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Mathematics>Standard Multiple Choice

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

If |a|-|b|=5, which of the following could be true?

(A) a=0
(B) b=0
(C) a=b
(D) a=-b
(E) a=1

答案和解析

答案：B

解析：

If b=0 and a=5, then (|a|)-(|b|)=(|5|)-(|0|)=5. Hence if (|a|)-(|b|)=5, it could be true that b=0.

If (|a|)-(|b|)=5, none of the other four statements could be true:

If a=0, then (|a|)-(|b|)=0-(|b|)=-(|b|). However, since (|b|) is greater than or equal to 0, there is no value of b for which -(|b|)=5.
If a=b, then (|a|)-(|b|)=(|a|)-(|a|)=0 does not equal 5.
If a=-b, then (|a|)-(|b|)=(-|b|)-(|b|)=(|b|)-(|b|)=0 does not equal 5.
If a=1, then (|a|)-(|b|)=(absolute value of 1)-(|b|)=1-(|b|). However, since (|b|) is greater than or equal to 0, there is no value of b for which 1-(|b|)=5.