student first reduced

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Aug 25, 2010 10:17 pm

A student first reduced a certain number by 20 percent, and then increased it again by 20 percent. If the difference between the last number and the original number was 8, then the original number was:
(A) 200
(B) 250
(C) 300
(D) 400
(E) 450

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Source: Beat The GMAT — Problem Solving | Wed Aug 25, 2010 10:17 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Wed Aug 25, 2010 10:55 pm

Solution:
Let the number be x.
After reduction by 20% the number becomes x*80%.
After a subsequent increase by 20%, the number becomes 120%*x*80% = 96%*x.
The difference between the original and the last number is x - 96%*x = 4%* x.
So 4%*x = 8.
Or x = 200.

The correct answer is (A).

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed Aug 25, 2010 11:28 pm

sanju09 wrote:A student first reduced a certain number by 20 percent, and then increased it again by 20 percent. If the difference between the last number and the original number was 8, then the original number was:
(A) 200
(B) 250
(C) 300
(D) 400
(E) 450

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www.crack-GMAT.com[/spoiler]

Perfect question for backsolving!

When we backsolve, we generally start with either B or D. 400 is an easier number with which to work, so let's start there.

Reduce 400 by 20%: 400 - 20%(400) = 400 - 80 = 320
Increase 320 by 20%: 320 + 20%(320) = 320 + 64 = 384

400 - 384 = 16. Is that what we want? No - eliminate (D).

Using 400 got us double the difference we wanted. Since all we're doing is multiplying, that means that 400 is twice as big as the correct answer - no need to do any more math, choose (A)200.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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samareshgupte: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Tue Jun 15, 2010 12:27 am

by samareshgupte » Mon Aug 30, 2010 12:58 am

sanju09 wrote:A student first reduced a certain number by 20 percent, and then increased it again by 20 percent. If the difference between the last number and the original number was 8, then the original number was:
(A) 200
(B) 250
(C) 300
(D) 400
(E) 450

[spoiler]Source: Crack-GMAT
www.crack-GMAT.com[/spoiler]

I feel the most easiest number to deal with in percentages is 100

1) Reduce 100 by 20 (of course that corresponds to 20%).That gives you 80
2) Increase 80 by 20% (or 1/5th of 80). That gives you 96.
3) Difference between original and new number is 4 (100-96)
4) But this is given to be 8. So double the number we have assumed 100*2=200

Answer is (A).

The advantage is that we can solve while reading the problem, that will save a lot of time

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