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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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Updated on: 14 Jun 2017, 08:47
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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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Originally posted by stonecold on 19 Apr 2017, 04:40.
Last edited by Bunuel on 14 Jun 2017, 08:47, 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
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15 May 2017, 04:17
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
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19 Apr 2017, 07:32
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
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19 Apr 2017, 08:00
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
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23 Apr 2017, 17:41
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
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15 May 2017, 03:34
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 crossmultiplication 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
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15 May 2017, 05:26
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
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08 Aug 2017, 09:07
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
5522> 3311> 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
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15 Aug 2017, 10:52
\([1][/55] < [1][/33] < x < [1][/22] < [1][/11]\)
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
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15 Aug 2017, 11:00
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
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05 Oct 2018, 03:03
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