ME test series.

Question

How 14? I am not able to understand. Why not 30.

Comments

It will be 1+ prime numbers from (60 to 120)

=1+13=14

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How? please explain

I know there will 13 unconnected vertexes from 60 to 120 because of prime numbers but how to find connected components?

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I think u counted all odd numbers from 60 to 120 +1

75 is odd but 75=k*5, so its a part of bigger component, same with other composite numbers

Answer 1

see

given that , there is an edge from vertex a to b if b = K a

then , 2 is connected with all the even numbers ??

2-->4

2--->6

2--->8 ..

.

.

2-->120

now only odd numbers are left

i:e but observe that  there is also an edge between 3--->6 7------>14   5----->10

and there is also an edge between 2---->6 2----->14  5-----> 10 ??

therefore it's form a one component upto which number ??

59 ---- 59*2 = 118

now observe that , after 59 only prime numbers remains which  is not in the form n = k*n

i:e 61 = 61*2 = 122 (range 2 to 120)

therefore , 61 , 67,71,73,79,83,89,97,101,103,107,109,113 form a single components

therefore total components = 13+ 1 = 14 components

Comments

Thanks. got it.

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Thank you. I considered even nos. 1 component and all primes other.

Your ans. really cleared my doubt.

Answer 2

GIven numbers from 2 to 120, need to find total number of connected components

2 connects every even number

So every even number is a part of a single component.

Since 118 is a part of first component its half i.e. 59 will have an edge to 118, same with all odd number till 59(incl)

Now lets see about the odd numbers from 61 to 119

Every composite number is also a part of first component.

Why so? Since every composite number has a divisor other than 1 and itself, the largest composite number in the range is 120 and the smallest number it can be divided is 2, 120/2 =60, any other composite number will have its factors between 2 and 60.Hence they form a part of first component.

The remaining number are prime numbers: 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113. The count is 13. They form a single vertex component.

Hence in total 14 components.

Comments

Thank you. I considered even nos. 1 component and all primes other.

Your ans. really cleared my doubt.