Aptitude

Question

A rod is out into 3 equal parts. The resulting portions are then cut into 12, 18 and 32 equal parts, respectively. If each of the resulting portions have integer length, then minimum number of smallest pieces of the road is  _________

Comments

It is 9.

initially x/3, x/3, x/3

then x/36, x/54, x/96

LCM = x =  864

Min number of smallesr pieces = 864/96 = 9

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Given Ans : 49

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@Ashwin

What does question mean by then "minimum number of smallest pieces of the road is"?

Answer 1

Since the rod is cut into three equal parts, so let the length of each part be 'x'

• Now, each part 'x' is divided into 12, 18 and 32 parts.
• So, when 'x' is divided into 12 parts, each part would have length of 'x/12'
• So, when 'x' is divided into 18 parts, each part would have length of 'x/18'
• So, when 'x' is divided into 32 parts, each part would have length of 'x/32'

Since the question says that those parts are of integer length, so x/12 or x/18 or x/32 must be an integer number

So, the minimum value of x should be greater than or equal to 32 (so that 'x/32' results in integer value)

and that value must be divisible by 12 and 18 and also 32. So that would be LCM of these numbers

which is 288

So, 288 is the value of each part i.e. 'x' = 288
So, minimum number of smallest pieces of a rod are 288 / 32 = 9

Comments

given ans 49

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here 9 is the size and not the number of pieces.Can you tell what does question ask exactly?