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

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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 14 Jun 2017, 09:47, edited 1 time in total.
Renamed the topic and edited the question.

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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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New post 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

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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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New post 19 Apr 2017, 09:00
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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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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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New post 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

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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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New post 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

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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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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.

Answer (B)
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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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New post 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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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink]

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New post 08 Aug 2017, 10:07
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

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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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New post 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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New post 15 Aug 2017, 12:00
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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.

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

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