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If 0 < a < < 1, then which of the following must be true? (A
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30 Aug 2018, 07:49
30 Aug 2018, 07:49
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If \(0 < a < \frac{1}{b}< 1\), then which of the following must be true?
(A) \(a^2 > a > b > b^2\)
(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) \(a^2 > a > b > b^2\)
(B) \(b > a > a^2 > b^2\)
(C) \(b^2 > a > a^2 > b\)
(D) \(b^2 > a^2 > b > a\)
(E) \(b^2 > b > a > a^2\)
Re: If 0 < a < < 1, then which of the following must be true? (A
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07 Sep 2018, 20:22
07 Sep 2018, 20:22
2
sandy wrote:
If \(0 < a < \frac{1}{b}< 1\), then which of the following must be true?
(A) \(a^2 > a > b > b^2\)
(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) \(a^2 > a > b > b^2\)
(B) \(b > a > a^2 > b^2\)
(C) \(b^2 > a > a^2 > b\)
(D) \(b^2 > a^2 > b > a\)
(E) \(b^2 > b > a > a^2\)
Note : both a and 1/b are fraction.
Now, b and 1/b are not same. Here is the tricks.
If b is an fraction 1/b becomes greater that 1. but what? we know 1/b is fraction , it's not greater than 1.
So, b is a integer greater that 1.
Thus ,\(b^2\) , b are largest and second largest integer.
Now a is fraction. So, a^2 is even smaller than a. If we square a fraction, it become even smaller.
So, sequence: \(b^2>b>a>a^2\)
The best answer is E.
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If 0 < a < < 1, then which of the following must be true? (A
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12 Sep 2018, 07:26
12 Sep 2018, 07:26
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sandy wrote:
If \(0 < a < \frac{1}{b}< 1\), then which of the following must be true?
(A) \(a^2 > a > b > b^2\)
(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) \(a^2 > a > b > b^2\)
(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
Cheers,
Brent
