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If 0 < a < 1/b <1 then which of the following must be true ?
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23 Nov 2021, 04:49
23 Nov 2021, 04:49
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If \(0 < a < \frac{1}{b} <1\) then which of the following must be true ?
(A) \(a > b > b^2\)
(B) \(b > a > a^2 > b^2\)
(C) \(b^2 > a > a^2 > b\)
(D) \(b^2 > a^2 > b > a\)
(E) \(b^2 > b > a > a^2\)
(A) \(a > b > b^2\)
(B) \(b > a > a^2 > b^2\)
(C) \(b^2 > a > a^2 > b\)
(D) \(b^2 > a^2 > b > a\)
(E) \(b^2 > b > a > a^2\)
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Re: If 0 < a < 1/b <1 then which of the following must be true ?
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23 Nov 2021, 05:27
23 Nov 2021, 05:27
Carcass wrote:
If \(0 < a < \frac{1}{b} <1\) then which of the following must be true ?
(A) \(a > b > b^2\)
(B) \(b > a > a^2 > b^2\)
(C) \(b^2 > a > a^2 > b\)
(D) \(b^2 > a^2 > b > a\)
(E) \(b^2 > b > a > a^2\)
(A) \(a > b > b^2\)
(B) \(b > a > a^2 > b^2\)
(C) \(b^2 > a > a^2 > b\)
(D) \(b^2 > a^2 > b > a\)
(E) \(b^2 > b > a > a^2\)
I believe the fastest approach is to find values for \(a\) and \(b\) that satisfy the condition \(0 < a < \frac{1}{b} <1\)
So, for example, it could be the case that \(a = 0.1\) and \(b = 2\), in which case \(a^2 = 0.01\) and \(b^2 = 4\)
When we arrange all 4 values, we get \(b^2 > b > a > a^2\)
Answer: E
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Re: If 0 < a < 1/b <1 then which of the following must be true ?
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05 Mar 2023, 08:45
05 Mar 2023, 08:45
1
Given that \(0 < a < \frac{1}{b} <1\) and we need to find which of the following must be true?
Now, \(0 < a < \frac{1}{b} <1\) => 0 < a < 1
=> a > \(a^2\) (Ex: if a = 0.1 then \(a^2\) = \(0.1^2\) = 0.01 < 0.1)
\(0 < a < \frac{1}{b} <1\) => \(0 < \frac{1}{b} <1\)
=> \(\frac{1}{b} <1\) and b is positive
Multiplying with b on the both the sides we get
b > 1 => b > a
Also, \(b^2\) > b (Ex: if b = 2 then \(b^2\) = \(2^2\) = 4 > 2)
=> \(b^2 > b > a > a^2\)
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Inequalities
Now, \(0 < a < \frac{1}{b} <1\) => 0 < a < 1
=> a > \(a^2\) (Ex: if a = 0.1 then \(a^2\) = \(0.1^2\) = 0.01 < 0.1)
\(0 < a < \frac{1}{b} <1\) => \(0 < \frac{1}{b} <1\)
=> \(\frac{1}{b} <1\) and b is positive
Multiplying with b on the both the sides we get
b > 1 => b > a
Also, \(b^2\) > b (Ex: if b = 2 then \(b^2\) = \(2^2\) = 4 > 2)
=> \(b^2 > b > a > a^2\)
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Inequalities
