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A certain catering company's cost to cater a dinner for n people is 5 24 Jan 2024, 01:17
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A certain catering company's cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Based on this formula, how much more was the company's cost per person for a dinner that it catered on Wednesday than for a dinner that it catered on Tuesday?

(1) The number of people for whom the company catered the dinner on Wednesday was twice the number for whom it catered on Tuesday.

(2) The number of people for whom the company catered the dinner on Tuesday was 25 less than the number for whom it catered on Wednesday.

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A certain catering company's cost to cater a dinner for n people is 5 24 Jan 2024, 13:34
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A certain catering company's cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Based on this formula, how much more was the company's cost per person for a dinner that it catered on Wednesday than for a dinner that it catered on Tuesday?

(1) The number of people for whom the company catered the dinner on Wednesday was twice the number for whom it catered on Tuesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was 2x. Hence, we need to calculate the difference in cost per person: \((50 + \frac{2x}{2}) - (50 + \frac{x}{2}) = \frac{x}{2}\). Without knowing the value of x, we cannot determine this value. Not sufficient.

(2) The number of people for whom the company catered the dinner on Tuesday was 25 less than the number for whom it catered on Wednesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was x + 25. Hence, we need to calculate the difference in cost per person: \((50 + \frac{x+25}{2})-(50 + \frac{x}{2})=12.5\).. This gives us a definitive value. Sufficient.

Answer: B.
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A certain catering company's cost to cater a dinner for n people is 5 03 Jun 2024, 04:52
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­Here is a detailed video solution for this interesting question.
See how this question can be solved in the test environment using "Owning the Dataset" approach.



Let us know if you have any questions.­
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A certain catering company's cost to cater a dinner for n people is 5 23 Oct 2024, 21:16
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Thank you for posting!

Can you please help me understand GMAT sense here? The way I'm looking at the problem, company's cost per person should be either:
(i) n/2 .... which would be equivalent for each as its given in the problem, and at that point would be sufficient, OR
(ii) (50 + (n/2))/n which would be the true cost per person... i.e. the total cost of the event divided by the number of atendees.

I believe you calculated the difference in total variable costs, and not the difference in cost per person

Using BOTH statements (1) and (2) we can calculate the number of attendees for both days as being 25 (Tuesday) and 50 (Wednesday), setting Wednesday = Tuesday + 25 equal to: Wednesday/Tuesday = 2

Knowing this, we can solve for the total costs on each day --> the total costs per person on each day and finally --> the delta in cost per person between Wednesday (1.5 / person) and Tuesday (2.5/person) = delta = 1.0 per person more expensive on Tuesday.

So the way I see it, the answer, while not clear, should be either:
– answer D (each statement alone is sufficient) in option (i) above since it is solveable WITHOUT either statements (1) or (2), and thus providing either answer is already sufficient... OR
– annswer C (BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient)

Any help greatly apprecaited. Thanks!




Bunuel
A certain catering company's cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Based on this formula, how much more was the company's cost per person for a dinner that it catered on Wednesday than for a dinner that it catered on Tuesday?

(1) The number of people for whom the company catered the dinner on Wednesday was twice the number for whom it catered on Tuesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was 2x. Hence, we need to calculate the difference in cost per person: \((50 + \frac{2x}{2}) - (50 + \frac{x}{2}) = \frac{x}{2}\). Without knowing the value of x, we cannot determine this value. Not sufficient.

(2) The number of people for whom the company catered the dinner on Tuesday was 25 less than the number for whom it catered on Wednesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was x + 25. Hence, we need to calculate the difference in cost per person: \((50 + \frac{x+25}{2})-(50 + \frac{x}{2})=12.5\).. This gives us a definitive value. Sufficient.

Answer: B.
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A certain catering company's cost to cater a dinner for n people is 5 24 Oct 2024, 02:00
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GMATnovice1410
Thank you for posting!

Can you please help me understand GMAT sense here? The way I'm looking at the problem, company's cost per person should be either:
(i) n/2 .... which would be equivalent for each as its given in the problem, and at that point would be sufficient, OR
(ii) (50 + (n/2))/n which would be the true cost per person... i.e. the total cost of the event divided by the number of atendees.

I believe you calculated the difference in total variable costs, and not the difference in cost per person

Using BOTH statements (1) and (2) we can calculate the number of attendees for both days as being 25 (Tuesday) and 50 (Wednesday), setting Wednesday = Tuesday + 25 equal to: Wednesday/Tuesday = 2

Knowing this, we can solve for the total costs on each day --> the total costs per person on each day and finally --> the delta in cost per person between Wednesday (1.5 / person) and Tuesday (2.5/person) = delta = 1.0 per person more expensive on Tuesday.

So the way I see it, the answer, while not clear, should be either:
– answer D (each statement alone is sufficient) in option (i) above since it is solveable WITHOUT either statements (1) or (2), and thus providing either answer is already sufficient... OR
– annswer C (BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient)

Any help greatly apprecaited. Thanks!




Bunuel
A certain catering company's cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Based on this formula, how much more was the company's cost per person for a dinner that it catered on Wednesday than for a dinner that it catered on Tuesday?

