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02 Sep 2012, 21:36
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
59% (01:38) correct
41%
(01:37)
wrong
based on 269
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Is |a – 2| = b^2 – c^3 ?
(1) a < 2
(2) a + b^2 = c^3 + 2
I'm struggling to solve this problem.
Any good material on absolute values/modules available?
(1) a < 2
(2) a + b^2 = c^3 + 2
I'm struggling to solve this problem.
Any good material on absolute values/modules available?
02 Sep 2012, 23:27
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Statement (1) is clearly insufficient.
Statement (2):
a + b^2 = c^3 + 2
b^2 - c^3 = 2 - a
Substituting b^2 - c^3 in the original equation:
Is |a - 2| = 2 - a
If a is higher than 2, the equation will not hold true.
If a is equal or lower than 2, the equation will be ok.
--> not sufficient
(1) + (2) together:
Because of statement (1) we know that "a" must be lower than 2.
Statement (2) told us, that if "a" is lower than 2, the equation is true.
--> sufficient
Statement (2):
a + b^2 = c^3 + 2
b^2 - c^3 = 2 - a
Substituting b^2 - c^3 in the original equation:
Is |a - 2| = 2 - a
If a is higher than 2, the equation will not hold true.
If a is equal or lower than 2, the equation will be ok.
--> not sufficient
(1) + (2) together:
Because of statement (1) we know that "a" must be lower than 2.
Statement (2) told us, that if "a" is lower than 2, the equation is true.
--> sufficient
03 Sep 2012, 03:59
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Is |a – 2| = b^2 – c^3 ?
(1) a < 2. Not sufficient, since no info about b and c.
(2) a + b^2 = c^3 + 2 --> re-arrange: \(b^2-c^3=2-a\). So, the question becomes: is \(|a-2|=2-a\)? Now, if \(a>{2}\), then \(|a-2|=a-2\) and the answer is NO but if \(a\leq{2}\), then \(|a-2|=-(a-2)=2-a\) and the answer is YES. Not sufficient.
(1)+(2) Since from (1) \(a < 2\), then \(|a-2|=-(a-2)=2-a\), so the answer is YES. Sufficient.
Answer: C.
Theory on absolute values: math-absolute-value-modulus-86462.html
PS questions on Absolute Values: search.php?search_id=tag&tag_id=58
DS questions on Absolute Values: search.php?search_id=tag&tag_id=37
Tough inequality and absolute value questions: inequality-and-absolute-value-questions-from-my-collection-86939.html
Hope it helps.
(1) a < 2. Not sufficient, since no info about b and c.
(2) a + b^2 = c^3 + 2 --> re-arrange: \(b^2-c^3=2-a\). So, the question becomes: is \(|a-2|=2-a\)? Now, if \(a>{2}\), then \(|a-2|=a-2\) and the answer is NO but if \(a\leq{2}\), then \(|a-2|=-(a-2)=2-a\) and the answer is YES. Not sufficient.
(1)+(2) Since from (1) \(a < 2\), then \(|a-2|=-(a-2)=2-a\), so the answer is YES. Sufficient.
Answer: C.
Theory on absolute values: math-absolute-value-modulus-86462.html
PS questions on Absolute Values: search.php?search_id=tag&tag_id=58
DS questions on Absolute Values: search.php?search_id=tag&tag_id=37
Tough inequality and absolute value questions: inequality-and-absolute-value-questions-from-my-collection-86939.html
Hope it helps.
