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/b <1 then which of the following must be true ?
[#permalink]
23 Nov 2021, 04:49
23 Nov 2021, 04:49
Expert Reply
00:00
Question Stats:
88% (01:23) correct
11% (03:12) wrong based on 9 sessions
Hide Show timer Statistics
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) \(b^2 > b > a > a^2\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 0 < a < 1/b <1 then which of the following must be true ?
[#permalink]
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
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1131
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: If 0 < a < 1/b <1 then which of the following must be true ?
[#permalink]
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
