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The figure above represents a circle graph of Company H's [#permalink]

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07 Dec 2012, 08:21

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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.

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. The expenses for Division R = 94/360*$5,400,000. Sufficient.

(2) The total expenses for Divisions S and T are twice as much as the expenses for Division R. Not sufficient.

Re: The figure above represents a circle graph of Company H's [#permalink]

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13 Dec 2012, 02:14

I resolved it alone i'm studying from october. i'd like to start an mba next year, but i have to pass the gmat with 670. I'm studying in this way: math (1 hour per day), verbal 5 hours per week. honestly i resolve 50% of the questions I try on the gmatclub. i don't know..maybe I should try a gmat practice test to assess myself, but i feel not so confident. when I read your posts you are amazing, being able to solve very hard question according to me.

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 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

From the circle graph, we can see that there are five 'divisions' of expenses for Company H and that "R" represents X degrees of the 360 degrees in the circle. Since this is a DS question though, we cannot trust the picture (meaning that it's possible that R could be the biggest piece, smallest piece, a 'middle' piece, etc. of the pie). We're told that the TOTAL expenses = $5,400,000. We're asked for the expenses from piece R.

1) X = 94

Since X = 94, we know that R = (94/360)($5,400,000). We don't have to calculate this value though (we know that we COULD though and that there would be just one answer to the question. Fact 1 is SUFFICIENT

2) The total expenses for Divisions S and T are twice as much as the expenses for Division R.

With this Fact, we don't know the actual values of any of the 5 divisions. For example: S, T and R could each equal $100, with the remaining $5,399,700 spread between P and Q. S, T and R could each equal $200, with the remaining $5,399,400 spread between P and Q. Fact 2 is INSUFFICIENT

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.

We are given that the total expenses of Company H are $5,400,000. We need to determine the total expenses for Division R. We see that angle x represents the central angle associated with Division R. We know that the central angle of a circle is proportional to the total degree measurement of a circle (360 degrees), so we can say that the expenses of Division R are also proportional to the total expenses of Company H.

We can now create the following proportion:

Degree measurement of angle x is to 360 degrees as the expenses of Division R are to the total expenses of Company H.

x/360 = R/5,400,000

5,400,000x = 360R

15,000x = R

We see that if we can determine a value for angle x, we can determine a value for R.

Statement One Alone:

x = 94

Because x = 94, we can determine a value for R.

15,000(94) = R

1,410,000 = R

(Note: We did not actually have to determine the product of 15,000 and 94. Since we knew we would get a unique answer for R, we knew we would have enough information to deem the statement sufficient.)

Statement one is sufficient to answer the question.

Statement Two Alone:

The total expenses for Divisions S and T are twice as much as the expenses for Division R.

The information in statement two does not give us enough information to determine the value of x. Statement two alone is not sufficient to answer the question.

Answer: A
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