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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]

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31 Dec 2013, 07:20
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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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Re: The total cost of an office dinner was shared equally by k o  [#permalink]

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31 Dec 2013, 07:20
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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]

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01 Jan 2014, 22:22

(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]

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02 Jan 2014, 00:41
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
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Re: The total cost of an office dinner was shared equally by k o  [#permalink]

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04 Jan 2014, 02:23
1
aja1991 wrote:

(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.
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Re: The total cost of an office dinner was shared equally by k o  [#permalink]

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04 Jan 2014, 03:33
1
1
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

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

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05 Jan 2014, 11:47
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]

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20 Mar 2019, 12:52
Bunuel wrote:
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.

Thanks for the solution, Bunuel.

When we consider both statements 1 and 2 together we make the equation equal. Why is that? I understand we can then solve for k but I don't understand why we have to make them equal.
Re: The total cost of an office dinner was shared equally by k o   [#permalink] 20 Mar 2019, 12:52
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