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

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Math Expert
Joined: 02 Sep 2009
Posts: 47109
(3^30−2^30)/(3^15−2^15) is equal to which of the following? [#permalink]

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30 Apr 2016, 03:45
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6
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Difficulty:

35% (medium)

Question Stats:

69% (01:24) correct 31% (01:42) wrong based on 188 sessions

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

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Math Expert
Joined: 02 Aug 2009
Posts: 6246
Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following? [#permalink]

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30 Apr 2016, 04:39
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2
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
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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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Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following? [#permalink]

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04 Mar 2018, 19:56
I have a silly question. Can't we simply subtract the denominator from the numerator as in (3^30-2^30)-(3^15-2^15) to get 3^15-2^15 or this is completely wrong?
Math Expert
Joined: 02 Sep 2009
Posts: 47109
Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following? [#permalink]

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04 Mar 2018, 21:14
csaluja wrote:
I have a silly question. Can't we simply subtract the denominator from the numerator as in (3^30-2^30)-(3^15-2^15) to get 3^15-2^15 or this is completely wrong?

1. Yes, this does not make sense. Does, 2/3 equal to 2 - 3?

2. The subtracting itself is not correct: how did you get 3^15-2^15 from (3^30-2^30)-(3^15-2^15)? Does 3^30 - 3^15 equal to 3^15? Does -2^30 - 2^15 = -2^15? No.
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Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following?   [#permalink] 04 Mar 2018, 21:14
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