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If a number between 0 and 1/2 is selected at random, which

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If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post Updated on: 14 Aug 2014, 02:03
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If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

A. 0 and 3/20
B. 3/20 and 1/5
C. 1/5 and 1/4
D. 1/4 and 3/10
E. 3/10 and 1/2

Originally posted by rishi2377 on 17 Oct 2008, 11:25.
Last edited by Bunuel on 14 Aug 2014, 02:03, edited 1 time in total.
Added the OA.
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Re: If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post 11 Aug 2014, 21:31
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AkshayDavid wrote:
scthakur wrote:
A. 0 and 3/20 - here difference is 0.15
B. 3/20 and 1/5 - here difference is 0.05
C. 1/5 and 1/4 - here difference is 0.05
D. 1/4 and 3/10 - here difference is 0.05
E. 3/10 and 1/2 - here difference is 0.2

Hence, E.



Can you please explain why did you eliminate first four choices?
as per my understanding 0 and 1/2 include these numbers also --> 0.15, 0.05, 0.05, 0.05
please correct me if i am missing something


The question is one of probability. You select a number between 0 and 1/2 at random.
The number is between 0 and 10/20 (for ease of calculations)

Now, wider the desired range of the options, more is the probability that the number will lie in that range.
The probability that the number will lie between 0 and 10/20 is 1 i.e. the number is in this range. The probability that the number will lie between 0 and 9/20 is a little less than 1 since it is quite possible that the number is in this range but there is a small chance that it lies between 9/20 and 10/20 which this range doesn't cover. The probability that the number will lie between 0 and 1/20 is very small since this range covers a small part of the total range.

A. 0 and 3/20 - covers 0 to 3/20 but leaves out 3/20 to 10/20. So in essence, covers only 3 parts out of 10 parts
B. 3/20 and 1/5 - covers 3/20 to 4/20 (= 1/5). So in essence, covers only 1 part out of 10 parts
C. 1/5 and 1/4 - covers 4/20 to 5/20. So in essence, covers only 1 part out of 10 parts
D. 1/4 and 3/10 - covers 5/20 to 6/20. So in essence, covers only 1 part out of 10 parts
E. 3/10 and 1/2 - covers 6/20 to 10/20. So in essence, covers 4 parts out of 10 parts. Since this range is the widest, so the probability of the number lying in this range is the highest.

Answer (E)
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Re: If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post 17 Oct 2008, 12:11
A. 0 and 3/20 - here difference is 0.15
B. 3/20 and 1/5 - here difference is 0.05
C. 1/5 and 1/4 - here difference is 0.05
D. 1/4 and 3/10 - here difference is 0.05
E. 3/10 and 1/2 - here difference is 0.2

Hence, E.
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Re: If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post 17 Oct 2008, 14:06
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rishi2377 wrote:
GMAT TIGER wrote:
rishi2377 wrote:
If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

A. 0 and 3/20
B. 3/20 and 1/5
C. 1/5 and 1/4
D. 1/4 and 3/10
E. 3/10 and 1/2



E. 3/10 and 1/2



GMAT TIGER. I guess it is understood that I have OA. It wont hurt if you explain your answer.


Definitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation.

Now you have excellent explanantion by scthakur. In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it.
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Re: If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post 11 Aug 2014, 08:56
scthakur wrote:
A. 0 and 3/20 - here difference is 0.15
B. 3/20 and 1/5 - here difference is 0.05
C. 1/5 and 1/4 - here difference is 0.05
D. 1/4 and 3/10 - here difference is 0.05
E. 3/10 and 1/2 - here difference is 0.2

Hence, E.



Can you please explain why did you eliminate first four choices?
as per my understanding 0 and 1/2 include these numbers also --> 0.15, 0.05, 0.05, 0.05
please correct me if i am missing something
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Re: If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post 14 Aug 2014, 02:05
rishi2377 wrote:
If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

A. 0 and 3/20
B. 3/20 and 1/5
C. 1/5 and 1/4
D. 1/4 and 3/10
E. 3/10 and 1/2


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Re: If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post 23 Apr 2018, 13:08
Top Contributor
rishi2377 wrote:
If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between?

A. 0 and 3/20
B. 3/20 and 1/5
C. 1/5 and 1/4
D. 1/4 and 3/10
E. 3/10 and 1/2


We need to determine the LENGTH OF EACH INTERVAL.

The interval that has the greatest length, will be the most likely interval.

To determine the length of each interval, it may be faster to first convert the fractions to decimals. We get:

A) 0 and 0.15 (interval length = 0.15)
B) 0.15 and 0.2 (interval length = 0.05)
C) 0.2 and 0.25 (interval length = 0.05)
D) 0.25 and 0.3 (interval length = 0.05)
E) 0.3 and 0.5 (interval length = 0.2)

Answer: E

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If a number between 0 and 1/2 is selected at random, which [#permalink]

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New post 24 Apr 2018, 02:44
Best way (perhaps) is to make all the answers in the "../20" fraction-format. Computing intervals will become easier.
We avoid computing decimal values through this way :)
If a number between 0 and 1/2 is selected at random, which   [#permalink] 24 Apr 2018, 02:44
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