What must be the least number of soldiers in a group such that they can be arranged in lines of 10 1...........

Quantitative Aptitude ( CCS) Number System

What must be the least number of soldiers in a group such that they can be arranged in lines of 10, 15 and 25 soldiers each and also in a square?

150

600

900

3,600

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Explanation:

You know that the number of soldiers must be a multiple of 10, 15 and 25.( Only then, can they be drawn into lines of 10, 15 or 25).
So now the possibilities are multiples of 150 ( LCM of 10,15,25). ( 150 = 2*3*5*5
As 10 is present and your final answer needs to be a perfect square, you need another factor of 2.
Also as 15 is present you need a factor of 3.
Therefore you multiply 150 by 2 and 3 to get 900 which is your answer.
900 = 2^2 *3^2*5^2

Hence, option 3 is the correct answer.