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

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

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New post 08 Jan 2010, 14:25
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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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Re: The total cost  [#permalink]

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New post 08 Jan 2010, 17:02
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2
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.
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Re: marked d as an aswer butit is wrong...  [#permalink]

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New post 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)

Answer C.

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.

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Re: The total cost  [#permalink]

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New post 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! :-D
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Re: The total cost  [#permalink]

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New post 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! :-D


"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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: The total cost  [#permalink]

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New post 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!!!!!!!!!!!!!!!!!

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

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New post 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

Answer: Option C
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The total cost of an office dinner was shared equally by k  [#permalink]

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New post 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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The total cost of an office dinner was shared equally by k &nbs [#permalink] 01 Apr 2018, 22:35
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