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29 Nov 2018, 02:13
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A
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Difficulty:
45%
(medium)
Question Stats:
60% (01:30) correct
40%
(01:42)
wrong
based on 486
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What is the value of p ?
(1) |p – |p|| = 3
(2) 2|p| = 3
M36-96
(1) |p – |p|| = 3
(2) 2|p| = 3
M36-96
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29 Nov 2018, 02:20
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Bunuel
We'll use a basic property of absolute value to help us solve.
This is a Precise approach.
Recall that |a| = x implies a = x or a = -x.
Then:
(1) |p - |p|| = 3 implies p - |p| = 3 so |p| = p - 3 or p - |p| = -3 in which case |p| = p+3.
We'll simplify again: p = p-3 is impossible and p = -p + 3 give p = 1.5. But - if p = 1.5 then p - 3 = -1.5 so |p| is negative, which is also impossible!
Looking at the other equation, p=p+3 is impossilbe and p = -p-3 gives p = -1.5. This time |p| = p+3=1.5, which is positive, as required. Then p = -1.5
Sufficient.
(2) |p| = 1.5 simplifies directly to p = 1.5 or p = -1.5
Insufficient.
(A) is our answer.
12 Nov 2021, 08:38
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Bunuel
Official Solution:
What is the value of \(p\) ?
(1) \(|p – |p|| = 3\):
When \(p \geq 0\), then \(|p|=p\), so in this case we'd have \(|p – p| = 3\), which gives \(0=3\). This is obviously incorrect. So, \(p\) cannot be 0 or positive.
So, \(p < 0\). In this case, \(|p|=-p\), so in this case we'd have \(|p + p| = 3\), which gives \(|2p|=3\). This gives \(p=-\frac{3}{2}\) (\(p=\frac{3}{2}\) is not possible because we know that \(p\) is negative). Sufficient..
(2) \(2|p| = 3\):
\(|p|=\frac{3}{2}\);
\(p=\frac{3}{2}\) or \(p=-\frac{3}{2}\). Not sufficient.
Answer: A
. Made a silly mistake 
