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If it is true that 1/55 < x < 1/22 and 1/33 < x < 1/11, then
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28 Mar 2019, 13:35
28 Mar 2019, 13:35
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Question Stats:
59% (01:42) correct
40% (02:33) wrong based on 52 sessions
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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
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Re: If it is true that 1/55 < x < 1/22 and 1/33 < x < 1/11, then
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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 3128 times ]
General Discussion
Re: If it is true that 1/55 < x < 1/22 and 1/33 < x < 1/11, then
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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.
