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28 Jan 2025, 01:30
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C
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Difficulty:
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Question Stats:
91% (01:25) correct
9%
(01:43)
wrong
based on 176
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If x is positive, which of the following may be true?
A. \(\frac{1}{x} < \frac{1}{ x^{2}} < x \)
B. \( 1 + x < \frac{1}{x}< 2x \)
C. \(\frac{1}{x} < 1 + x < 2x \)
D. \( 2 + x < \frac{1}{x} < 4x \)
E. \( 1 + x < \frac{1}{x} < x \)
A. \(\frac{1}{x} < \frac{1}{ x^{2}} < x \)
B. \( 1 + x < \frac{1}{x}< 2x \)
C. \(\frac{1}{x} < 1 + x < 2x \)
D. \( 2 + x < \frac{1}{x} < 4x \)
E. \( 1 + x < \frac{1}{x} < x \)
28 Jan 2025, 04:14
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Let's calculate for x = 3,
\(\frac{1}{x^2} < \frac{1}{x} < x < 1+x < 2+x < 2x < 4x = 1/9 < 1/3 < 3 < 4 < 5 < 6 < 12\)
Only one of the options holds true =>
\(\frac{1}{x} < 1 + x < 2x \) = 1/3 < 4 < 6
If none would have matched, then test for numbers b/w 0 and 1.
IMO: C
\(\frac{1}{x^2} < \frac{1}{x} < x < 1+x < 2+x < 2x < 4x = 1/9 < 1/3 < 3 < 4 < 5 < 6 < 12\)
Only one of the options holds true =>
\(\frac{1}{x} < 1 + x < 2x \) = 1/3 < 4 < 6
If none would have matched, then test for numbers b/w 0 and 1.
IMO: C
28 Jan 2025, 05:56
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If x is positive, which of the following may be true?
Let's try for numbers greater than 1, (If several options remain, then we will try numbers between 0 and 1)
As x has been given to be only a number (hence can be a fraction), Assume x = 1.1
A. \(\frac{1}{1.1}<\frac{1}{1.21}<1.1\)
Not true, as \(\frac{1}{1.1}>\frac{1}{1.21}\)
B. \(1+1.1<\frac{1}{1.1}<2*1.1\)
Not true, as \(2.1>\frac{1}{1.1}\)
C.\(\frac{1}{1.1}<1+1.1<2*1.1\)
Can be true as: \(\frac{1}{1.1}<2.1<2.2\)
D.\(2+1.1<\frac{1}{1.1}<4*1.1\)
Not true, as \(3.1>\frac{1}{1.1}\)
E.\(1+1.1<\frac{1}{1.1}<1.1\)
Not true, as \(2.1>\frac{1}{1.1}\)
Hence IMO Ans C
Let's try for numbers greater than 1, (If several options remain, then we will try numbers between 0 and 1)
As x has been given to be only a number (hence can be a fraction), Assume x = 1.1
A. \(\frac{1}{1.1}<\frac{1}{1.21}<1.1\)
Not true, as \(\frac{1}{1.1}>\frac{1}{1.21}\)
B. \(1+1.1<\frac{1}{1.1}<2*1.1\)
Not true, as \(2.1>\frac{1}{1.1}\)
C.\(\frac{1}{1.1}<1+1.1<2*1.1\)
Can be true as: \(\frac{1}{1.1}<2.1<2.2\)
D.\(2+1.1<\frac{1}{1.1}<4*1.1\)
Not true, as \(3.1>\frac{1}{1.1}\)
E.\(1+1.1<\frac{1}{1.1}<1.1\)
Not true, as \(2.1>\frac{1}{1.1}\)
Hence IMO Ans C
