 Mathematics
20 May, 21:41

# Prajna is listing squares of two-digit numbers in such a way that the digit in their units place is 6.How many numbers should he have listed?

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1. 21 May, 00:30
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2 (option B)

Question:

Prajna is listing squares of two-digit numbers in such a way that the digit in their units place is 6.

How many numbers should he have listed?

a) 9 b) 2 c) 18 d) 20

Step-by-step explanation:

We would find the perfect squares that are two digit numbers

For two digit perfect squares:

Largest two digit number = 81 = 9²

Smallest two digit number = 16 = 4²

Total Two digit number perfect squares = Highest number - lowest number + 1

= 9-4+1 = 6

There are 6 two digit perfect squares

Next, we have to find how many of them have 6 in their units place.

The rule to be applied: If a number has 4 or 6 in the unit place, then its square has 6 in the units place.

Following this, the possibilities are 4², 6².

We have two of such numbers.

Therefore, he would have listed 2 numbers.