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2^5+2^5+3^5+3^5+3^5

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nga.kam.lai
 Post subject: 2^5+2^5+3^5+3^5+3^5
 Post Posted: Sun Jul 11, 2010 1:51 pm 
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Course Students


Posts: 4
Hi - can anyone please help me with the following GMAT Prep Math Question?

What is the value of 2^5+2^5+3^5+3^5+3^5?

the correct answer is 2^6+3^6

thanks!
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nga.kam.lai
 Post subject: Re: 2^5+2^5+3^5+3^5+3^5
 Post Posted: Sun Jul 11, 2010 3:14 pm 
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Course Students


Posts: 4
I found a previous thread that had this question.

thanks!
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mschwrtz
 Post subject: Re: 2^5+2^5+3^5+3^5+3^5
 Post Posted: Tue Jul 13, 2010 1:11 am 
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ManhattanGMAT Staff


Posts: 506
Thanks for checking on that. Saves us some work.
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yousuf_azim
 Post subject: Re: 2^5+2^5+3^5+3^5+3^5
 Post Posted: Tue Jul 13, 2010 7:20 am 
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Students


Posts: 45
Hello
How the question is solved?
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dinesh19aug
 Post subject: Re: 2^5+2^5+3^5+3^5+3^5
 Post Posted: Tue Jul 13, 2010 3:55 pm 
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Course Students


Posts: 37
Solution:
2Let's break it in two parts.
base 2 + base 3
Base 2 = 2^5 + 2^5 = 2 times 2^5 = 2* 2^5 = 2^6
Base 3 = 3^5 + 3^5 + 3^5 = 3 times 3^5 = 3* 3^5 = 3^6

hence Soln: 2^6 + 3^6
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RonPurewal
 Post subject: Re: 2^5+2^5+3^5+3^5+3^5
 Post Posted: Thu Aug 05, 2010 4:58 am 
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ManhattanGMAT Staff


Posts: 6765
dinesh's solution, above mine, is good.

BUT ALSO
by the way - even if you have NO IDEA how to solve this problem, there's still no excuse for getting it wrong.

because...

you can easily solve this problem WELL within the time guidelines, simply by DOING OUT THE ARITHMETIC.

2^5 is 32; 3^5 is 243. (you should probably have these memorized, but you can calculate them in a matter of seconds if necessary.)
so the prompt is 32 + 32 + 243 + 243 + 243, which works out to 793.

(a) wrong, since all powers of 5 end with the digit 5.

(b) this is ridiculously big. note that 13^2 = 169 (a value you should know by heart), so that 13^3 is already much bigger than 793. and 13^5 is two powers above that.

(c) = 64 + 729 = 793

(d) and especially (e) are both several orders of magnitude larger than 793.

done.

don't forget these sorts of lowbrow, scrappy ways to solve problems. remember that there are no style points; if you can solve the problem, then you can solve the problem. "ugly" solutions are worth the same points as "pretty" solutions.
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