Bunuel wrote:

(3^30−2^30)/(3^15−2^15) is equal to which of the following?

A. 14,381,675

B. 14,441,623

C. 14,485,772

D. 14,609,707

E. 14,722,819

The first thing that strikes is that 30 is DOUBLE of 15, and 3^{30}-2^{30} is in the form a^2-b^2

and the NEXT is that all the choices have DIFFERENT units digit, so if we find units digit we can answer..

\(\frac{(3^{30}−2^{30})}{(3^{15}−2^{15})}= \frac{(3^{15}−2^{15})(3^{15}+2^{15})}{(3^{15}−2^{15})} = 3^{15}+2^{15}\)

3 has a cylicity of 3,9,7,1 and 2 has 2,4,8,6.

15 means 3rd in cylicity so 7+8 = 15..

UNITS digit =5

ans A

Also \(a^n+b^n\) is div by a+b if n is ODD

so \(a^{15}+b^{15}\) will be div by a+b or 3+2 in this case..

so \(3^{15}+2^{15}\)should be div by 3+2 or 5...so units digit must be 5 as the SUM will be ODD also

Only A has 5 in its units place

ans A

_________________

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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