2014-09-01 09:00:08

If |x - y| = 6 and x and y are both negative numbers, which of the following is NOT a possible value of y?

(A) -2
(B) -3
(C) -4
(D) -5
(E) -6

The correct answer is E
Explanation: The best approach to this question is to simply plug in the answer choices until one does not work. If |x - y| = 6, then x - y equals either 6 or -6. Plug in the listed values for y and see if there is a possible x value that can be created to make the equation true:

(A) If y is -2 and x is -8, then |-8 - -2| = |-8 + 2| = |-6| = 6. So, y could be -2.
(B) If y is -3 and x is -9, then |-9 - -3| = |-9 + 3| = |-6| = 6. So, y could be -3.
(C) If y is -4 and x is -10, then |-10 - -4| = |-10 + 4| = |-6| = 6. So, y could be -4.
(D) If y is -5 and x is -11, then |-11 - -5| = |-11 + 5| = |-6| = 6. So, y could be --5.
(E) If y is -6, then x would have to be 0 to make the equation work. Since the question stem states that x and y both have to be negative numbers, x cannot be 0, so y cannot be -6. As the question asks for the value of y that does NOT work, choice E is correct.