Least possible value of k

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

by Vemuri » Sat Apr 18, 2009 5:47 am

If k is an integer 0.0010101 x 10^k is greater than 1000, what is the least possible value of k?

A. 2
B. 3
C. 4
D. 5
E. 6

OA is E. Source is www.gmatfix.com

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Source: Beat The GMAT — Problem Solving | Sat Apr 18, 2009 5:47 am

m&m: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Feb 15, 2009 7:44 pm; Thanked: 14 times

by m&m » Sat Apr 18, 2009 6:49 am

by moving the decimal to the right one place you increase k by 1. SO:

0.0010101 x 10^0 = 0.0010101 < 1000
0.0010101 x 10^1 = 0.010101 < 1000
0.0010101 x 10^2 = 0.10101 < 1000
0.0010101 x 10^3 = 1.0101 < 1000
0.0010101 x 10^4 = 10.101 < 1000
0.0010101 x 10^5 = 101.01 < 1000
0.0010101 x 10^6 = 1010.1 > 1000

so the answer is k=6, E

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