GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If 0 < a < < 1, then which of the following must be true? (A
[#permalink]
30 Aug 2018, 07:49
30 Aug 2018, 07:49
Expert Reply
6
Bookmarks
00:00
Question Stats:
87% (01:24) correct
12% (01:16) wrong based on 116 sessions
Hide Show timer Statistics
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
[#permalink]
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 0 < a < < 1, then which of the following must be true? (A
[#permalink]
12 Sep 2018, 07:26
12 Sep 2018, 07:26
1
2
Bookmarks
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
