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25 Apr 2024, 01:30
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B
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Difficulty:
55%
(hard)
Question Stats:
64% (01:35) correct
36%
(01:24)
wrong
based on 396
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If \(|p – |p|| = 3\), how many values of \(p\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
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05 May 2024, 00:15
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Official Solution:
If \(|p – |p|| = 3\), how many values of \(p\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
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. Therefore, \(p\) cannot be 0 or positive.
Thus, \(p < 0\). In this case, \(|p| = -p\), so we'd have \(|p + p| = 3\), which gives \(|2p| = 3\). This simplifies to \(p = -\frac{3}{2}\) (since \(p = \frac{3}{2}\) is not possible because we know that \(p\) is negative). Therefore, one value of \(p\) satisfies the given equation.
Answer: B
If \(|p – |p|| = 3\), how many values of \(p\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
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. Therefore, \(p\) cannot be 0 or positive.
Thus, \(p < 0\). In this case, \(|p| = -p\), so we'd have \(|p + p| = 3\), which gives \(|2p| = 3\). This simplifies to \(p = -\frac{3}{2}\) (since \(p = \frac{3}{2}\) is not possible because we know that \(p\) is negative). Therefore, one value of \(p\) satisfies the given equation.
Answer: B
General Discussion
25 Apr 2024, 01:45
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Bunuel
Assume p = +ve
\(|p – |p|| = 3\)
\(|p – p| = 3\)
This is invalid. Hence, we can conclude that p is not positive
Assume p = -ve
\(|p – |p|| = 3\)
\(|p – (-p)| = 3\)
\(|2p| = 3\)
\(-2p = 3\)
\(p = \frac{-3}{2}\)
Hence, only for one value of p, the equation hold.
Option B
