GMATPrep software test question

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bradyhopkins: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Apr 15, 2011 7:45 am

by bradyhopkins » Tue Apr 19, 2011 9:25 am

Can anyone explain the reasoning behind this? The only way it makes sense to me is when I do the arithmetic to get the answer.

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Source: Beat The GMAT — Problem Solving | Tue Apr 19, 2011 9:25 am

brood1989: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Thu Apr 07, 2011 5:06 pm; Thanked: 1 times

by brood1989 » Tue Apr 19, 2011 9:38 am

Here is how you should approach this problem.

2^5 + 2^5 is really just 2(2^5)...once it is in
this form we know that 2 is just 2^1. So 2^1 * 2^5
means we add the exponents hence 2^6. Same thing for
the 3's...3(3^5) = 3^1 + 3^5 = 3^6.

Last edited by brood1989 on Tue Apr 19, 2011 9:44 am, edited 2 times in total.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Apr 19, 2011 9:42 am

Sometimes it's hard to see that numbers behave the same as variables do.

We know that x + x + y + y + y can be rewritten as 2x + 3y

Similarly, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2(2^5) + 3(3^5)

From here we can simplify 2(2^5) + 3(3^5) as 2^6 + 3^6

Brent Hanneson - Creator of GMATPrepNow.com

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Tue Apr 19, 2011 9:48 am

bradyhopkins wrote:

Can anyone explain the reasoning behind this? The only way it makes sense to me is when I do the arithmetic to get the answer.

well concept involved here is that, when two or more numbers are multiplied whose bases are same, then their powers get added. i.e. x^y*x^2=x^(y+2),

now 2^5+2^5= 2^5(1+1)=2^5*2=2^(5+1);=2^6;
similarly 3^5+3^5+3^5=3^5(1+1+1)=3^5*3=3^6;
hence our answer is 2^6+3^6;

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