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# If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following

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BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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Updated on: 14 Jun 2017, 09:47
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Difficulty:

55% (hard)

Question Stats:

60% (01:33) correct 40% (01:28) wrong based on 231 sessions

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If $$\frac{1}{55}<x<\frac{1}{22}$$ and $$\frac{1}{33}<x<\frac{1}{11}$$, then which of the following could be the value of x?

(I)$$\frac{1}{54}$$

(II)$$\frac{1}{23}$$

(III)$$\frac{1}{12}$$

A) Only I
B) Only II
C) I and II
D) II and III
E) I, II, III

Source => NOVA.

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Originally posted by stonecold on 19 Apr 2017, 05:40.
Last edited by Bunuel on 14 Jun 2017, 09:47, edited 1 time in total.
Renamed the topic and edited the question.
Director
Joined: 05 Mar 2015
Posts: 971
Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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19 Apr 2017, 08:32
stonecold wrote:
If $$\frac{1}{55}<x<\frac{1}{22}$$ and $$\frac{1}{33}<x<\frac{1}{11}$$ , then which of the following could be the value of x?

(I)$$\frac{1}{54}$$

(II)$$\frac{1}{23}$$

(III)$$\frac{1}{12}$$

A)Only I
B)Only II
C)I and II
D)II and III
E)I,II,III

Source => NOVA.

II satisfies both condition

Ans B
Intern
Joined: 07 Mar 2016
Posts: 46
Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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19 Apr 2017, 09:00
4
The question is asking about the value of x that fits both ranges.

The ranges are: -55<x<-22 and -33<x<-11

The only value that fits both ranges in -23; choice "B"
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Posts: 776
Location: United States
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GMAT 1: 650 Q43 V37
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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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23 Apr 2017, 18:41
stonecold wrote:
If $$\frac{1}{55}<x<\frac{1}{22}$$ and $$\frac{1}{33}<x<\frac{1}{11}$$ , then which of the following could be the value of x?

(I)$$\frac{1}{54}$$

(II)$$\frac{1}{23}$$

(III)$$\frac{1}{12}$$

A)Only I
B)Only II
C)I and II
D)II and III
E)I,II,III

Source => NOVA.

The most efficient way to solve this problem is to just cross multiply the denominators all across the expression- for example

[1/55] < [1/23]
[23/(55)(23)] < [55/(55)(23)]

and then

1/23 < 1/22
22/(23)(22) < 23/(23)(22)

The most efficient way, then, is to just compare the denominators

* once you cross multiply two fractions such as - [23/(55)(23)] < [55/(55)(23)] - do not cross multiply again by the next fraction for example
[23/(55)(23)] < [55/(55)(23)] cross multiplied by 1/22
Intern
Joined: 13 Dec 2016
Posts: 44
Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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15 May 2017, 04:34
I solved it the traditional way (taking LCM and comparing each fraction option with the ranges given and it took me almost 3 mins to conclude the right answer. Request you to advise the best approach to solve such problems.

Nunuboy1994 : I could not understand the cross-multiplication approach you are suggesting
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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15 May 2017, 05:17
5
stonecold wrote:
If $$\frac{1}{55}<x<\frac{1}{22}$$ and $$\frac{1}{33}<x<\frac{1}{11}$$ , then which of the following could be the value of x?

(I)$$\frac{1}{54}$$

(II)$$\frac{1}{23}$$

(III)$$\frac{1}{12}$$

A)Only I
B)Only II
C)I and II
D)II and III
E)I,II,III

Source => NOVA.

Two ranges of x are given.

$$\frac{1}{55}<x<\frac{1}{22}$$ and $$\frac{1}{33}<x<\frac{1}{11}$$ translates to

1/33 < x < 1/22

Note why on the number line:

.......... (1/55)......................(1/33) ........................ (1/22).......................(1/11).........

.............<---------------------------- x -------------------------->
and
................................................<---------------------------- x ---------------------->

1/33 < x < 1/22
So all values such as 1/23, 1/24, 1/25.... 1/32 will lie within this range.

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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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15 May 2017, 06:26
If 155<x<122155<x<122 and 133<x<111133<x<111 , then which of the following could be the value of x?

Cond 1) 155<x<122155<x<122

Cond 2) 133<x<111133<x<111

(I)154154 it cant satisfy both conditions

(II)123123

(III)112112 it cant satisfy both conditions

A)Only I
B)Only II
C)I and II
D)II and III
E)I,II,III
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Manager
Joined: 24 Jun 2017
Posts: 122
Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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08 Aug 2017, 10:07
1
For me the best way to resolve this was to write the numbers with negative exponents
1/55 = (55)^-1
1/33 = (33)^-1
1/22 = (22)^-1
1/11 = (11)^-1

So if 1/55<x<1/22 and 1/33<x<1/11
then

------55---------------22------------->
------------33---------------11------->
range that covers both conditions is (33)^-1<x<(22)^-1
then only B (23)^1 satisfies it
Intern
Joined: 12 Aug 2017
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GMAT 1: 730 Q45 V45
GMAT 2: 710 Q48 V40
GMAT 3: 720 Q44 V45
Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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15 Aug 2017, 11:52
$$[1][/55] < [1][/33] < x < [1][/22] < [1][/11]$$

x must be between $$[1][/33]$$ and $$[1][/22]$$

Only II fits this criteria
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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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15 Aug 2017, 12:00
1
I did it like this:-

First says 1/55<x<1/22 - multiplying everything by 330 --> 6 < 330x < 15

Second says 1/33 < x < 1/11 - again multiplying by 330 --> 10 < 330x < 33

Combining, we get 10 < 330x < 15

Divide above by 330, we get

1/33 < x < 1/22

Analysing answer choices, only ii satisfies above.
Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following   [#permalink] 15 Aug 2017, 12:00
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