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# George baked a total of 125 pizzas for 7 straight days, beginning on

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Math Expert
Joined: 02 Sep 2009
Posts: 60484
George baked a total of 125 pizzas for 7 straight days, beginning on  [#permalink]

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18 Nov 2015, 01:36
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Difficulty:

85% (hard)

Question Stats:

49% (02:36) correct 51% (02:49) wrong based on 100 sessions

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George baked a total of 125 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?

A. 3
B. 4
C. 5
D. 7
E. 10

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Re: George baked a total of 125 pizzas for 7 straight days, beginning on  [#permalink]

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18 Nov 2015, 02:01
Number of pizzas George baked on Saturday = (3/5)*125 = 75
Number of pizzas George baked on Sunday = (3/5)*(125-75)=(3/5)*50 = 30
We now have 20 pizzas which has to distributed among the remaining 5 days - Monday- Friday
Average pizzas per day for last 5 days = 20/5 = 4
Since each successive day George baked fewer pizzas than the previous day , to maximize number of pizzas
baked on Wednesday , we need to bake the least number of pizzas possible on Monday and Tuesday .
Number of pizzas baked on Monday = 7
Number of pizzas baked on Tuesday = 6
Max number of pizzas baked on Wednesday = 5
number of pizzas baked on Thursday = 2
number of pizzas baked on Friday = 0

P.S-If there was restriction that atleast one pizza was baked on each day then max number of pizzas baked on Wednesday would have been =4
Pizzas baked from Monday - Friday would have been 6,5,4,3,2
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Re: George baked a total of 125 pizzas for 7 straight days, beginning on  [#permalink]

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29 Nov 2015, 12:48
Hi All,

This question could have been written in a slightly clearer way (The intent is that a total number of pizzas is meant to be 125 over the course of 7 days; at least one pizza is cooked on each day).

3/5 of the 125 pizzas cooked on Saturday = 75 pizzas
3/5 of the remaining pizzas on Sunday = 30 pizzas

We're left with 20 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers. We're asked for the maximum number of pizzas that could have been made on Wednesday (re: on the 5th day). To maximize THAT number, we have to minimize all of the other numbers, while still following all of the other restrictions that the prompt described.

_ _ _ _ _

We'll start by making the 6th and 7th days 2 pizzas and 1 pizza, respectively...

_ _ _ 2 1

This leaves us with 17 pizzas for the remaining 3 days....we could have....

10 4 3 2 1 with 3 on Wednesday, but that's NOT the maximum
8 5 4 2 1 here we have 4 on Wednesday.

_ _ 5 2 1 is NOT possible though, since we would have 12 pizzas for the remaining 2 days, but no way to satisfy the other restrictions.

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Joined: 30 Nov 2015
Posts: 3
Re: George baked a total of 125 pizzas for 7 straight days, beginning on  [#permalink]

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15 Dec 2015, 08:16
EMPOWERgmatRichC wrote:
Hi All,

This question could have been written in a slightly clearer way (The intent is that a total number of pizzas is meant to be 125 over the course of 7 days; at least one pizza is cooked on each day).

3/5 of the 125 pizzas cooked on Saturday = 75 pizzas
3/5 of the remaining pizzas on Sunday = 30 pizzas

We're left with 20 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers. We're asked for the maximum number of pizzas that could have been made on Wednesday (re: on the 5th day). To maximize THAT number, we have to minimize all of the other numbers, while still following all of the other restrictions that the prompt described.

_ _ _ _ _

We'll start by making the 6th and 7th days 2 pizzas and 1 pizza, respectively...

_ _ _ 2 1

This leaves us with 17 pizzas for the remaining 3 days....we could have....

10 4 3 2 1 with 3 on Wednesday, but that's NOT the maximum
8 5 4 2 1 here we have 4 on Wednesday.

_ _ 5 2 1 is NOT possible though, since we would have 12 pizzas for the remaining 2 days, but no way to satisfy the other restrictions.

GMAT assassins aren't born, they're made,
Rich

Why isn't 75 30 8 6 5 1 0 possible? It satisfies all the conditions of the question. The question doesn't say that george cannot bake a non-zero pizza any day.
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Joined: 02 Aug 2009
Posts: 8347
Re: George baked a total of 125 pizzas for 7 straight days, beginning on  [#permalink]

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15 Dec 2015, 09:59
voraniket wrote:
EMPOWERgmatRichC wrote:
Hi All,

This question could have been written in a slightly clearer way (The intent is that a total number of pizzas is meant to be 125 over the course of 7 days; at least one pizza is cooked on each day).

3/5 of the 125 pizzas cooked on Saturday = 75 pizzas
3/5 of the remaining pizzas on Sunday = 30 pizzas

We're left with 20 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers. We're asked for the maximum number of pizzas that could have been made on Wednesday (re: on the 5th day). To maximize THAT number, we have to minimize all of the other numbers, while still following all of the other restrictions that the prompt described.

_ _ _ _ _

We'll start by making the 6th and 7th days 2 pizzas and 1 pizza, respectively...

_ _ _ 2 1

This leaves us with 17 pizzas for the remaining 3 days....we could have....

10 4 3 2 1 with 3 on Wednesday, but that's NOT the maximum
8 5 4 2 1 here we have 4 on Wednesday.

_ _ 5 2 1 is NOT possible though, since we would have 12 pizzas for the remaining 2 days, but no way to satisfy the other restrictions.

GMAT assassins aren't born, they're made,
Rich

Why isn't 75 30 8 6 5 1 0 possible? It satisfies all the conditions of the question. The question doesn't say that george cannot bake a non-zero pizza any day.

Hi,
if the 7th day there have been none pizzas cooked, the Q would hav esaid that "George baked a total of 125 pizzas for 6 straight days, beginning on Saturday"...
we have 20 for remaining 5 days..
for the middle term, wednesday here, to be max, the higher term should be as close as possible to middle term and the lower terms the smallest possible..
so last two days.. 2,1
remaining three ddays 20-3=17..
as all are different, the middle should be closest to average..
17/3 nearly 6,,
if we take three terms then as 7,6,5, total =18, which is one shorter..
that shortage has to be made up from the lowest term here, ..
so wed , max can be 4..
B
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Re: George baked a total of 125 pizzas for 7 straight days, beginning on   [#permalink] 15 Dec 2015, 09:59
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