62) What would be a quick way of doing this?

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ern5231: Master | Next Rank: 500 Posts; Posts: 226; Joined: Sun Aug 09, 2009 4:34 am

by ern5231 » Wed May 12, 2010 3:38 am

{7^(-2)+7^6} divided by 7^4

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Source: Beat The GMAT — Problem Solving | Wed May 12, 2010 3:38 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed May 12, 2010 3:44 am

ern5231 wrote:{7^(-2)+7^6} divided by 7^4

7^(-2) is too small as compared to 7^6 that its addition to 7^6 doesn't make any remarkable difference to its value, hence {7^(-2)+7^6} divided by 7^4 will be equivalent to 7^6 divided by 7^4, the result equals [spoiler]7^2 or 49[/spoiler].

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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analyst218: Master | Next Rank: 500 Posts; Posts: 140; Joined: Fri Feb 05, 2010 2:43 pm; Thanked: 3 times; GMAT Score:720

by analyst218 » Wed May 12, 2010 10:57 am

ern5231 wrote:{7^(-2)+7^6} divided by 7^4

or you could just

[7^4(7^-2 + 7^2)] /7^4 = 7^-2 + 7^2 = 49.0..

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jeffedwards: Master | Next Rank: 500 Posts; Posts: 109; Joined: Mon Oct 12, 2009 4:58 amFollowed by: 1 member; Thanked: 12 times; GMAT Score:720

by jeffedwards » Wed May 12, 2010 12:00 pm

Start out by simplifying

When you divide a number raised to a number by another number raised to another number with the same base (I hope you followed that),you just subtract the powers.

Let's reduce as follows:

(7^(-2)+7^6) / 7^4
7^(-2 - 4)+7^(2 - 4)
7^(-6)+7^2

Now think a little more

7^(-6) is the same as 1/(7^6)

Add that to 49...so your just a little above 49...

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu May 13, 2010 1:41 am

analyst218 wrote:
ern5231 wrote:{7^(-2)+7^6} divided by 7^4
or you could just

[7^4(7^-2 + 7^2)] /7^4 = 7^-2 + 7^2 = 49.0..

are you sure with what's in bold? rest is great

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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