Question

Which of the following number, some of whose digits have been replaced by @symbol, could possibly be the perfect square of a 3 digits odd number ? (A) 65@@@1
(B) 9@@1
(C) 10@@@4 (D) 9@@@@@@5

Answer 1

Answer:

A

Step-by-step explanation:

We are searching for the square of a three-digit odd number.

(i) Note that the units digit of the square of any odd number is also an odd number.

Therefore, C is ruled out/incorrect. (Its unit digit is 4)

(ii) Also, the number of digits in the square of the least three-digit odd number (101) is 5.

$101^2= 10201$

Therefore, our number should have at least 5 digits in it, as it is greater than 101.

Therefore, B is ruled out/incorrect. (It has only 4 digits)

(iii) Also, the number of digits in the square of the largest three-digit odd number (999) is 6.

$999^2 = 998001$

Therefore, our number should have at most 6digits in it, as it is less than 999.

Therefore, D is ruled out/incorrect. (It has 8 digits)

From the above observations, we can conclude that only A can be the square of a three-digit odd number.

Hence, A is the correct choice.

P.S In fact, A = 65@@@1 corresponds to 657721, which is the square of 811.

Hope this helps!