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# Over the course of 5 days, Monday through Friday, Danny collects a tot

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Director
Joined: 12 Feb 2015
Posts: 841
Over the course of 5 days, Monday through Friday, Danny collects a tot  [#permalink]

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20 Jul 2018, 10:30
1
7
00:00

Difficulty:

85% (hard)

Question Stats:

52% (02:38) correct 48% (02:46) wrong based on 188 sessions

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Over the course of 5 days, Monday through Friday, Danny collects a total of 76 baseball cards. Each day, he collects a different number of cards. If Danny collects the largest number of cards on Friday and the second largest number of cards on Thursday, did Danny collect more than 8 cards on Thursday?

(1) On Friday, Danny collected 49 cards.

(2) On one of the first 3 days, Danny collected 6 cards.

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Manish

"Only I can change my life. No one can do it for me"
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Posts: 841
Re: Over the course of 5 days, Monday through Friday, Danny collects a tot  [#permalink]

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20 Jul 2018, 10:33
1

Over the course of 5 days, Monday through Friday, Danny collects a total of 76 baseball cards. Each day, he collects a different number of cards. If Danny collects the largest number of cards on Friday and the second largest number of cards on Thursday, did Danny collect more than 8 cards on Thursday?

Step 1: Analyze the Question Stem
This is a Yes/No question that is packed with information in the stem. Danny collects a different number of cards each of the 5 days. He collects the largest number of cards on Friday and the second largest number on Thursday. The question asks if Danny collected more than 8 cards on Thursday.

Step 2: Evaluate the Statements
Statement (1): The largest number of cards collected on Thursday that would result in a “no” answer to the question is 8. Since the number of cards collected Monday, Tuesday, and Wednesday is different each day and must be less than 8, the maximum numbers of cards he could collect on those days are 5, 6, and 7. Totaling up all the days, 5 + 6 + 7 + 8 + 49 = 75.
Collecting 8 cards on Thursday does not enable Danny to collect 76 cards in total given the constraints of the question, so the information in Statement (1) means that Danny must have collected more than 8 cards on Thursday. Statement (1) is sufficient to answer “always yes,” so eliminate choices (B), (C), and (E).

Statement (2): If Danny collects 6 cards on one of the first 3 days, the fewest cards he could have collected on those days would be 6 + 2 + 1 = 9, leaving 76 − 9 = 67 cards to be collected on Thursday and Friday. Danny could have collected 7 cards on Thursday and 60 on Friday, in which case the answer to the question is “no.” Alternatively, he could have collected as many as 33 cards on Thursday and 34 on Friday and the answer would be “yes.” Therefore, statement (2) is insufficient.

Choice (A) is correct.
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Manish

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Re: Over the course of 5 days, Monday through Friday, Danny collects a tot  [#permalink]

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20 Jul 2018, 14:50
CAMANISHPARMAR wrote:
Over the course of 5 days, Monday through Friday, Danny collects a total of 76 baseball cards. Each day, he collects a different number of cards. If Danny collects the largest number of cards on Friday and the second largest number of cards on Thursday, did Danny collect more than 8 cards on Thursday?
1. On Friday, Danny collected 49 cards.
2. On one of the first 3 days, Danny collected 6 cards.

1. On Friday, Danny collected 49 cards.
Cards remaining 27
we have to maximize Monday in order to minimize the number of cards he can collect on Thursday.
since he collects different number of cards and he collects second largest number of cards on Thursday
He will always collect > 8 cards on Thurs day

2. On one of the first 3 days, Danny collected 6 cards.
Clearly insufficient

A
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Re: Over the course of 5 days, Monday through Friday, Danny collects a tot  [#permalink]

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24 Sep 2018, 09:48
CounterSniper wrote:
CAMANISHPARMAR wrote:
Over the course of 5 days, Monday through Friday, Danny collects a total of 76 baseball cards. Each day, he collects a different number of cards. If Danny collects the largest number of cards on Friday and the second largest number of cards on Thursday, did Danny collect more than 8 cards on Thursday?
1. On Friday, Danny collected 49 cards.
2. On one of the first 3 days, Danny collected 6 cards.

1. On Friday, Danny collected 49 cards.
Cards remaining 27
we have to maximize Monday in order to minimize the number of cards he can collect on Thursday.
since he collects different number of cards and he collects second largest number of cards on Thursday
He will always collect > 8 cards on Thursday

2. On one of the first 3 days, Danny collected 6 cards.
Clearly insufficient

A

Just adding a different view S(1), CounterSniper solution is the best and fastest way!

Only Case 1 is possible.
Case 2 is not possible, since the question stem states that "Each day, he collects a different number of cards.".
Case 3 is not possible, since Friday is no longer the day with the second largest number.
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Screen Shot 2018-09-24 at 18.46.27.png [ 22.65 KiB | Viewed 843 times ]

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Re: Over the course of 5 days, Monday through Friday, Danny collects a tot   [#permalink] 24 Sep 2018, 09:48
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