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The wait time in minutes, w, for a table at a certain

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The wait time in minutes, w, for a table at a certain

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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

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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
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:

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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