In a variant of Hopscotch game being played by three friends, 100

Question

In a variant of Hopscotch game being played by three friends, 100 small square blocks are made in a line and numbered 1 to 100 consecutively. The kids are then asked to choose a digit from 2, 3 and 5. The kid has to cross all the 100 blocks by jumping on every second, third or fifth block depending on the digit chosen.

If the probability to choose any of the 3 digit is same, select for  Must  the block number that would surely be stepped by all three friends and select for  Must not  the block number that would surely not be stepped on by all three.

demawtf · Answer

Must  
All three friends will step on the blocks that are multiples of 2, 3, and 5. These are the blocks that are multiples of the least common multiple (LCM) of 2, 3, and 5.

The LCM of 2, 3, and 5 is 2*3*5 : = 30

Must not 
Blocks that are not multiples of 2, 3, or 5
- 30 multiple of all 3 numbers
- 31 not a multiple of any of them but continue in order to check
- 32 multiple of 2
- 33 multiple of 3
- 34 multiple of 2
- 35 multiple of 5

So 31 should be "must not" number

thisischelso · Answer

In a variant of Hopscotch game being played by three friends, 100 small square blocks are made in a line and numbered 1 to 100 consecutively. The kids are then asked to choose a digit from 2, 3 and 5. The kid has to cross all the 100 blocks by jumping on every second, third or fifth block depending on the digit chosen.

If the probability to choose any of the 3 digit is same, select for Must the block number that would surely be stepped by all three friends and select for Must not the block number that would surely not be stepped on by all three.

> To step on the same block, this question is essentially asking for the LCM. So the LCM(2,3,5) is 30. Everyone will hit Block #30 at some point.

> Find a number that is NOT divisible by 2,3,5. Only '31' applies here.

z.helen17 · Answer

I chose the right answer, but I think all others other than 30 are Must Nots because the question is asking for squares not stepped on "by all three". It should have been phrased as "by neither" to make sense - otherwise, 32 is a valid Must Not, it is stepped on by the one jumping on the second, but not by the others. So it is not stepped on "by all three"

chetan2u · Answer

The question is correct. You do not know what has each chosen. If all three have chosen 2, then all three would step on 32 and 34.

‘Must not’ means there should be no possibility of that and for that we ensure that we choose a number where none of 2, 3 or 5 steps can lead to.

Posted from my mobile device

Saurabh_Moharir · Answer

Answer is simple for: 
Must: Just simply have a LCM (2,3,5) among given options which is 30.
Must not: Prime Number which is 31 here.

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