Question

The alphabets a, b, c represent integers forming a two digit number 'ab' and a three digit
number 'ccb. Both are defined under the usual decimal number system. If (ab)2 = ccb and
ccb > 300, then the value of b is:
1) 1
2) 0
3) 5
4) 6
(Past CAT question)​

Answer 1

Answer:

I am assuming that the question is (ab)*(ab) = ccb.

Ok so ab as well as (ab)*(ab) also has its unit's digit as b as (ab)*(ab) = ccb. This can only be possible when b is one of these: 1, 5, 6, 0.

25 is the only 2 digit number whose square 625 is 3 digit and is greater than 300. 15,35,45… don't satisfy the conditions.

Similarly 26*26=676 is the only one which satisfies the above conditions.

Similarly 20*20= 400 and 30*30= 900 are the only squares satisfying the above conditions.

Similarly 21*21= 441 is the only square satisfying the conditions.

Out of 625,676,400,900 and 441, only 441 is of the form ccb as the first digit and the second digit are same.

Hence ccb= 441 and b=1.