paddy41 wrote:

Bunuel wrote:

Official Solution:

If \(y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2}}\), then \(y\) is NOT divisible by which of the following?

A. \(6^4\)

B. \(62^2\)

C. \(65^2\)

D. \(15^4\)

E. \(52^4\)

\(y=\frac{(3^5-3^2)^2}{(5^7-5^4)^{-2}}=(3^5-3^2)^2*(5^7-5^4)^2=\)

\(=3^4*(3^3-1)^2*5^8*(5^3-1)^2=\)

\(=3^4*26^2*5^8*124^2=\)

\(=2^6*3^4*5^8*13^2*31^2\).

Now, if you analyze each option you'll see that only \(52^4=2^8*13^4\) is not a factor of \(y\), since the power of 13 in it is higher than the power of 13 in \(y\).

Answer: E

Bunuel, could you please elaborate the following steps?

\(=3^4*26^2*5^8*124^2=\)

\(=2^6*3^4*5^8*13^2*31^2\).

Thank you!

hi,

let me do it for you from \(=3^4*26^2*5^8*124^2=\)

\(=3^4*(2*13)^2*5^8*(4*31)^2\)

=> \(=3^4*2^2*13^2*5^8*4^2*31^2\)

=> \(=3^4*2^{(2+4)}*13^2*5^8*31^2\)

=> \(2^6*3^4*5^8*13^2*31^2\)

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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