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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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stonecold
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If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink] New post   Updated on: 14 Jun 2017, 09:47
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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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B

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.
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KarishmaB
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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink] New post   15 May 2017, 05:17
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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] 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] 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] 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] 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] 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] New post   08 Aug 2017, 10:07
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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] 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] 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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If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink] New post   18 Oct 2020, 15:21
VeritasKarishma wrote:
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)


Hi VeritasKarishma - Isn't there overlap between the two ranges ?

I thought I could combine both the ranges and assume x can be ANY VALUE on this combined giant range

Here is what I put the range down as (After combining the two individual ranges into one large range given the overlap)

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

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

Thus i chose E

Where do you think is the break in my logic ?

Thank you !
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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink] New post   21 Oct 2020, 00:30
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jabhatta2 wrote:
VeritasKarishma wrote:
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)


Hi VeritasKarishma - Isn't there overlap between the two ranges ?

I thought I could combine both the ranges and assume x can be ANY VALUE on this combined giant range

Here is what I put the range down as (After combining the two individual ranges into one large range given the overlap)

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

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

Thus i chose E

Where do you think is the break in my logic ?

Thank you !


This is not correct. Notice the 'and' between the inequalities. x has to satisfy both the conditions.

For example, if you have 2 < x < 6 and 4 < x < 8, what values can x take? Can it be 3? No because it doesn't satisfy the second inequality.
x can be 5 because it satisfies both inequalities. But it again cannot be 7 because it doesn't satisfy the first inequality.
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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink] New post   23 Oct 2020, 12:55
VeritasKarishma, is it fine to simply remove the fractions to solve?

55 < x < 22 AND 33 < x < 11

33 < x < 11

Only '23' is within 33 < x < 11, giving us 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] New post   26 Oct 2020, 02:58
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basshead wrote:
VeritasKarishma, is it fine to simply remove the fractions to solve?

55 < x < 22 AND 33 < x < 11

33 < x < 11

Only '23' is within 33 < x < 11, giving us answer B.


basshead - Yes you can. But note the thing about reciprocals.
If both sides have the same sign, then when you take reciprocal, the inequality sign flips.
But if the two sides have opposite signs, then the inequality sign does not flip.
So before you take reciprocal, ensure you understand this very well. Else, it could lead to an error.
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Re: If 1/55 < x < 1/22 and 1/33 < x < 1/11, then which of the following [#permalink] New post   11 Jun 2023, 18:31
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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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