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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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

by Vincen » Fri Jun 19, 2020 2:23 am

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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.

[spoiler]OA=C[/spoiler]

Source: Official Guide

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 19, 2020 2:23 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

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

by deloitte247 » Sun Jun 21, 2020 10:18 am

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Target question => What was the total cost of the dinner?
Let total cost = t

Statement 1 => Each of the k employees who shared the cost of the dinner paid $19
Each k employee paid $19
Therefore, t = 19k, but the value of k is not known. Hence, t cannot be evaluated. Statement 1 is 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
If it was shared equally by k + 1 then each k + 1 employees paid $18
Therefore, t = 18(k + 1). The value of k is not known and t cannot be evaluated, statement 2 is NOT SUFFICIENT

Combining both statements together =>
t = 19k .........eqn 1
t = 18(k + 1)..........eqn 2 substitute t in eqn 2
19k = 18(k + 1)
19k = 18k + 18
19k - 18k = 18
k = 18
Therefore, t = 19k where k = 18
t = 19 * 18 = $342

Both statements together ARE SUFFICIENT
Answer = C

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

by Scott@TargetTestPrep » Wed Jun 30, 2021 9:35 am

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Vincen wrote: ↑
Fri Jun 19, 2020 2:23 am
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.

[spoiler]OA=C[/spoiler]

Source: Official Guide

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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