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# If 12^13/x is an integer, which of the following could be the value of

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If 12^13/x is an integer, which of the following could be the value of [#permalink]
Bunuel wrote:
If 12^13/x is an integer, which of the following could be the value of x ?

I. 36
II. 64
III. 432

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

So lets see, if i got this part right then the question is

(12^13) / x

$$(2^2 * 3)^{13}$$

$$2^{26} * 3^{13}$$

All 3 are sufficient

36 = 2*2*3*3
64 = $$2^6$$
432 = $$2^4 * 3^3$$
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If 12^13/x is an integer, which of the following could be the value of [#permalink]
Bunuel wrote:
If $$\frac{12^{13}}{x}$$ is an integer, which of the following could be the value of x ?

I. 36
II. 64
III. 432

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

Keyord: could be the value of x ?

We see 12*13/x

So anything that has mutiples 2's ,3's and one 13 can be a contender since they can be part of cancellation from Numerator

1.36 has 12*3 yes possible
2.64 has 4^3 which is definitely possible since 12^13 will yield (3*4)^13 so 13 powers of 4
3.432 again is definitely possible 432=4*4*3^3

Hence all three are sufficient!!

Hope it helps!!
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Re: If 12^13/x is an integer, which of the following could be the value of [#permalink]
Bunuel wrote:
If $$\frac{12^{13}}{x}$$ is an integer, which of the following could be the value of x ?

I. 36
II. 64
III. 432

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

for $$\frac{12^{13}}{x}$$ to be an integer , value of x must be a factor of m]\frac{12^{13}}{x}[/m]

which can be written as : 2^26 * 3^13

upon reviewing all given options ; we can say that all the no 36,64 & 432 would be give an integer value when replaced as x in m]\frac{12^{13}}{x}[/m]

IMO E
Re: If 12^13/x is an integer, which of the following could be the value of [#permalink]
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