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 it is true that 1/55 < x < 1/22 and 1/33 < x < 1/11, then
[#permalink]
28 Mar 2019, 13:35
28 Mar 2019, 13:35
Expert Reply
2
Bookmarks
00:00
Question Stats:
59% (01:43) correct
40% (02:24) wrong based on 47 sessions
Hide Show timer Statistics
If it is true that \(\frac{1}{55} < x < \frac{1}{22}\) and \(\frac{1}{33} < x < \frac{1}{11}\), then which of the following numbers could x equal?
I. \(\frac{1}{54}\)
II. \(\frac{1}{23}\)
III. \(\frac{1}{12}\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
I. \(\frac{1}{54}\)
II. \(\frac{1}{23}\)
III. \(\frac{1}{12}\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: If it is true that 1/55 < x < 1/22 and 1/33 < x < 1/11, then
[#permalink]
14 Jun 2021, 09:47
14 Jun 2021, 09:47
3
Carcass wrote:
If it is true that \(\frac{1}{55} < x < \frac{1}{22}\) and \(\frac{1}{33} < x < \frac{1}{11}\), then which of the following numbers could x equal?
I. \(\frac{1}{54}\)
II. \(\frac{1}{23}\)
III. \(\frac{1}{12}\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
I. \(\frac{1}{54}\)
II. \(\frac{1}{23}\)
III. \(\frac{1}{12}\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
The inequality flips when we reciprocate the terms i.e.
If \(a < b\) then, \(\frac{1}{a} > \frac{1}{b}\)
Given:
\(\frac{1}{55} < x < \frac{1}{22}\)
Also, \(55 > \frac{1}{x} > 22\)
\(\frac{1}{33} < x < \frac{1}{11}\)
Also, \(33 > \frac{1}{x} > 11\)
Draw a number line (refer to the figure) and find the common region!
All the number between 22 and 33 are our answers
Here, Option B
Attachments
which of the following numbers could x equal.png [ 2.28 KiB | Viewed 2423 times ]
General Discussion
Re: If it is true that 1/55 < x < 1/22 and 1/33 < x < 1/11, then
[#permalink]
30 Mar 2019, 10:26
30 Mar 2019, 10:26
1
Expert Reply
There are several things to do here, but I just used some number sense with each choice. For instance, a greater denominator means a smaller fraction, so \(\frac{1}{54}\) is less than \(\frac{1}{33}\). But we are told that x is greater than \(\frac{1}{33}\). So statement I is out.
We want to keep running with that idea that a greater denominator means a smaller fraction. \(\frac{1}{23}\) is indeed bigger than \(\frac{1}{54}\), and smaller than \(\frac{1}{22}\). It is also greater than \(\frac{1}{33}\) and smaller than \(\frac{1}{11}\). So choice II works.
For choice III, \(\frac{1}{12}\) is greater than \(\frac{1}{22}\), but we are told that x is less than \(\frac{1}{22}\). So choice B is the right answer: only II works.
We want to keep running with that idea that a greater denominator means a smaller fraction. \(\frac{1}{23}\) is indeed bigger than \(\frac{1}{54}\), and smaller than \(\frac{1}{22}\). It is also greater than \(\frac{1}{33}\) and smaller than \(\frac{1}{11}\). So choice II works.
For choice III, \(\frac{1}{12}\) is greater than \(\frac{1}{22}\), but we are told that x is less than \(\frac{1}{22}\). So choice B is the right answer: only II works.
