Percentage Increase

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MI3: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Sat Feb 26, 2011 11:22 amFollowed by: 1 member; Thanked: 1 times

by MI3 » Sat Jul 16, 2011 1:08 am

Q. What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25% (B) 50% (C) 75% (D) 100% (E) 200%

IMO answer is D, am I correct?

Last edited by MI3 on Sat Jul 16, 2011 2:51 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sat Jul 16, 2011 1:08 am

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by MBA.Aspirant » Sat Jul 16, 2011 1:29 am

D) 100%

replace smallest with 2 primes

so smallest are -4, -1

to have the min. increase we replace with the min. prime no.s i.e 2,3

so set becomes {0,2,3,6,9}

new mean = 20/5 = 4

% increase = 4-2/2 = 100%

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by GMATGuruNY » Sat Jul 16, 2011 2:55 am

MI3 wrote:Q. What is the minimum percentage increase in the mean of set X {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A) 25% (B) 50% (C) 75% (D) 100% (E) 200%

IMO answer is E, am I correct?

Average = Sum/Number.
Since the number of elements is not changing, the increase in the average will come solely from the increase in the sum.
Thus, to determine the percent increase in the average, we just need to compare the smaller sum to the larger sum.
Old sum = -4 + -1 + 0 + 6 + 9 = 10.
The two smallest primes are 2 and 3.
Replacing -4 and -1 with 2 and 3, we get:
New sum = 2+3+0+6+9 = 20.

20 is 100% greater than 10:
Difference/Original * 100 = (20-10)/10 * 100 = 100%.
The correct answer is D.

Answer choice E is a trap.
Although 20 is 200% of 10 -- answer choice E -- it is only 100% greater than 10.

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