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If X is a positive integer and 405^4 is a multiple of 3^X, what is the

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Bunuel
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If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   04 Sep 2019, 01:03
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If X is a positive integer and 405^4 is a multiple of 3^X, what is the largest possible value of X?

(A) 5.
(B) 12.
(C) 16.
(D) 20.
(E) 26
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C
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Harsh9676
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Re: If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   04 Sep 2019, 01:10
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IMO C

405 = 3^4 * 5

(405)^4 = (3^4 *5)^4

Largest value of X = 16

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Poju4real
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Re: If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   04 Sep 2019, 02:20
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Prime factorization of 405 is
3^4×5.
Therefore, (405)^4 = (3^4×5)^4
= 3^16×5^4. Since 3^16×5^4 is a multiple of 3^x, in other words, 3^x is a factor of 3^16×5^4. 3^x = 3^16, x = 16.
The largest possible value of x is 16.

Option C.

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Re: If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   04 Sep 2019, 22:39
Poju4real wrote:
Prime factorization of 405 is
3^4×5.
Therefore, (405)^4 = (3^4×5)^4
= 3^16×5^4. Since 3^16×5^4 is a multiple of 3^x, in other words, 3^x is a factor of 3^16×5^4. 3^x = 3^16, x = 16.
The largest possible value of x is 16.

Option C.

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I have exactly the same, why is it wrong though? :shh:
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Bunuel
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If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   05 Sep 2019, 00:55
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Bunuel wrote:
If X is a positive integer and 405^4 is a multiple of 3^X, what is the largest possible value of X?

(A) 5.
(B) 12.
(C) 16.
(D) 20.
(E) 26


Given: \(405^4=3^xk\).

\(405^4=(3^4*5)^4=3^{16}5^4=3^xk\). Hence the largest possible value of x is 16 (for \(k=5^4\))

Answer: C.
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Re: If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   05 Sep 2019, 01:10
Bunuel wrote:
Bunuel wrote:
If X is a positive integer and 405^4 is a multiple of 3^X, what is the largest possible value of X?

(A) 5.
(B) 12.
(C) 16.
(D) 20.
(E) 26


Given: \(405^4=3^xk\).

\(405^4=(3^4*5)^4=3^{16}5^4=3^xk\). Hence the largest possible value of x is 16 (for \(k=5^4\))

Answer: B.


What now?

"The largest possible value x is 16, Answer B"

B is 12 though, what is the right solution now? :dazed
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Re: If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   05 Sep 2019, 01:13
How B ?

Max value of X is 16

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Bunuel
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Re: If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink] New post   05 Sep 2019, 01:23
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Richa2816 wrote:
How B ?

Max value of X is 16

Posted from my mobile device

________________
The OA is C, 16.
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Re: If X is a positive integer and 405^4 is a multiple of 3^X, what is the [#permalink]
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