Questions & Answers

Question

Answers

(A)$ 10 $ (B)$ 8 $ (C)$ 6 $ (D)$ 5 $

Answer
Verified

The number of two-digit numbers from$ 10 $ to $ 99 $ = $ 100 $

The number of two digit numbers having digit $ 3 $ in their unit place \[(13,23,33,43,53,63,73,83,93)\]= \[10\]

We have to find the prime numbers from the above \[10\] numbers; therefore we need to check these numbers one by one that they are prime numbers or not. To check whether a number is a prime number we have to check that the number is divisible by the prime number less than the square root of itself or not.

1)$ 13 $is not divisible by any of the prime numbers less than $ \sqrt {13} $.

2)$ 23 $ is not divisible by any of the prime numbers less than $ \sqrt {23} $.

3)$ 33 $is clearly divisible by $ 3 $(which is less than $ \sqrt {33} $), we can check this by applying the divisibility rule of $3$.

4)$ 43 $is not divisible by any of the prime numbers less than $ \sqrt {43} $.

5)$ 53 $ is not divisible by any of the prime numbers less than $ \sqrt {53} $.

6)$ 63 $ is clearly divisible by $ 3 $( which is less than $ \sqrt {63} $), we can check this by applying the divisibility rule of $ 3 $.

7)$ 73 $ is not divisible by any of the prime numbers less than $ \sqrt {73} $.

8)$ 83 $is not divisible by any of the prime numbers less than $ \sqrt {83} $.

9)$ 93 $is clearly divisible by $ 3 $( which is less than $ \sqrt {93} $), we can check this by applying the divisibility rule of $3 $.

So, there are a total of 6 prime numbers in the given range

×

Sorry!, This page is not available for now to bookmark.