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# The figure above represents a circle graph of Company H's total expens

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The figure above represents a circle graph of Company H's total expens [#permalink]
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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. 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 Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100 Now 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 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 = RELATED VIDEO GMAT Club Legend Joined: 19 Dec 2014 Status:GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Posts: 21832 Own Kudos [?]: 11865 [3] Given Kudos: 450 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 The figure above represents a circle graph of Company H's total expens [#permalink] 3 Kudos Expert Reply Hi All, 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 Final Answer: GMAT assassins aren't born, they're made, Rich Target Test Prep Representative Joined: 04 Mar 2011 Status:Head GMAT Instructor Affiliations: Target Test Prep Posts: 3036 Own Kudos [?]: 6825 [0] Given Kudos: 1646 The figure above represents a circle graph of Company H's total expens [#permalink] Expert Reply 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.

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 VP Joined: 09 Mar 2016 Posts: 1138 Own Kudos [?]: 1038 [0] Given Kudos: 3851 Re: The figure above represents a circle graph of Company H's total expens [#permalink] Bunuel 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. Answer: A. Bunuel hello there by this $$\frac{94}{360}*\frac{5,400,000}{1}$$ you imply that we need to find a fraction of R division ? is my reasoning correct ? Math Expert Joined: 02 Sep 2009 Posts: 95462 Own Kudos [?]: 657810 [1] Given Kudos: 87247 Re: The figure above represents a circle graph of Company H's total expens [#permalink] 1 Kudos Expert Reply dave13 Bunuel 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. Answer: A. Bunuel hello there by this $$\frac{94}{360}*\frac{5,400,000}{1}$$ you imply that we need to find a fraction of R division ? is my reasoning correct ? Yes. Angle x, which represents sector for Division R, is 94/360th of the whole circle. Since the whole circle = total expenses =$5,400,000, then the expenses for Division R = 94/360*$5,400,000. Senior Manager Joined: 05 Aug 2017 Posts: 361 Own Kudos [?]: 481 [1] Given Kudos: 277 Location: India Concentration: Strategy, Marketing WE:Engineering (Energy and Utilities) Re: The figure above represents a circle graph of Company H's total expens [#permalink] 1 Bookmarks 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 ?

P+Q+R+S+T=360
We need to find R=x

(1) x = 94
This statement is sufficient

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

S+T=2R

P+Q+3R=360

This statement is insufficient

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

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. Attachment: Expenses.png Solve the Official Questions more productively Click here for Timed Sectional Tests with Video solutions of each question Also explore Dedicated Data Sufficiency (DS) Course Answer: Option A Video solution by GMATinsight Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK. Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub GMAT Club Legend Joined: 08 Jul 2010 Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator Posts: 6065 Own Kudos [?]: 14123 [0] Given Kudos: 125 Location: India GMAT: QUANT+DI EXPERT Schools: IIM (A) ISB '24 GMAT 1: 750 Q51 V41 WE:Education (Education) Re: The figure above represents a circle graph of Company H's total expens [#permalink] Expert Reply 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.

Attachment:
Expenses.png

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Re: The figure above represents a circle graph of Company H's total expens [#permalink]
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Re: The figure above represents a circle graph of Company H's total expens [#permalink]
Bunuel
dave13
Bunuel

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.

Bunuel hello there

by this $$\frac{94}{360}*\frac{5,400,000}{1}$$ you imply that we need to find a fraction of R division ?

is my reasoning correct ?
Yes. Angle x, which represents sector for Division R, is 94/360th of the whole circle. Since the whole circle = total expenses = $5,400,000, then the expenses for Division R = 94/360*$5,400,000.
­Can second statement, can we not say that sector p would be equal to sector r due to vertically opposite angles? And sector Q would be equal to 2r ?
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Re: The figure above represents a circle graph of Company H's total expens [#permalink]
Bunuel
dave13

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.
Bunuel hello there

by this $$\frac{94}{360}*\frac{5,400,000}{1}$$ you imply that we need to find a fraction of R division ?

is my reasoning correct ?
Yes. Angle x, which represents sector for Division R, is 94/360th of the whole circle. Since the whole circle = total expenses = $5,400,000, then the expenses for Division R = 94/360*$5,400,000.
­Can second statement, can we not say that sector p would be equal to sector r due to vertically opposite angles? And sector Q would be equal to 2r ?
The radii which made up these sectors do not make stright lines.
Re: The figure above represents a circle graph of Company H's total expens [#permalink]
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