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E
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Difficulty:
55%
(hard)
Question Stats:
61% (02:18) correct
39%
(01:58)
wrong
based on 54
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18 Jun 2022, 12:07
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nahid78
Is |a - c| + |a| = |c|?
(1) ab > bc
(2) bc < 0
(1) ab > bc
(2) bc < 0
Statement 1 Alone:
We know nothing about b, so this may result in \(a > c\) or \(a < c\) depending on the sign of b.
If \(a > c > 0\), then Left side = \(2a - c\) and Right side = \(c\), equating gives \(a = c\) which is not possible. Then the statement can be answered with a "no" for this case.
If \(0 < a < c\), then we have \(c - a + a = c\) and \(c = c\), so the statement is true in this case. Since we have both "yes" and "no" cases, this statement is insufficient.
Statement 2 Alone:
b is not really our concern so this statement provides no value (we can interpret this statement as b and c have opposite signs). Insufficient.
Both Statements Combined:
If b > 0, then a > c while c < 0. Then we can have \(a > 0 > c\), plugging in the questioned equation gives \(a - c + a = -c\) and \(a = 0\), which is a possible scenario. Then this case alone already provides possible "yes" and "no" scenarios. Insufficient.
Answer: E
20 Jun 2022, 20:28
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JerryAtDreamScore
nahid78
Is |a - c| + |a| = |c|?
(1) ab > bc
(2) bc < 0
(1) ab > bc
(2) bc < 0
Statement 1 Alone:
We know nothing about b, so this may result in \(a > c\) or \(a < c\) depending on the sign of b.
If \(a > c > 0\), then Left side = \(2a - c\) and Right side = \(c\), equating gives \(a = c\) which is not possible. Then the statement can be answered with a "no" for this case.
If \(0 < a < c\), then we have \(c - a + a = c\) and \(c = c\), so the statement is true in this case. Since we have both "yes" and "no" cases, this statement is insufficient.
Hello JerryAtDreamScore can you please explain why while testing 0 < a < c , the new equation (c - a + a = c) will have different signs only for the first c and a and not the following a and c as well? something like c - a - a = - c ... I imagine because the other c and a terms are alone inside the absolute value and do not "interact" with other terms, something actually happening in |a - c|?
Please help me clarify this better than just a vague intuition
