## Quant Question Of The Day: 57

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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’: **

Ans is (1) i.e 4.

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

(1) 4

4

4

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.

1. 4