Percentage DS

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guerrero: Master | Next Rank: 500 Posts; Posts: 227; Joined: Sun Apr 08, 2012 4:53 amFollowed by: 3 members; Thanked: 12 times

by guerrero » Sun Feb 10, 2013 10:43 pm

Price increased by M% from 1991 to 1992 and by N% from 1992 to 1993. What was the percentage increase in price from 1991 to 1993?

(1) MN=300

(2) 100M+100N+MN=4300

Please show me the Quickest approach

thanks!

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Source: Beat The GMAT — Data Sufficiency | Sun Feb 10, 2013 10:43 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Feb 11, 2013 4:22 am

If you increase something by M%, you multiply it by (1 + M/100). So here, the price is multiplied by:

(1 + M/100)(1 + N/100) = 1 + M/100 + N/100 + MN/10000

So we need to find the value of this expression. Statement 1 alone isn't much help. Using Statement 2 alone, if we divide both sides by 10,000, we get:

M/100 + N/100 + MN/10000 = 0.43

So 1 + M/100 + N/100 + MN/10000 = 1.43, and the overall increase is 43%.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Feb 11, 2013 4:36 am

guerrero wrote:Price increased by M% from 1991 to 1992 and by N% from 1992 to 1993. What was the percentage increase in price from 1991 to 1993?

(1) MN=300

(2) 100M+100N+MN=4300

Let the original price = 100.
Increase from 1991 to 1992 = M/100 * 100 = M.
New price = 100+M.
Increase from 1992 to 1993 = N/100*(100+M) = N + MN/100
Total increase = increase from 1991 to 1992 + increase from 1992 to 1993 = M + N + MN/100.

Since the original price was 100, the total increase and the PERCENT increase are the same.
Thus, the question becomes:

What is the value of M + N + MN/100?

Statement 1: MN = 300.
Not sufficient to determine the value of M + N + MN/100.

Statement 2:
100M + 100N + MN = 4300
M + N + MN/100 = 43.
SUFFICIENT.

The correct answer is B.

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