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0 < p < 1, then which of the following inequalities must be true?
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16 Sep 2024, 23:09
16 Sep 2024, 23:09
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\(0 < p < 1\), then which of the following inequalities must be true? Indicate all the answers that apply.
A. \(p^5 < p^3\)
B. \(p < p^2\)
C. \(p^4– p^3< p^2– p^5\)
D. \(p^4– p^5< p^2– p^3\)
A. \(p^5 < p^3\)
B. \(p < p^2\)
C. \(p^4– p^3< p^2– p^5\)
D. \(p^4– p^5< p^2– p^3\)
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0 < p < 1, then which of the following inequalities must be true?
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03 Nov 2024, 01:20
03 Nov 2024, 01:20
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The answer is A, C and D.
A. p^5 < p^3
Raising p to a higher power results in a smaller number when 0<p<1. True.
B. p < p^2
When 0<p<1, higher exponents lead to smaller numbers. Hence, this is the opposite. False.
C. p^4 - p^3 < p^2 - p^5
Note that when 0<p<1, p^2>p^3>p^4>p^5.
Hence p^2 - p^5 will be a bigger number than p^4 - p^3.
You can plug in a number such as 0.5 if you want to check. True.
D. p^4 - p^5 < p^2 - p^3
Same logic as option C. When 0<p<1, p^2>p^3>p^4>p^5, p^4 - p^5 will be a smaller number than p^2 - p^3.
You can plug in a number such as 0.5 to check. True.
A. p^5 < p^3
Raising p to a higher power results in a smaller number when 0<p<1. True.
B. p < p^2
When 0<p<1, higher exponents lead to smaller numbers. Hence, this is the opposite. False.
C. p^4 - p^3 < p^2 - p^5
Note that when 0<p<1, p^2>p^3>p^4>p^5.
Hence p^2 - p^5 will be a bigger number than p^4 - p^3.
You can plug in a number such as 0.5 if you want to check. True.
D. p^4 - p^5 < p^2 - p^3
Same logic as option C. When 0<p<1, p^2>p^3>p^4>p^5, p^4 - p^5 will be a smaller number than p^2 - p^3.
You can plug in a number such as 0.5 to check. True.
gmatclubot
0 < p < 1, then which of the following inequalities must be true? [#permalink]
03 Nov 2024, 01:20
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