Breakup of total expenses

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Breakup of total expenses

by conquistador » Mon Apr 13, 2015 5:24 am
Breakup of total expenses of the five divisions M, N, O, P and Q of company X

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Note -: The figure shown is not necessarily to scale.
The figure above shows a circle graph. The circle has a centre of C and gives the division wise breakup of the total expenses of company X in terms of percentages. How many of the five divisions have an expense which is more than the average (arithmetic mean) of the expenses of the five divisions?
(1) a > 19 > b > c > d > e
(2) a > 21 > b > c > d > e

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by DavidG@VeritasPrep » Mon Apr 13, 2015 5:46 am
The average of all the divisions, in terms of percent, will be 20. (100% total; and we have 5 divisions. 100/5 = 20.) So the question is really asking, "how many of these pie slices are more than 20% of the pie?"

S1: We know b, c, d, and e are all less than 19%. Well, if those four slices are below 20%, the remaining slice, a, will have to be greater than 20% to compensate. So the division that corresponds to 'a' will be the only one that is above the 20% average. Sufficient.

S2: Possibility one: a = 25, b = 20.5, c = 19.5, d = 18, e = 17; Two of the divisions are over 20%
Possibility two: a = 30 b = 19 c = 18 d = 17, e = 16; one division is above 20% ; Different result, so Not Sufficient.

Answer is A
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by Brent@GMATPrepNow » Mon Apr 13, 2015 5:48 am
Mechmeera wrote:Breakup of total expenses of the five divisions M, N, O, P and Q of company X

Image

Note -: The figure shown is not necessarily to scale.
The figure above shows a circle graph. The circle has a centre of C and gives the division wise breakup of the total expenses of company X in terms of percentages. How many of the five divisions have an expense which is more than the average (arithmetic mean) of the expenses of the five divisions?
(1) a > 19 > b > c > d > e
(2) a > 21 > b > c > d > e
Target question: How many of the five divisions have an expense which is more than the average (arithmetic mean) of the expenses of the five divisions?

IMPORTANT: If we add the percentages (a%, b%, c%, d%, and e%), we get 100%
So, the average percent share = 100%/5 = 20%

So, we can REPHRASE the target question....
REPHRASED target question: How many of the five divisions have MORE than 20% of the TOTAL expenses

Statement 1: a > 19 > b > c > d > e
We know that b, c, d and e have less than 19% of the total expenses, which means they each have less than 20% of the TOTAL expenses.
If b, c, d and e each = less than 19%, then b+c+d+e is less than (4)(19%)
(4)(19%) = 74%, which means division a must comprise more than 26% percent of the TOTAL expenses.
So, exactly 1 division has MORE than 20% of the TOTAL expenses
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: a > 21 > b > c > d > e
There are several values of a, b, c, d and e that satisfy statement 2. Here are two:
Case a: a = 23, b = 20.5, c = 19.5, d = 19 and e = 18. In this case, 2 divisions have MORE than 20% of the TOTAL expenses
Case b: a = 62, b = 11, c = 10, d = 9 and e = 8. In this case, 1 division has MORE than 20% of the TOTAL expenses
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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