exponents

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nisha.menon294: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sat Apr 10, 2010 8:33 am

by nisha.menon294 » Sat Apr 17, 2010 3:05 am

Question from Gmat prep . i would like to know an easier way to solve it if possible. thanks

what is the closest value of 10^8-10^2\10^7-10^3

a)0
b)1
c)10
d)10^2
e)10^3

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Source: Beat The GMAT — Problem Solving | Sat Apr 17, 2010 3:05 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 » Sat Apr 17, 2010 3:43 am

nisha.menon294 wrote:Question from Gmat prep . i would like to know an easier way to solve it if possible. thanks

what is the closest value of 10^8-10^2\10^7-10^3

a)0
b)1
c)10
d)10^2
e)10^3

When they talk about the closest value in such cases, take a judicious look at the choices. In the present case, the choices are far apart in most of the cases.

Try with the smaller degrees of 10 for comparison, as the difference between 10^0 and 10^1 is close to 10^1, hence the difference between 10^0 and 10^2 will be incredibly close to 10^2, and so on. We can now safely predict that 10^8 - 10^2 is incredibly close to 10^8, and that 10^7 - 10^3 is incredibly close to 10^7, such that

(10^8 - 10^2)\(10^7 - 10^3) is incredibly close to 10^8/10^7 = [spoiler]10.

C[/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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nisha.menon294: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sat Apr 10, 2010 8:33 am

by nisha.menon294 » Sat Apr 17, 2010 4:02 am

thanks .. that was helpful. i wasted a lot of time trying to get to that answer

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Sat Apr 17, 2010 4:23 am

10^8 - 10Â² / 10^7 - 10Â³
10Â²(10^6 -1) / 10Â³(10^4-1)
(10^6 -1) /10(10^4-1)
app 10^6/10^5 or 10

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