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gdshamain: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Thu Jan 09, 2014 10:45 pm

OG 13 - PS 199

by gdshamain » Wed May 07, 2014 5:34 pm

199i 0.99999999 0.99999991_
1.0001 1.0003
180
(A) io-8
(B) 3U0-8)
(0 3(10-4)
(D) 2(10-4)
(E) io-4

Is there an approximation method for this problem?

Quote

Source: Beat The GMAT — Problem Solving | Wed May 07, 2014 5:34 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed May 07, 2014 6:32 pm

0.99999999/1.0001 - 0.99999991/1.0003 =

A. 10^-8
B. 3(10^-8)
C. 3(10^-4)
D. 2(10^-4)
E. 10^-4

One approach is to recognize that both 9999.9999 and 9999.9991 can be rewritten as differences of squares.

First, 0.99999999 = 1 - 0.00000001
= (1 - 0.0001)(1 + 0.0001)

Similarly, 9999.9991 = 1 - 0.00000009
= (1 - 0.0003)(1 + 0.0003)

Original question: 0.99999999/1.0001 - 0.99999991/1.0003
= (1 - 0.0001)(1 + 0.0001)/(1.0001) - (1 - 0.0003)(1 + 0.0003)/(1.0003)
= (1 - 0.0001)(1.0001)/(1.0001) - (1 - 0.0003)(1.0003)/(1.0003)
= (1 - 0.0001) - (1 - 0.0003)
= 1 - 0.0001 - 1 + 0.0003
= 0.0002
= 2 x 10^(-4) = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com