题目：我选的C.错了 If ? represents one of the operations +, -, *, or ÷, is it true that x ? y ≠ y ? x for all values of x and y?
(1) 1 ? x = x
(2) x ? 1 = x
解释：Note that ? is one of the basic operations, and then go to the statements.
Statement 1 Plug each of the basic operations for ? in the expression 1 ? x and see which ones give you x: 1 + x ≠ x, so ? cannot be +. 1 – x ≠ x, so ? cannot be -. 1 x = x, so ? CAN be x. 1 ÷ x = x only if x is 1, other wise it is not true. So ? can't be ÷. So ? can only be . Statement 1 is sufficient by itself, so eliminate answer choices (B), (C) and (E).
Statement 2 Plug each of the basic operations for ? in the expression x ? 1 and see which ones give you x: x + 1 ≠ x, so ? cannot be +. x – 1 - x, so ? cannot be -. x 1 = x, so ? can be . x ÷ 1= x, so ? can be ÷. So ? can be x or ÷. Statement 2 is insufficient by itself, so the correct answer is choice (A).
还有一题，也错了，大家看看，解释满恶心的 问题是：On a certain fishing boat that catches tuna, wheeled carts are used to move the fish around the deck. If a cart can hold 1,600 lbs of fish, what is the maximum number of tuna that can be put in one cart?
(1) A tuna will slip through the net and not get caught unless it weighs over 5 lbs.
(2) A net full of tuna, which is 100 fish, weighs on average 800 lbs
In order to have sufficiency, you must be able to find the maximum number of fish that can be put in a cart given a 1,600-lb. weight limit. The number of fish that the cart can hold is represented by the equation (number of fish) = 1,600 ÷ (average weight of fish). To find the maximum number of fish (and have sufficiency), you need to know the minimum weight of a fish.
Statement (I): sufficient. This information gives an explicit minimum value for the weight of a fish, so it would enable you to find the maximum number of fish.
Statement (2): insufficient. This information allows you to find the average weight of a tuna but does not give you any information about the minimum weight for an individual tuna. Thus, (2) is insufficient, and the answer is (A).
第一题的第一个条件可以推出对于所有的x,y，要使得1 ? x = x 成立，只有?为乘号。此时可以得出问题所问x ? y ≠ y ? x is not true. 第二个条件可以推出对于所有的x,y，要使得 x ? 1 = x成立，可以是?为乘号或者除号。如果?为乘号，那么可以得出问题的答案是not true。但如果是除号，那么问题的答案就变成true了。所以条件二不能给出唯一的答案，因此不充分。
第一题的第一个条件可以推出对于所有的x,y，要使得1 ? x = x 成立，只有?为乘号。此时可以得出问题所问x ? y ≠ y ? x is not true. 第二个条件可以推出对于所有的x,y，要使得 x ? 1 = x成立，可以是?为乘号或者除号。如果?为乘号，那么可以得出问题的答案是not true。但如果是除号，那么问题的答案就变成true了。所以条件二不能给出唯一的答案，因此不充分。
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发表于 2010-7-8 08:05:22
x = x, so ? CAN be x. 
. Statement 1 is sufficient by itself, so eliminate answer choices (B), (C) and (E). 
1 = x, so ? can be 
. 
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