GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Oct 2019, 22:12

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58428
(3^30−2^30)/(3^15−2^15) is equal to which of the following?  [#permalink]

Show Tags

New post 30 Apr 2016, 03:45
1
6
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:48) correct 30% (01:58) wrong based on 222 sessions

HideShow timer Statistics

Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8015
Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following?  [#permalink]

Show Tags

New post 30 Apr 2016, 04:39
1
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
_________________
Senior Manager
Senior Manager
avatar
P
Joined: 27 Dec 2016
Posts: 309
CAT Tests
Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following?  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 58428
Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following?  [#permalink]

Show Tags

New post 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.
_________________
GMAT Club Bot
Re: (3^30−2^30)/(3^15−2^15) is equal to which of the following?   [#permalink] 04 Mar 2018, 21:14
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne