The Guests at a football banquet consumed a total of 401 : GMAT Problem Solving (PS)
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# The Guests at a football banquet consumed a total of 401

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The Guests at a football banquet consumed a total of 401 [#permalink]

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18 Mar 2011, 07:05
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The Guests at a football banquet consumed a total of 401 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?

A. 160
B. 161
C. 162
D. 163
E. 164

[Reveal] Spoiler:
to minimize the number of guests we have to take the maximum consumption of food which is 2.5

minimum number of guests= 401/2.5 = 160.4

as we cannot have decimal number of guests we need to round off for minimum number of guests we must round down which ill become 160.

But OA is 161.

Why guys.pls help

Open discussion of this question is here: the-guests-at-a-football-banquet-consumed-a-total-of-139648.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Sep 2012, 11:23, edited 2 times in total.
Renamed the topic and edited the question.
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18 Mar 2011, 07:10
u are right and in case of people will 161.
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18 Mar 2011, 07:45
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When you take 160 people the average consumption per capita is 401/160=2.50625. Following the Pigeonhole principle there should be at least one man who consumed more than 2.5 pounds.
Actually, you should take higher estimate of number of people to keep yourself under the constraint of 2.5. That is why the answer is 161
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18 Mar 2011, 08:03
GMATD11 wrote:
The guest at a football banquet consumed a total of 401 pounds of food. If no individual guest consumed more than 2.5 pounds of food, what is the minimum number of guests that could have attended the banquet?

to minimize the number of guests we have to take the maximum consumption of food which is 2.5

minimum number of guests= 401/2.5 = 160.4

as we cannot have decimal number of guests we need to round off for minimum number of guests we must round down which ill become 160.

But OA is 161.

Why guys.pls help

In GMAT, please take care before rounding off, esp. in the word problems. For "simplify" type of problems, where approximation is allowed, it is okay to follow the usual rounding off rule.

For this question, visualize it using small numbers;

Say, there was just 6 lbs of food. If 1 person can consume a maximum of 2.5 lbs, what is the minimum number of people you would need to finish off everything?

6/2.5 = 2.4; Usually 2.4 would be rounded off to 2.0 or 2. You are right; but not in this case.

1st person ate 2.5 lbs(He can't eat more than 2.5 lbs)
2nd person ate 2.5 lbs(He can't eat more than that 2.5 lbs)
Food eaten so far = 2.5+2.5=5lbs
6-5= 1 lbs of food is still left. You will have to call in another person to finish off the leftover.

Thus, minimum of 3 people required, not 2.

2.4 is rounded off to the nearest integer greater than 2.4 here.
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27 Sep 2012, 09:03
GMATD11 wrote:
The guest at a football banquet consumed a total of 401 pounds of food. If no individual guest consumed more than 2.5 pounds of food, what is the minimum number of guests that could have attended the banquet?

to minimize the number of guests we have to take the maximum consumption of food which is 2.5

minimum number of guests= 401/2.5 = 160.4

as we cannot have decimal number of guests we need to round off for minimum number of guests we must round down which ill become 160.

But OA is 161.

Why guys.pls help

I believe that this question is vague. It mentions that none eats more than 2.5pounds and it does not mention whether all have eaten to maximum of 2.5 pounds and whether all those who came ate.

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Re: The Guests at a football banquet consumed a total of 401 [#permalink]

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27 Sep 2012, 11:22
The Guests at a football banquet consumed a total of 401 pounds of food. if no individual guest consumed more than 2.5 pounds of food, What is the minimum number of guests that could have attended the banquet?

A. 160
B. 161
C. 162
D. 163
E. 164

To minimize one quantity maximize other.

160*2.5 (max possible amount of food a guest could consume) = 400 pounds, so there must be more than 160 guests, next integer is 161.

Open discussion of this question is here: the-guests-at-a-football-banquet-consumed-a-total-of-139648.html
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Re: The Guests at a football banquet consumed a total of 401   [#permalink] 27 Sep 2012, 11:22
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