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

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Manager
Joined: 22 Jul 2009
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Location: Manchester UK
The total cost of an office dinner was shared equally by k  [#permalink]

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08 Jan 2010, 14:25
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78% (01:28) correct 22% (01:17) wrong based on 242 sessions

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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.
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Joined: 02 Sep 2009
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08 Jan 2010, 17:02
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sagarsabnis wrote:
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.

Cost (C)=?

(1) 19k=C, insufficient;
(2) 18(k+1)=C, insufficient;

(1)+(2) 19k=C=18(k+1) --> 19k=18(k+1) --> k=18 --> C=19k=19*18. Sufficient.

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Manager
Joined: 30 Aug 2010
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Location: Bangalore, India
Re: marked d as an aswer butit is wrong...  [#permalink]

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11 Feb 2011, 03:59
4
alltimeacheiver wrote:
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

stmnt1:

$$K$$members each paid $$19$$
==> total cost is $$19K$$
but the total cost can not be found as we do not know how many ($$K$$) members paid that amount.
NOT SUFF.

stmnt2:

$$K+1$$ members paid $$18$$ each
==> total cost is $$18(K+1)$$
but the total cost can not be found as we do not know how many ($$k+1$$) members paid that amount.
NOT SUFF.

1&2 together

it is implied that the amount paid by $$K$$ members, each paying $$19$$, is equilent to that paid by $$K+1$$ members, each paying $$18$$

==> $$19K$$ = $$18(K+1)$$

==> $$K=18$$
==> the toal cost of the dinner is $$19K$$ = $$18(K+1)$$ = $$18*19$$= $$342$$ (costly dinner, i would never go to that restaurant)

Now in the $$GMAT$$ way (with out using variables such as x).

the total cost is paid by K members each paying $19 and also given that the total cost could have been paid by K+1 members if each had payed$18

Means

if we added one person into the payees list, the cost for each person would be REDUCED by $$1$$ (from $$19$$to $$18$$) making the new person to pay $$18$$. this implies that the new person has bared $$18$$ of the total cost and made each of the original list of ppl to pay $$1$$ less. implies, The # of original ppl shud be $$18$$ so that the new person can pay $18 baring $$1$$ from each of the original list of people (original payees). means the orginal people were $$18$$ and paid $$19$$ each OR with an additional person , the total # of people is $$19$$ each paying $$18$$ ==> the total cost = $$18*19$$ OR $$19*18$$ TRY solving the GMAT questions in the second way. Most of the word problems can be. It is called "THINK without INK". Hope it helps. Regards, Murali. Kudos? Intern Joined: 09 Dec 2012 Posts: 3 Re: The total cost [#permalink] ### Show Tags 22 Dec 2012, 14:56 Bunuel wrote: sagarsabnis wrote: 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. Cost (C)=? (1) 19k=C, insufficient; (2) 18(k+1)=C, insufficient; (1)+(2) 19k=C=18(k+1) --> 19k=18(k+1) --> k=18 --> C=19k=19*18. Sufficient. Answer: C. Hi! Thanks for the explanation! Please help me with this phrase: "k of the n employees" I cannot understand what for is "n" near employees? THANKS! Math Expert Joined: 02 Sep 2009 Posts: 50002 Re: The total cost [#permalink] ### Show Tags 23 Dec 2012, 06:13 1 GMATCan wrote: Bunuel wrote: sagarsabnis wrote: 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. Cost (C)=? (1) 19k=C, insufficient; (2) 18(k+1)=C, insufficient; (1)+(2) 19k=C=18(k+1) --> 19k=18(k+1) --> k=18 --> C=19k=19*18. Sufficient. Answer: C. Hi! Thanks for the explanation! Please help me with this phrase: "k of the n employees" I cannot understand what for is "n" near employees? THANKS! "The total cost of an office dinner was shared equally by k of the n employees who attended the dinner" means that there were total of n employees and k employees out of n shared equally the cost of the dinner. _________________ Intern Joined: 09 Dec 2012 Posts: 3 Re: The total cost [#permalink] ### Show Tags 23 Dec 2012, 07:29 "The total cost of an office dinner was shared equally by k of the n employees who attended the dinner" means that there were total of n employees and k employees out of n shared equally the cost of the dinner. THANKS for the clear explanation!!!!!!!!!!!!!!!!! +1 KUDOS CEO Joined: 08 Jul 2010 Posts: 2559 Location: India GMAT: INSIGHT WE: Education (Education) Re: The total cost of an office dinner was shared equally by k [#permalink] ### Show Tags 07 Jul 2015, 14:59 1 sagarsabnis wrote: 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. Question : Total Cost of Dinner = No. of Contributor*Contribution amount of each person = ? Statement 1: Each of the k employees who shared the cost of the dinner paid$19.

i.e. Total Cost of Dinner = 19*k
Since k is unknown hence
NOT SUFFICIENT

Statement 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. i.e. Total Cost of Dinner = 18*(k+1) Since k is unknown hence NOT SUFFICIENT Combining the two statements i.e. Total Cost of Dinner = 18*(k+1) = 19*k i.e. k =18 i.e. Total Cost = 19*18 =$342
SUFFICIENT

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Manager
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The total cost of an office dinner was shared equally by k  [#permalink]

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01 Apr 2018, 22:35
Let the cost be C.

(1) C = 19K , Insufficient
(2) C = 18(k+1) , Insufficient

Combining 1 and 2 :

$$1 = \frac{C}{K} - \frac{C}{K+1}$$
$$1 = \frac{19K}{K} - \frac{19K}{K+1}$$
Solving we get K=20

Option C.
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