(1) The number of people for whom the company catered the dinner on Wednesday was twice the number for whom it catered on Tuesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was 2x. Hence, we need to calculate the difference in cost per person: \((50 + \frac{2x}{2}) - (50 + \frac{x}{2}) = \frac{x}{2}\). Without knowing the value of x, we cannot determine this value. Not sufficient.

(2) The number of people for whom the company catered the dinner on Tuesday was 25 less than the number for whom it catered on Wednesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was x + 25. Hence, we need to calculate the difference in cost per person: \((50 + \frac{x+25}{2})-(50 + \frac{x}{2})=12.5\).. This gives us a definitive value. Sufficient.

Answer: B.
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The stem clearly says that the cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Thus, if there is 1 person to cater for, so if n = 1, the cost per person would be \(50 + \frac{1}{2}\). For 2 people, so if n = 2, the cost per person would be \(50 + \frac{2}{2}\), and so on.
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A certain catering company's cost to cater a dinner for n people is 5 02 Nov 2024, 21:26
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I see now where I misunderstood. Thank you very much for the reply!
Bunuel
GMATnovice1410
Thank you for posting!

Can you please help me understand GMAT sense here? The way I'm looking at the problem, company's cost per person should be either:
(i) n/2 .... which would be equivalent for each as its given in the problem, and at that point would be sufficient, OR
(ii) (50 + (n/2))/n which would be the true cost per person... i.e. the total cost of the event divided by the number of atendees.

I believe you calculated the difference in total variable costs, and not the difference in cost per person

Using BOTH statements (1) and (2) we can calculate the number of attendees for both days as being 25 (Tuesday) and 50 (Wednesday), setting Wednesday = Tuesday + 25 equal to: Wednesday/Tuesday = 2

Knowing this, we can solve for the total costs on each day --> the total costs per person on each day and finally --> the delta in cost per person between Wednesday (1.5 / person) and Tuesday (2.5/person) = delta = 1.0 per person more expensive on Tuesday.

So the way I see it, the answer, while not clear, should be either:
– answer D (each statement alone is sufficient) in option (i) above since it is solveable WITHOUT either statements (1) or (2), and thus providing either answer is already sufficient... OR
– annswer C (BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient)

Any help greatly apprecaited. Thanks!




Bunuel
A certain catering company's cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Based on this formula, how much more was the company's cost per person for a dinner that it catered on Wednesday than for a dinner that it catered on Tuesday?

(1) The number of people for whom the company catered the dinner on Wednesday was twice the number for whom it catered on Tuesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was 2x. Hence, we need to calculate the difference in cost per person: \((50 + \frac{2x}{2}) - (50 + \frac{x}{2}) = \frac{x}{2}\). Without knowing the value of x, we cannot determine this value. Not sufficient.

(2) The number of people for whom the company catered the dinner on Tuesday was 25 less than the number for whom it catered on Wednesday.

Assuming the number for whom the company catered on Tuesday was x, then the number of people for whom the company catered the dinner on Wednesday was x + 25. Hence, we need to calculate the difference in cost per person: \((50 + \frac{x+25}{2})-(50 + \frac{x}{2})=12.5\).. This gives us a definitive value. Sufficient.

Answer: B.

The stem clearly says that the cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Thus, if there is 1 person to cater for, so if n = 1, the cost per person would be \(50 + \frac{1}{2}\). For 2 people, so if n = 2, the cost per person would be \(50 + \frac{2}{2}\), and so on.
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A certain catering company's cost to cater a dinner for n people is 5 29 Jan 2025, 22:16
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guddo
A certain catering company's cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person. Based on this formula, how much more was the company's cost per person for a dinner that it catered on Wednesday than for a dinner that it catered on Tuesday?

(1) The number of people for whom the company catered the dinner on Wednesday was twice the number for whom it catered on Tuesday.

(2) The number of people for whom the company catered the dinner on Tuesday was 25 less than the number for whom it catered on Wednesday.

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Cost to cater a dinner for n people is \(50 + \frac{n}{2}\) dollars per person.

Cost for 1 person = $50.5/person
Cost with 2 people = $51/person
Cost with 3 people = $51.5/person
etc. So cost per person simply increases by $0.5 for every additional person.

Question: how much more was the company's cost per person for a dinner that it catered on Wednesday than for a dinner that it catered on Tuesday?
For this, we need to find how many more people were present on Wednesday than on Tuesday.

(1) The number of people for whom the company catered the dinner on Wednesday was twice the number for whom it catered on Tuesday.

We do not know how many additional people were there on Wednesday.
If there were 100 people on Tuesday and 200 on Wednesday, additional per person cost on Wednesday will be $50.
If there were 10 people on Tuesday and 20 on Wednesday, additional per person cost on Wednesday will be $5.
Not sufficient.

(2) The number of people for whom the company catered the dinner on Tuesday was 25 less than the number for whom it catered on Wednesday.

There were 25 additional people on Wednesday. This means the additional per person cost on Wednesday was $12.5.
Sufficient alone

Answer (B)
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