Need Help...Manhattan GMAT Word Problem

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usis: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Tue Oct 28, 2008 6:00 am

by usis » Wed Oct 29, 2008 4:52 am

Can you show me the logic process in working out this problem? I fully understand all calculations, but the logic of how to work it out as proposed by Manhattan GMAT.... I don't understand.

Problem: 8 years ago, George was half as old as Sarah. Sarah is now 20 years older than George. How old will George be in 10 years?

Take George's age 8yrs ago: G-8=S-8/2 rewritten 2G - 16 = S-8

Sarah is now 20 years older than George: G + 20 = S OR G = S - 20

2G - 16 = S - 8 - [G = S - 20]
EQUALS G - 16 = 12
G = 28YRS TODAY.
G= 38YRS OLD 10 yrs from now

THIS LAST STEP I DO NOT UNDERSTAND. PLEASE EXPLAIN THE LOGIC....WHY WOULD SUBTRACT GEORGE'S AGE 8YRS AGO FROM GEORGE'S AGE TODAY TO GET 28?

Source: Beat The GMAT — GMAT Strategy | Wed Oct 29, 2008 4:52 am

nandansingh: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Sep 27, 2008 11:38 am; Location: Hyderabad; Thanked: 3 times

by nandansingh » Wed Oct 29, 2008 7:05 am

Take George's age 8yrs ago: G-8=S-8/2 rewritten 2G - 16 = S-8

Sarah is now 20 years older than George: G + 20 = S OR G = S - 20

2G - 16 = S - 8
=> 2(S-20)-16 = S-8
=> 2S-40-16 = S-8
=> 2S-S-56 = -8
=> S-56 = -8
=> S = 56-8
=> S = 48
G = S-20
G=48-20
G=28 (Present age of George)
In, ten years, George will be 38 Yrs.

jimmiejaz: Master | Next Rank: 500 Posts; Posts: 207; Joined: Sun Mar 11, 2007 6:16 pm; Location: Mumbai; Thanked: 11 times

by jimmiejaz » Fri Oct 31, 2008 5:31 am

here's my approach....
lets say george age 8 yrs ago was x, sarah's age was 2x ....1
Present age of george - x+8
Present age of sarah - x+28, as current age of sarah is 20 years more than george.
but, from 1, current age of sarah is 2x + 8
equate 2 eqns.
2x+8=x+20
x=20.
so current age of george is 20+8=28
after 10yrs = 28+10=38

Hope it helps.

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