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Mathematics>Standard Multiple Choice

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

t costs d dollars to ship a package that weighs p pounds if and only if 6 is less than or equal to p is less than or equal to 10. If Alan's package weighs p pounds and costs d dollars to ship, which of the following must be true?

(A) | p-6| is less than or equal to 2
(B) | p-10| is less than or equal to 2
(C) | p-8| is less than or equal to 2
(D) | p+6| is less than or equal to 10
(E) | p+10| is less than or equal to 6

答案和解析

答案：C

解析：

If Alan's package weighs p pounds and costs d dollars to ship, then 6 is less than or equal to p is less than or equal to 10. Subtracting 8 across these inequalities gives the equivalent (6-8) is less than or equal to (p-8) is less than or equal to (10-8), and so (-2) is less than or equal to (p-8) is less than or equal to 2. By the definition of absolute value, it follows that |p-8| is less than or equal to 2 must be true.