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# The total cost of an office dinner was shared equally by k o

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The total cost of an office dinner was shared equally by k o [#permalink]  31 Dec 2013, 06:20
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner?

(1) Each of the k employees who shared the cost of the dinner paid $19. (2) If the total cost of the dinner had been shared equally by k +1 of the n employees who attended the dinner, each of the k +1 employees would have paid$18.

Data Sufficiency
Question: 13
Category: Algebra Simultaneous equations
Page: 154
Difficulty: 650

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Math Expert
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Posts: 31301
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Kudos [?]: 62490 [0], given: 9457

Re: The total cost of an office dinner was shared equally by k o [#permalink]  31 Dec 2013, 06:20
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SOLUTION

The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner?

(1) Each of the k employees who shared the cost of the dinner paid $19 --> the total cost of the dinner was 19k. Not sufficient. (2) If the total cost of the dinner had been shared equally by k +1 of the n employees who attended the dinner, each of the k +1 employees would have paid$18 --> the total cost of the dinner was 18(k+1). Not sufficient.

(1)+(2) We can solve the two equations we have to get k and then get the value of 19k. Sufficient.

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Re: The total cost of an office dinner was shared equally by k o [#permalink]  01 Jan 2014, 21:22

(1) is obviously sufficient.

(2) is also sufficient because (k+1)18=19k. From this euality we can find k wich can lead us the solution of the problem.
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Re: The total cost of an office dinner was shared equally by k o [#permalink]  01 Jan 2014, 23:41
The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner?

(1) Each of the k employees who shared the cost of the dinner paid $19. (2) If the total cost of the dinner had been shared equally by k +1 of the n employees who attended the dinner, each of the k +1 employees would have paid$18.

Sol: Since the cost was shared equally by K employees. Let the contribution of each of the K employees be x then Total Cost of the dinner = K*x

From St 1 we have that x=19 so Total cost =19K (Not sufficient)
From st 2 we have (K+1)*18= Total cost of Dinner (Not Sufficient)

Combining we get that St 1 = St2 ie. Total Dinner cost is same. So

19K= (K+1)*18 or K =18 and Total Cost of Dinner : 18*19 = $342 Ans C _________________ “If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.” Manager Joined: 27 May 2012 Posts: 213 Followers: 0 Kudos [?]: 57 [1] , given: 428 Re: The total cost of an office dinner was shared equally by k o [#permalink] 04 Jan 2014, 01:23 1 This post received KUDOS aja1991 wrote: The correct answer is D! (1) is obviously sufficient. (2) is also sufficient because (k+1)18=19k. From this euality we can find k wich can lead us the solution of the problem. A is not suff. B also not suff. how did you get 19K from statement B alone ? This 19 is obviously given in statement 1 let total cost be x then from (1) x/k = 19 we do not know K hence insuff. from (2) x/(k+1) = 18 again we do not know k+1 hence insuff. 1+2 2 linear distinct equations hence we can solve for x = total cost which is 342, suff. answer is C _________________ - Stne Manager Joined: 20 Dec 2013 Posts: 125 Followers: 6 Kudos [?]: 76 [1] , given: 1 Re: The total cost of an office dinner was shared equally by k o [#permalink] 04 Jan 2014, 02:33 1 This post received KUDOS 1 This post was BOOKMARKED The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner? (1) Each of the k employees who shared the cost of the dinner paid$19.
(2) If the total cost of the dinner had been shared equally by k +1 of the n employees who attended the dinner, each of the k +1 employees would have paid $18. Total cost of the dinner: k(cost paid by each employee) Statement I is insufficient It just tells about the cost paid by each employee however we need the total cost of the dinner means the value of k as well. Statement II is insufficient Total cost of dinner = 18(k+1) Again value of k is unknown Combining is sufficient Total cost = 19k = 18(k+1) 18k + k = 18k + 18 k = 18 Hence answer is C Math Expert Joined: 02 Sep 2009 Posts: 31301 Followers: 5362 Kudos [?]: 62490 [0], given: 9457 Re: The total cost of an office dinner was shared equally by k o [#permalink] 05 Jan 2014, 10:47 Expert's post SOLUTION The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner? (1) Each of the k employees who shared the cost of the dinner paid$19 --> the total cost of the dinner was 19k. Not sufficient.

(2) If the total cost of the dinner had been shared equally by k +1 of the n employees who attended the dinner, each of the k +1 employees would have paid \$18 --> the total cost of the dinner was 18(k+1). Not sufficient.

(1)+(2) We can solve the two equations we have to get k and then get the value of 19k. Sufficient.

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Re: The total cost of an office dinner was shared equally by k o [#permalink]  24 Feb 2015, 02:50
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Re: The total cost of an office dinner was shared equally by k o   [#permalink] 24 Feb 2015, 02:50
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