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) (absolute value of p minus 6) is less than or equal to 2
(B) (absolute value of p minus 10) is less than or equal to 2
(C) (absolute value of p minus 8) is less than or equal to 2
(D) (absolute value of p plus 6) is less than or equal to 10
(E) (absolute value of p plus 10) is less than or equal to 6
The correct answer is C
Explanation
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 minus 8) is less than or equal to (p minus 8) is less than or equal to (10 minus 8), and so (negative 2) is less than or equal to (p minus 8) is less than or equal to 2. By the definition of absolute value, it follows that (absolute value of p minus 8) is less than or equal to 2 must be true.