Percentage difference

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sarahw_gmat: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Fri Mar 12, 2010 1:39 pm; Thanked: 1 times

by sarahw_gmat » Thu Dec 30, 2010 5:36 pm

Jason's salary & Karen's salary were each p percent greater in 1998 than in 1995.What is the value of P?
1. In 1995 Karen's salary was $2000 greater than Jason's.
2. In 1998 Karen's salary was $2440 greater than Jason's.

I solved this question using equations and got p = 22.

Just want to know if my answer is right and better way to do it.

Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Dec 30, 2010 5:36 pm

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Thu Dec 30, 2010 5:48 pm

sarahw_gmat wrote:Jason's salary & Karen's salary were each p percent greater in 1998 than in 1995.What is the value of P?
1. In 1995 Karen's salary was $2000 greater than Jason's.
2. In 1998 Karen's salary was $2440 greater than Jason's.

I solved this question using equations and got p = 22.

Just want to know if my answer is right and better way to do it.

Thanks.

If two things change by same %, their diff. will also change by same %.

Hence, the required % here = (440/2000) * 100 = 22%.

For e.g. Consider 100 and 50,
100 -> 30 % increase -> 130
50 -> 30% inc -> 65

The difference (100-50 = 50) will also increase by 30%(i.e 15 .) which is right (130-65 = 65).

Thanks
Anshu

(Every mistake is a lesson learned )

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 amFollowed by: 1 member; Thanked: 2 times

by HPengineer » Fri Dec 31, 2010 9:45 am

@Sarah what did your equations look like to solve this problem?

I used the logic mentioned above to come up with C however i am unable to solve this algebraically.

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Fri Dec 31, 2010 10:17 am

HPengineer wrote:@Sarah what did your equations look like to solve this problem?

I used the logic mentioned above to come up with C however i am unable to solve this algebraically.

Jason's salary in 1995 -> x -> in 1998 -> x(1+p/100)
Karen's salary in 1995 -> y -> in 1998 -> y(1+p/100)

1. y-x = 2000
2. y(1+p/100)-x(1+p/100) = 2440 => (y-x)(1+p/100) = 2440
=> 2000(1+p/100) = 2440
=> 1+p/100 = 2440/2000 = 244/200
=> p/100 = 244/200 - 1 = 44/200
=> p = 44*100/200 = 22%

Thanks
Anshu

(Every mistake is a lesson learned )

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 amFollowed by: 1 member; Thanked: 2 times

by HPengineer » Fri Dec 31, 2010 10:23 am

thanks i always forget to use the difference to eliminate a variable... I missed the X - Y = 2000

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