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Each card in a deck has an integer written on it, and the integers on
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28 Sep 2021, 00:25
28 Sep 2021, 00:25
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Question Stats:
26% (02:16) correct
73% (02:06) wrong based on 26 sessions
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Each card in a deck has an integer written on it, and the integers on each of the 12 cards in the deck are consecutive. In a certain game, the number points awarded for each turn is determined by drawing two cards and multiplying the numbers shown on the cards. If the points awarded in three turns are 40, 72, and 60, all of the following could be the smallest numbered card in the deck EXCEPT:
(A) -1
(B) 0
(C) 4
(D) 5
(E) 6
(A) -1
(B) 0
(C) 4
(D) 5
(E) 6
Re: Each card in a deck has an integer written on it, and the integers on
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28 Sep 2021, 01:20
28 Sep 2021, 01:20
How is the answer E? It can be a multiple of every score given.
Re: Each card in a deck has an integer written on it, and the integers on
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28 Sep 2021, 01:36
28 Sep 2021, 01:36
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In the space of the 12 consecutive integers on the cards, you must be able to multiply two of them and get 40, two others and get 72, and two others and get 60. (There can be overlap.) So, determine which numbers you could use to get each of those numbers:
40: 4 and 10, 5 and 8 (1 and 40, and 2 and 20 are too far apart)
72: 6 and 12, 8 and 9
60: 4 and 15, 5 and 12, 6 and 10
Due to 40, there must be at least one number in the deck that is 5 or lower. While, due to 72, one number must be 6 or higher. So, the correct answer is (E), 6: if the smallest numbered card is 6, there’s no way for two of the cards to multiply to 40.
40: 4 and 10, 5 and 8 (1 and 40, and 2 and 20 are too far apart)
72: 6 and 12, 8 and 9
60: 4 and 15, 5 and 12, 6 and 10
Due to 40, there must be at least one number in the deck that is 5 or lower. While, due to 72, one number must be 6 or higher. So, the correct answer is (E), 6: if the smallest numbered card is 6, there’s no way for two of the cards to multiply to 40.
