An algebra problem by Ritik Devnani

Algebra Level 2

Which of the following numbers, some of whose digits have been replaced by @ symbol, could possibly be the perfect square of a 3 digit odd number?

9@@1 65@@@1 9@@@@@5 10@@@4

1 solution

Guillermo Templado
Jan 21, 2018

$809^2 = 654481$ . The square of a 3- digit number has at least 5 digits and at most 6 digits. This implies 2 answers are imposible. The answer 10@@@4 is also possible because it would be a square of a number $n$ belonging to $(316, 331)$ and $n$ has to finish in 2 or 8. For example $322^2 = 103684$ .

what is the answer in your poinion then?

Ritik Devnani - 3 years, 4 months ago

There are 3 possible 3- digit numbers such that their squares are of the shape 10@@@4. These are 318, 322 and 328. And there are 2 possible 3- digit numbers such that their squares are of the shape 65@@@1. These are 809 and 811. Therefore, this problem has 2 answers right.

Guillermo Templado - 3 years, 4 months ago

Then report it

Saksham Jain - 3 years, 4 months ago

@Saksham Jain – Thanks. This is the paper where I got the question -: https://www.examrace.com/d/pdf/14cbb148/NSTSE-Class-8-Solved-Paper-2014.pdf

Ritik Devnani - 3 years, 4 months ago

@Ritik Devnani – Question no?

Saksham Jain - 3 years, 4 months ago

The square of a 3 digit number can have a maximum of 6 digits. So, 9@@@@@5 and 9@@1 are not possible. Also the square of an odd number doesn't end with an even number so 1@@@4 is also not possible. Therefore , the answer is 65@@@1

Praveena Nookala - 1 year, 11 months ago

An algebra problem by Ritik Devnani

1 solution

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