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bobdylan: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Wed Nov 30, 2011 3:12 pm

by bobdylan » Fri Apr 13, 2012 1:12 pm

If (1/5)^m . (1/4)^18= 1/2(10)^35, then m:
a)17
b)18
c)34
d)35
e)36

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Source: Beat The GMAT — Problem Solving | Fri Apr 13, 2012 1:12 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Fri Apr 13, 2012 1:18 pm

If (1/5)^m (1/4)^18 = 1/ 2(10)^35, then m =

a.17
b.18
c.34
d.35
e.36

(1/5)^m (1/4)^18 = 1/ 2(10)^35
(1/5)^m * (1/2*2)^18 = 1/(2(2*5)^35)
(1/5)^m * (1/2)^36 = 1/(2(2^35)(5^35))
(1/5)^m * (1/2)^36 = 1/(2^36 * 5^35)
multiply left hand side and right hand side with 2^36, leaving:
1/5^m = 1/5^35
Bases are equal, so should be exponents. Hence the value of m = 35
Option D

Anil Gandham
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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Apr 13, 2012 5:33 pm

bobdylan wrote:If (1/5)^m . (1/4)^18= 1/2(10)^35, then m:
a)17
b)18
c)34
d)35
e)36

(1/5)^m * (1/4)^18= 1/2(10)^35
(1/5)^m * (1/4)^18= 1/[2 * 2^35 * 5^35]
Now all the answer choices are only integers, and power of 5 on both sides should be equal. The power of 5 is 35.

The correct answer is D.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Apr 13, 2012 6:04 pm

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