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Problem Solving (PS) | 30^20 – 20^20 is divisible by all of the following

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GMATPrepNow wrote:

\(30^{20} – 20^{20}\) is divisible by all of the following values, EXCEPT:

A) 10
B) 25
C) 40
D) 60
E) 64

*kudos for all correct solutions


\(30^{20} – 20^{20}\)
=\(10^{20}\)*\(3^{20}\)-\({10}^{20}\)*\(2^{20}\)
=\(10^{20}\)(\(3^{20}\)-\(2^{20}\) )
=\(5^{20}\) m]2^{20}\(]([m]3^{20}\)\(2^{20}\) )

A) 10 = 2 * 5. divisible by this value.
B) 25 =\(5^2\) . Clearly divisible by this value.
C) 40 =\(2^3 * 5\) . divisible by this value.
D) 60 =\(2^2 *3 * 5\) .NOT divisible by this value.
E) 64 =\(2^6\) . divisible by this value.

Ans - D.
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