Source: Manhattan GMAT
The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula w=d2+knw=d2+kn, where d is the number of diners in the party, k is a constant, and n is the number of parties ahead in line at the beginning of the wait. If a party of 4 has an estimated wait time of 40 minutes when 6 other parties are ahead of it, how many minutes would the estimated wait time be for a party of 6 if there are 3 parties ahead of it?
A. 28
B. 33
C. 39
D. 42
E. 48
The OA is E
The wait time in minutes, w, for a table at a certain
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We are given that a party of 4 has a wait time of 40 minutes when 6 other parties are ahead of it. We can use this information to determine the value of k in the following equation:BTGmoderatorLU wrote:Source: Manhattan GMAT
The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula w=d2+knw=d2+kn, where d is the number of diners in the party, k is a constant, and n is the number of parties ahead in line at the beginning of the wait. If a party of 4 has an estimated wait time of 40 minutes when 6 other parties are ahead of it, how many minutes would the estimated wait time be for a party of 6 if there are 3 parties ahead of it?
A. 28
B. 33
C. 39
D. 42
E. 48
40 = 4^2 + k(6)
40 = 16 + 6k
24 = 6k
4 = k
Now that we know that k = 4, we can find the wait time of a party of 6 when there are 3 parties ahead of it:
w = 6^2 + 4(3) = 36 + 12 = 48
Answer: E
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