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The wait time in minutes, w, for a table at a certain restau
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sandy
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
The wait time in minutes, w, for a table at a certain restau [#permalink] New post  30 Jul 2018, 09:36
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The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula \(w = d^2 + kn\), 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
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sandy
Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: The wait time in minutes, w, for a table at a certain restau [#permalink] New post  12 Aug 2018, 05:38
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Explanation

Start by solving for the constant, k. A party of 4 (d = 4) has an estimated wait time of 40 minutes (w = 40) when 6 other parties are ahead of it (n = 6). Plug these values into the formula:

\(w = d^2 + kn\)
\(40 = 4^2 + k(6)\)
\(40 = 16 + 6k\)
\(24 = 6k\)
\(k = 4\)

Then solve for the wait time for a party of 6 (d = 6) if there are 3 parties ahead of it (n = 3), using the constant k = 4 determined above:
\(w = d^2 + kn\)
\(w = 6^2 + 4(3)\)
\(w = 36 + 12\)
\(w = 48\) minutes
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Re: The wait time in minutes, w, for a table at a certain restau [#permalink] New post  21 Jan 2019, 18:28
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sandy wrote:
The wait time in minutes, w, for a table at a certain restaurant can be estimated by the formula \(w = d^2 + kn\), 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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