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(42)^9 is divisible by each of the following except?

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(42)^9 is divisible by each of the following except?  [#permalink]

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New post 01 Apr 2020, 09:35
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\((42)^9\) is divisible by each of the following except?

A. 16

B. 36

C. 49

D. 84

E. 132
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(42)^9 is divisible by each of the following except?  [#permalink]

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New post 01 Apr 2020, 09:42
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sjuniv32 wrote:
\((42)^9\) is divisible by each of the following except?

A. 16

B. 36

C. 49

D. 84

E. 132


Time for some prime factorization!

\((42)^9= (2 \times 3 \times 7)^9 = (2^9)(3^9)(7^9) \)

Scan the answer choices....
E) 132
132 = (2)(2)(3)(11)
Since there are no 11's in the prime factorization of \((42)^9\), we can conclude that \((42)^9\) is NOT divisible by 132

Answer: E

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Re: (42)^9 is divisible by each of the following except?  [#permalink]

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New post 08 Apr 2020, 04:40
Prime factorization is the weapon you need to solve this question. Let us prime factorize the base of the given number, \((42)^9\).

The base is 42. Upon prime factorization, we have 42 = 2*3*7. Therefore,
\((42)^9\) = \((2*3*7)^9\) = \(2^9\) * \(3^9\) * \(7^9\).

Let us look at the options now.

Option A is 16 which is nothing but \(2^4\). Can 2^4 divide \(2^9\)*\(3^9\)*\(7^9\) fully? Certainly. Eliminate option A.

Option B is 36. 36 = \(2^2\) * \(3^2\). Do we have a \(2^2\) * \(3^2\) in \((42)^9\)? For sure. Eliminate option B.

Option C is 49. 49 = \(7^2\) which is definitely there in \(2^9 * 3^9 * 7^9\). Eliminate option C.

Option D is 84. 84 = \(2^2\) * 3 * 7 which CAN divide \(2^9 * 3^9 * 7^9\). Eliminate option D.

The only answer option left is option E which HAS TO be the correct answer option. 132 = \(2^2\)*3*11. Although we have a 2^2 and a 3 in the numerator, we don’t have a 11. Therefore, 132 cannot divide \((42)^9\).

The correct answer option is E.

Remember – If the exponent of the prime factor in the numerator IS higher than the exponent of the SAME prime factor in the denominator, the denominator HAS to be factor of the numerator.

Hope that helps!
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Re: (42)^9 is divisible by each of the following except?  [#permalink]

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New post 08 Apr 2020, 05:56
\((42)^9\) is divisible by each of the following except?

A. 16 --> 42^9 = 2^9*3^9*7^9 & 16= 2^4, so 42^9 is divisible by 16

B. 36--> 42^9 = 2^9*3^9*7^9 & 36= 2^2*3^2, so 42^9 is divisible by 36

C. 49--> 42^9 = 2^9*3^9*7^9 & 49= 7^2, so 42^9 is divisible by 49

D. 84--> 42^9 = 2^9*3^9*7^9 & 84= 2^2*3*7, so 42^9 is divisible by 84

E. 132 --> correct: 42^9 = 2^9*3^9*7^9 & 132= 2^2*3*11, so 42^9 is NOT divisible by 132
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Re: (42)^9 is divisible by each of the following except?  [#permalink]

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New post 08 Apr 2020, 07:17
42=2×3×7
Search for a option which has some prime number apart from these.
Option E
132= 2×2×3×11
Since 42^9 does not have 11 in it so it won't be divisible by 132
Option E is the answer

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Re: (42)^9 is divisible by each of the following except?  [#permalink]

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New post 10 Apr 2020, 07:01
sjuniv32 wrote:
\((42)^9\) is divisible by each of the following except?

A. 16

B. 36

C. 49

D. 84

E. 132


Since 42^9 = (2 x 3 x 7)^49, it only has prime factors of 2, 3, and 7. However, since 132 = 12 x 11 = 2^2 x 3 x 11 has a prime factor of 11, 42^9 is not divisible by 132.

Answer: E
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Re: (42)^9 is divisible by each of the following except?   [#permalink] 10 Apr 2020, 07:01

(42)^9 is divisible by each of the following except?

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