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

IMO : E

I think the easiest way to solve these is to convert them to percentages

1/2 becomes 50
13/20 becomes 65
7/10 becomes 70
3/4 becomes 75
4/5 becomes 80

so our options are

1. 50 to 65 Difference : 15
2. 65 to 70 Difference : 5
3. 70 to 75 Difference : 5
4. 75 to 80 Difference : 5
5. 80 to 100 Difference : 20

largest diff is option E

number is selected from values 0.5 to 1
possible range would be 4/5 and 1
option e

Common denominator can be 20 also. LCM of all the denominators. Any multiple of LCM will work. - 40, 60 , 80 ..etc

Archit3110
What was your approach for fast calculation?

I still didn't understand this question... Could yashikaaggarwal, MathRevolution, Bunuel help me out ?

See, we are told to find the chances of a value lying in between 1 and 0.5
the probability of getting a number in between 1 and 0.5 is 1/50
so we have 50 such numbers to get in between 1 and 0.5
the maximum options we have to select from the more chances we have to get the number in between 1 and 1/2
Going by options:

A values lie in between 1/2 and 13/20
that is 0.5 and 0.65
the probability of getting a number in between 0.5 and 0.65 is 1/15 (15 numbers)

B values lie in between 13/20 and 7/10
that is 0.65 and 0.7
the probability of getting a number in between 0.65 and 0.7 is 1/5 (5 numbers)

C values lie in between 7/10 and 3/4
that is 0.7 and 0.75
the probability of getting a number in between 0.7 and 0.75 is 1/5 (5 numbers)

D values lie in between 3/4 and 4/5
that is 0.75 and 0.8
the probability of getting a number in between 0.75 and 0.8 is 1/5 (5 numbers)

E values lie in between 4/5 and 1
that is 0.8 and 1
the probability of getting a number in between 0.8 and 1 is 1/20 (20 numbers)

The maximum probability of getting a number in between 0.5 and 1 is 20 numbers
because if you select rest options there will be less numbers in the set to select from.
E option have the most numbers we can select from
Hence Answer is E

I find the easiest way is to convert the fractions into LCM of 20.

A) 10/20 - 13/20
B) 13/20 - 14/20
C) 14/20 - 15/20
D) 15/20 - 16/20
E) 16/20 - 20/20

We can see here that E covers the widest range within 1 to 1/2. Answer is E.

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