The total cost of an office dinner was shared equally by k of the n em

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

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

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

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

Answer: Option C

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.

Hi,
Can anyone plz tell me what is the meaning of k of the n employees? Isnt it total employees are k and n are selected? Hence equation will ne n*k?
Please guide

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That means that there were n employees at the dinner and only k of them payed. For example, there were 20 (n) employees and only 18 (k) of them payed, the remaining 2 did not.

Thank you so much, its clear now

Solution:

Question Stem Analysis:

We need to determine the total cost of the dinner given that k people contribute an equal amount for the dinner. Notice that if we know the value of k and the amount that each of these k people contributes, then we can determine the total cost of the dinner.

Statement One Alone:

The total cost of the dinner was 19k. However, since we don’t know the value of k, we can’t determine the total cost of the dinner. Statement one alone is not sufficient.

Statement Two Alone:

The total cost of the dinner was 18(k + 1). Again, since we don’t know the value of k, we can’t determine the total cost of the dinner. Statement two alone is not sufficient.

Statements One and Two Together:

From statement one, we know the total cost of the dinner was 19k, and from statement two, we know that the total cost of the dinner was 18(k + 1). Therefore,, we can create the equation:

19k = 18(k + 1)

19k = 18k + 18

k = 18

It follows that the total cost of the dinner is 19 x 18 = $342. Both statements together are sufficient.

Answer: C

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