(单词翻译:单击)
每日一题
Mathematics>Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
It 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 (absolute value of p-8) is less than or equal to 2 must be true.