my exam is tomrrow - please help with this stupid simple eqn - The Beat The GMAT Forum

my exam is tomrrow - please help with this stupid simple eqn

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desiguy: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu Jul 10, 2008 1:51 pm; Location: london

by desiguy » Tue Jul 22, 2008 3:51 am

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

options:
5^6
13^5
2^6+3^6
2^7+3^8
4^5+9^5

how to solve this without breaking it up ?

my exam is tomorrow.....please can someone help !!

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Source: Beat The GMAT — Problem Solving | Tue Jul 22, 2008 3:51 am

sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Tue Jul 22, 2008 3:57 am

take 2^5 comon and 3^5 comon

2^5(2)+ 3^5(3)

hence 2^6+3^6

hope its clear..

All the very best for ur exam...

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desiguy: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu Jul 10, 2008 1:51 pm; Location: london

thanks sudhir...

by desiguy » Tue Jul 22, 2008 4:25 am

Thanks sudhir ...a ton

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evansbd: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Tue Jul 01, 2008 10:50 am

The solution provided seems simple...but can someone explain the math?

Are the exponents being multiplied or is there more factoring not shown in the solution.

2(2^5) + 3(3^5)

I see that 2^5 = 32, so 2(2^5) = 64, which is 2^6.
I would have picked the correct answer because the others do not have the same first term on a real GMAT but what about factoring or doing the math of 3^5 or something similar w/o a calculator.

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evansbd: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Tue Jul 01, 2008 10:50 am

by evansbd » Tue Jul 22, 2008 8:39 am

repost

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Canman: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Fri Jul 11, 2008 5:00 am; Thanked: 4 times

by Canman » Tue Jul 22, 2008 10:02 am

Don't overthink the problem. No need to multiply out.

Once you recognize that 2^5+2^5+3^5+3^5+3^ = 2(2^5)+3(3^5) you need to just take the next step and realize that you now have:

2^1(2^5) + 3^1(3^5) and add the exponents to arrive at:

2^6+3^6

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Confused...

by Ian Stewart » Tue Jul 22, 2008 10:08 am

evansbd wrote:The solution provided seems simple...but can someone explain the math?

Are the exponents being multiplied or is there more factoring not shown in the solution.

2(2^5) + 3(3^5)

I see that 2^5 = 32, so 2(2^5) = 64, which is 2^6.
I would have picked the correct answer because the others do not have the same first term on a real GMAT but what about factoring or doing the math of 3^5 or something similar w/o a calculator.

There are (at least) two ways to see why the answer is correct. We can factor:

2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2^5(1+1) + 3^5(1+1+1) = 2*2^5 + 3*3^5 = 2^6 + 3^6

Or we can understand that when we add something to itself, this is exactly what it means to multiply something by 2: x+x = 2x. Thus 2^5 + 2^5 = 2*2^5 = 2^6. And if you add something to itself three times, that's the same as multiplying by 3: x+x+x = 3x, so 3^5 + 3^5 + 3^5 = 3*3^5 = 3^6.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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