Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares? (CAT 2007)

The correct option is C 1
Soln:

Using the technique of finding squares of numbers upto 100 by keeping the base of 50 and 100( refer to the e-booklet for further details). We see that only squares of 12 will end with 144 (or the last 2 digits being the same). Hence we will have to find out if the first 2 digits will be the same for squares of 38, 62 (absolute difference of 12 from 50) and also for 88 (absolute difference of 12 from 100), we see that only 88 satisfies the condition, hence option 4.