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01 Apr 2020, 10:35
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:16) correct
24%
(01:03)
wrong
based on 230
sessions
History
Date
Time
Result
Not Attempted Yet
\((42)^9\) is divisible by each of the following except?
A. 16
B. 36
C. 49
D. 84
E. 132
A. 16
B. 36
C. 49
D. 84
E. 132
01 Apr 2020, 10:42
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sjuniv32
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
Cheers,
Brent
General Discussion
08 Apr 2020, 05:40
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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!
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!
