Fractions

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Nycgrl: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon May 19, 2008 1:12 pm; Thanked: 3 times

by Nycgrl » Tue Jul 01, 2008 5:54 pm

If R = 1+1/3+1/9+1/27 and S= 1+1/3*r , then s exceeds r by

(A) 1/3 (B)1/6 (C) 1/9 (D) 1/27 (E) 1/81

Any other methos to solve it without doing the actual calculation?

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Source: Beat The GMAT — Problem Solving | Tue Jul 01, 2008 5:54 pm

szapiszapo: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Jun 30, 2008 1:45 pm; Thanked: 3 times

by szapiszapo » Wed Jul 02, 2008 1:52 am

well... depends what you mean by calculation

R = 1 + 1/3 + 1/3 + 1/9 + 1/27
S = 1 + 1/3 * r

then S = 1 + 1/3 + 1/9 + 1/27 + 1/81

visually, we see that S exceeds R by 1/81, i.e. answer E

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Nycgrl: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon May 19, 2008 1:12 pm; Thanked: 3 times

by Nycgrl » Wed Jul 02, 2008 3:44 am

Can you please explain

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szapiszapo: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Jun 30, 2008 1:45 pm; Thanked: 3 times

by szapiszapo » Wed Jul 02, 2008 4:18 am

wording is:
R = 1 + 1/3 + 1/9 + 1/27
S = 1 + 1/3 * r

I just replace R in the equation forming S

therefore
S = 1 + 1/3 * ( 1 + 1/3 + 1/9 + 1/27)
S = 1 + 1/3*1 + 1/3*1/3 + 1/3*1/9 + 1/3*1/27
S = 1 + 1/(3*1) + 1/(3*3) + 1/(9*3) + 1/(27*3)
S = 1 + 1/3 + 1/9 + 1/27 + 1/81

S - R equals 1/81

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