Question

how many numbers less than 1000 are there such that the ten's digit of their square is odd?​

Answer 1

Step-by-step explanation:

One, two, three can be crossed out seeing their square is a single digit.

4’s square has 1 at it's ten's place. 5 has 2, 6 has 3, 7 has 4, 8 has 6, 9 has 8, etc.

The list of numbers less than 1000 having their ten's digit odd:

4,6,14,16,24,26,34,36,44,46,54,56,64,66,74,76,84,86,94,96,104,106,114,116,124,126,…,204,206,214,216,…,304,306,…,904,906,914,916,..,994,996.

There are 200 numbers.

Reasoning: Let a two digit number be (10a+p). Squaring it:

20ap (the ten's digit) will stay an even number unless his neighbour do not give some odd carry to it.

Numbers ending with 4 and 6 passes 1 and 3, respectively to 20ap, proselytizing it from even to odd

Answer 2

$\small\sf\underline\purple{Required \: Answer}$

One, two, three can be crossed out seeing their square is a single digit. 4's square has 1 ... 9 has 8, etc. The list of numbers less than 1000 having their ten's digit odd: 4,6,14,16,24,26,34, 3.

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