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# Numbers/Algebra

If S = (A + 20) + ( A + 21) + ( A + 22)+………+ ( A + 100) , where A is a positive integer . What is the smallest value of A such that S is a perfect square ?

1. 4
2. 16
3. 324
4. None of the above

### See our previous ‘Questions of the Day’:

Quant Question Of The Day: 56

Quant Question Of The Day: 55

1. Abhishek Tandon

4
S= 81A+4860
Since A is a postive integer
A=1 => S=4941 not ps
A can’t be 2/3 because unit digit of any square is not 2/3
So, A=4 => S= 5184 =72^2

Hence A=4

2. shivam mukherjee

Option 1.

Approach:-

I first calculated the value of S i.e,

S= 4860+81A

Then i used options

I realised that S is a perfect square when A is 4.

Hence, option 1 is the answer.

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