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.
sqrt96<x<sqrt6
[#permalink]
09 Aug 2018, 03:54
09 Aug 2018, 03:54
Expert Reply
00:00
Question Stats:
74% (01:19) correct
25% (02:04) wrong based on 99 sessions
Hide Show timer Statistics
\(\sqrt{96} < x \sqrt{6}\) and \(\frac{x}{\sqrt{6}}\) \(< \sqrt{6}\). If x is an integer, which of the following is the value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Re: sqrt96<x<sqrt6
[#permalink]
12 Aug 2018, 01:08
12 Aug 2018, 01:08
1
Carcass wrote:
\(\sqrt96 < x \sqrt6\) and \(\frac{x}{\sqrt{6}}\) \(< \sqrt{6}\). If x is an integer, which of the following is the value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
\(\sqrt96 < x \sqrt6\)
or \(4\sqrt6 < x \sqrt6\)
or\(4 < x\)
From the 2nd statement,
\({\frac{x}{\sqrt{6}}} < \sqrt6\)
or \(x < \sqrt6 * \sqrt6\)
or\(x < 6\)
So the value of x lies between \(4 < x < 6\)
So the answer is D i.e. 5
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: sqrt96<x<sqrt6
[#permalink]
29 Dec 2021, 05:28
29 Dec 2021, 05:28
1
Given that \(\sqrt{96} < x \sqrt{6}\) and \(\frac{x}{\sqrt{6}}\) \(< \sqrt{6}\) and we need to find the value of x
\(\sqrt{96} < x \sqrt{6}\) => \(\sqrt{16 * 6} < x \sqrt{6}\)
=> \(\sqrt{16} * \sqrt{6} < x \sqrt{6}\)
Cancelling \(\sqrt{6}\) from both the sides we get
\(\sqrt{16} < x \)
=> x > 4
\(\frac{x}{\sqrt{6}}\) \(< \sqrt{6}\)
Multiply with \(\sqrt{6}\) on both the sides we get
x < \(\sqrt{6} * \sqrt{6}\)
=> x < 6
=> 4 < x < 6
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Inequalities
\(\sqrt{96} < x \sqrt{6}\) => \(\sqrt{16 * 6} < x \sqrt{6}\)
=> \(\sqrt{16} * \sqrt{6} < x \sqrt{6}\)
Cancelling \(\sqrt{6}\) from both the sides we get
\(\sqrt{16} < x \)
=> x > 4
\(\frac{x}{\sqrt{6}}\) \(< \sqrt{6}\)
Multiply with \(\sqrt{6}\) on both the sides we get
x < \(\sqrt{6} * \sqrt{6}\)
=> x < 6
=> 4 < x < 6
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Inequalities
