be scaled up as, for instance,  \frac{10}{48}  or  \frac{50}{240} , and so on, so in fact there is no maximum value of  N . Your reasoning for the minimum looks correct, though.

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A number is called “terminating in base N” if that number can be expre

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