DS
A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid $12 more than he or she would have if all diners had contributed equally. Was the total cost of the meal, in dollars, an integer? (1) Four diners left without paying. (2) Six diners paid for the meal.
OA: A
Please explain. Also, Is there any organised way to handle such question. Please explain
@ Priyanshu: Your method is pretty much the way to go for the question. I dont see thats lengthier method, as long as your clear with wat the question has asked ?
Hi Nitish,
Here, the question didn’t ask you to find any particular value.
Rather, its a YES-NO DS asking to check whether cost of the meal is an integer ?
Let say,
X is the cost of the meal.
So, we have to check whether, X is an integer ?
lets consider, initially all the N people agreed to pay, then some “R” people dropped out.
So, according to the information given in the question,
X/N is what supposed to be paid,
But since “R” people dropped out, so then each people will pay,
X/(N-R)
given,
X/(N-R) = X/N + 12
i.e.,
(X/(N-R)) – X/N = 12
RX/N*(N-R) = 12
The above equation we formed it based out of information given in the question,
So, we can re-write it as,
X = {12 * N*(N-R)} / R
Statement I is sufficient:
Given R = 4
So, that means,
X = 3 * N * (N-4),
The above equation clearly says, X is an integer, because N is an integer, then (N-4) is also an integer, then in that case X also an integer and a multiple of 3.
So statement I is sufficient.
Statement II is insufficient:
Given, N-R = 6
Substituting in the equation X,
So, we get,
X = 12 * N * 6 / R
So, X = 72 * N / R
we dont know what is R is ? R may or may not be a factor of 72 or N.
So, statement II is insufficient.
So remember, strategy for these type of questions would be to try forming a expression or relation based out of the given information in the question.
Answer is A.
Hope this helps
Let say there are N ppl at party.
total bill = T
Let X be the share for each = T/N
no some people left without paying bill = let say a
So new share is (T/N )+12 = T/(N-a)
Ta/N =12
option A gives a =4
=> share per head (When all in)= 3$ = T/N
=> So share when when 4 left = 15$ =T/(N-a)
equating we get N =15*a/12
a=4 so N= 5
So T= N*3=15
(* every one leave except the one who paid the bills )
Option B : Six diners paid for the meal.
N-a =6 => N=6+a
this is not helping in removing the additional variable or getting way to remove variables from equations So we probably don’t get the answers with this option.
hence Answer choice A.
This is my method bit lengthy but still my way for GMAT.
Experts Please help with any shortcuts / better ways …
Amazing explanation Aditya! Thanks a lot!