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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

On the line above, if A B less than B C less than C D less than D E, which of the following must be true?

(A) A C less than C D
(B) A C less than C E
(C) A D less than C E
(D) A D less than D E
(E) B D less than D E

答案和解析

答案：B

解析：

You can rewrite A C as A B + B C, A D as AB + BC + CD, C E as C D + D E, and B D as B C + C D, and then consider the five answer choices.

The first answer choice is equivalent to A B + B C is less than C D. You know that A B is less than C D and that B C is also less than C D, but the sum of A B and B C might not be less than C D. Since the question asks which statement must be true, the first answer choice is not the correct answer.

The second answer choice is equivalent to A B + B C is less than C D + D E. This statement must be true, because A B is less than C D and B C is less than D E. Although there is no need to consider the other answer choices once you see that the second answer choice must be true, each of the remaining choices could be rewritten in the same way and you could see that they need not be true.