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
\(K\)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.
\(K+1\) 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.
it is implied that the amount paid by \(K\) members, each paying \($19\), is equilent to that paid by \(K+1\) members, each paying \($18\)
==> \(19K\) = \(18(K+1)\)
==> 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
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
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.