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Word Problems: Manhattan GMAT chapter 7(Optimization)

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by Anantjit » Thu May 19, 2016 1:53 am
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?

I understand by considering the extreme case in which each guest eats as much food as possible, or 2.5 pounds
apiece. The corresponding number of guests at the banquet works out to 401/2.5 = 160.4 people.

Please advise how this number is rounded to 161 and not 160.What is the rationale behind that ?
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by GMATGuruNY » Thu May 19, 2016 2:16 am
Anantjit wrote: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?

I understand by considering the extreme case in which each guest eats as much food as possible, or 2.5 pounds
apiece. The corresponding number of guests at the banquet works out to 401/2.5 = 160.4 people.

Please advise how this number is rounded to 161 and not 160.What is the rationale behind that ?
Let g = the number of guests.
The result in red indicates the following:
g ≥ 160.4.
The value of g must be an INTEGER.
The smallest integer value for g such that g ≥ 160.4 is 161.

Consider the following:
If 160 guests each consume the maximum amount of food -- 2.5 pounds -- then the total weight of the food = (160)(2.5) = 400 pounds.
Since the ACTUAL total weight of the food = 401 pounds, an additional guest is required.
Thus, the minimum value for g is 161.
Last edited by GMATGuruNY on Thu May 19, 2016 11:26 am, edited 1 time in total.
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by OptimusPrep » Thu May 19, 2016 3:20 am
Anantjit wrote: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?

I understand by considering the extreme case in which each guest eats as much food as possible, or 2.5 pounds
apiece. The corresponding number of guests at the banquet works out to 401/2.5 = 160.4 people.

Please advise how this number is rounded to 161 and not 160.What is the rationale behind that ?
Note that we are not rounding off the decimal here.

The maximum food consumed by a guest = 2.5 pounds.
160 people consume 160*2.5 = 400 pounds of food.

The remaining 1 pound would be consumed by one additional guest.

Hence total guests = 161
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by regor60 » Thu May 19, 2016 5:25 am
Or, recognize that if it takes 160.4 people at the maximum consumption level, fewer people, say 160, would have to consume more than the maximum consumption level, therefore needing to increase the number of people to the next person
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by Anantjit » Thu May 19, 2016 7:29 am
How many days after the purchase of Product X does its standard warranty expire?
(1997 is not a leap year.)
(1) When Mark purchased Product X in January 1997, the warranty did not expire
until March 1997.
(2) When Santos purchased Product X in May 1997, the warranty expired in May
1997.


can anyone help me with the above problem .advise me for both 1997 being a leap year and not a leap year
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by DavidG@VeritasPrep » Thu May 19, 2016 7:36 am
Anantjit wrote:How many days after the purchase of Product X does its standard warranty expire?
(1997 is not a leap year.)
(1) When Mark purchased Product X in January 1997, the warranty did not expire
until March 1997.
(2) When Santos purchased Product X in May 1997, the warranty expired in May
1997.


can anyone help me with the above problem .advise me for both 1997 being a leap year and not a leap year
Please start a new thread when posting a fresh question - it's harder for users to search for specific problems when questions are mixed together.
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by Anantjit » Thu May 19, 2016 7:45 am
https://www.beatthegmat.com/word-problem ... tml#774570

I started that but did not get response so added here
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