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08 Feb 2019, 04:18
Kudos
Bookmarks
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:
71% (01:30) correct
29%
(01:34)
wrong
based on 146
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
08 Feb 2019, 04:40
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Bunuel
I hope the question is \(\frac{12^{13}}{x}\) is an Integer
i.e. x is a factor of \(12^{13} = 2^{26}*3^{13}\)
I. 36 =\(2^2*3^2\) which is a factor of \(2^{26}*3^{13}\)
II. 64 = \(2^6\) which is a factor of \(2^{26}*3^{13}\)
III. 432 = 8*54 = \(2^4*3^3\) which is a factor of \(2^{26}*3^{13}\)
Hence all given values can be values of x
Answer: Option E
Bunuel
\(12^{13} is quite a big number .\)
suppose we are just dealing with \(12^2\)
\(12^2 = 144.\)
\(144 = 12 * 12 = 3^2 2^4.\)
I) \(36 = 3*12 = 3 * 3*4 = 3^2 2^2.\)
II) \(64 = 2^3 2^3. 2^{3 + 3} = 2^6.\)
144 gives us \(2^4\). If we get 2^4 from \(12^2\). \(12^13\) will surely yield \(2^6.\)
III) \(432 = 3 *144. = 3 * 12 * 12 = 3 * 3*4 * 3 * 4 = 3^3 2^2 2^2 = 3^3 2^4.\)
\(12^2 = 3^2 2^4.\) So, \(2^4\)matches. \(12^2\) yields \(3^2\) . \(12^13\) will surely give us 3^3.
****\(12 = 3*2^2\). If we consider the primes of 12, we can easily predict that all of the integers , which are the values of x, can divide into \(12^13\).
