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04 Mar 2020, 22:05
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
35% (01:35) correct
65%
(01:37)
wrong
based on 165
sessions
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Is |x| = y - z ?
(1) x + y = z
(2) y < z
Posted from my mobile device
(1) x + y = z
(2) y < z
Posted from my mobile device
04 Mar 2020, 22:11
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statement 1: we can rephrase this to x = z - y.
there are thus 3 possibilities for the absolute value |x| :
(a) if z - y is positive, then |x| = z - y, and will NOT equal y - z (which is a negative quantity).
(b) if z - y is negative, then |x| = y - z (the opposite of z - y).
(c) if z - y = 0, then |x| equals both y - z and z - y, since each is equal to 0.
TAKEAWAY: when you consider absolute value equations, you'll often do well by considering the different CASES that result from different combinations of signs.
in this problem, you can get away with not thinking about this case (case (c)), because cases (a) and (b) already show that statement (1) is insufficient.
(2) y < z
in this case, y - z is negative and therefore CAN'T equal |x| -- no matter what x is -- since |x| must be nonnegative.
so, this statement is a definitive NO, and is thus sufficient even though it doesn't mention x at all. this is evil!
Answer is (B).
Posted from my mobile device
there are thus 3 possibilities for the absolute value |x| :
(a) if z - y is positive, then |x| = z - y, and will NOT equal y - z (which is a negative quantity).
(b) if z - y is negative, then |x| = y - z (the opposite of z - y).
(c) if z - y = 0, then |x| equals both y - z and z - y, since each is equal to 0.
TAKEAWAY: when you consider absolute value equations, you'll often do well by considering the different CASES that result from different combinations of signs.
in this problem, you can get away with not thinking about this case (case (c)), because cases (a) and (b) already show that statement (1) is insufficient.
(2) y < z
in this case, y - z is negative and therefore CAN'T equal |x| -- no matter what x is -- since |x| must be nonnegative.
so, this statement is a definitive NO, and is thus sufficient even though it doesn't mention x at all. this is evil!
Answer is (B).
Posted from my mobile device
05 Mar 2020, 00:02
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