Q5 REPRESENTATIONS

Let a, b, c be distinct digits. Consider a two-digit number 'ab' and a three-digit number 'ccb', both defined under the usual decimal number system, if (ab)² = ccb> 300, then the value of b is

a. 1

b. 0

c. 5

d. 6

(ab)^2 = ccb

ccb > 300

The last digit of the number ab must be same as that of the square of ab

So, b can be 0, 1, 5 or 6.

20^2 = 400 and 30^2 = 900 are three digit numbers and greater than 300.

But the first 2 digits are not same.

Hence, b is not 0.

If b is 5, then the ten's digit of ab square will be 2 => c = 2. But if c is 2, then ccb is not greater than 300. Hence, b is not 5.

If b is 6, then 26² = 676 is the only three digit number that is greater than 300. But, it is not in the form of ccb  => b is not 6.

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