Official Answer:-

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 StemThis 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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