Can you explain the answer?
You have 4 cards, labeled with the letters A and D and the numerals 3 and 6. The rule of the game is that a card with a vowel on it always has an even number on the other side. How many cards do you need to turn over to prove the rule true?
The answer is 2 - the A card and the 3 card, but I don't understand the answer. I would think either 1 card (just the A) or all 4 would be needed. If it only matters what is on the "opposite" side, then only the "A" card matters for the rule, and the others are irrelevant. If the rule matters going both ways, then it seems like any of the cards could disprove the rule. The 6 card could have a consonant under it, disproving the rule, or the D card have an even number under it, disproving the rule.
I just don't get it.
Thanks for any help.
2006-09-26 12:46:13 · 3 answers · asked by tutti frutti 1 in Science & Mathematics ➔ Mathematics
You must check the A card because A is a vowel and so there must be an even number on the other side.
You have to check the 3 card because odd numbers can only have consonants on the other side.
The statement "a card with a vowel on it always has an even number on the other side" is equivalent to the statement "a card with an odd number on it always has a consanant on the other side."
If an odd number card had a vowel on the other side, then that would contradict the given statement.
2006-09-26 12:49:30 · answer #1 · answered by MsMath 7 · 2⤊ 2⤋
The reason is that it says cards with a vowel on it has an even number on the other side. It does not say that ONLY cards with a vowel on them have an even number on the other side. Ergo, (D, 2) and (6, C) would be consistent with the rule.
By the way, the problem as stated is incorrect - you only need to check A and 3 if you know that every card has a letter on one side and a number on the other side - a fact which is usually stated in this type of problem, but was not stated here. Since this is not known, you need to check the D card as well, since it might have an A on the back.
2006-09-26 19:53:46 · answer #2 · answered by Pascal 7 · 0⤊ 0⤋
I would say all except the 6, there's nothing in the question that says all cards have a number on one side and a letter on the other, you might turn over the D and find an A there.
The 6 is the only one that you don't need to turn over to find out if there has been a violation of the rule as it could have anything or nothing and still comply.
2006-09-26 20:01:09 · answer #3 · answered by Anonymous · 0⤊ 1⤋