Walkabout
The figure above represents a circle graph of Company H's total expenses broken down by the expenses for each of its five divisions. If O is the center of the circle and if Company H's total expenses are $5,400,000, what are the expenses for Division R ?
(1) x = 94
(2) The total expenses for Divisions S and T are twice as much as the expenses for Division R.
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?This is a great candidate for REPHRASING the target question.
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 expensesAside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100Now onto the statements....
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 expensesSince 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 expensesCase b: a = 62, b = 11, c = 10, d = 9 and e = 8. In this case,
1 division has MORE than 20% of the TOTAL expensesSince we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
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