Integer quest

jawad wrote:hi ,
Pls help in resolving the below question :-

How many 4-digit numbers begin with a digit that is prime and end with a digits that prime ?

options are below

16
80
800
1440
1600

regards/jawad

The prime digits are 2, 3, 5 and 7

So, the question is: how many 4 digit integers start with 2, 3, 5 or 7 and end with 2, 3, 5 or 7?

Let's simplify one step further and just think about 2 digit intgers:

how many 2 digit integers start with 2, 3, 5 or 7 and end with 2, 3, 5 or 7?
Well, that's going to be 4 * 4 = 16

The two digits in the middle of our 4 digit integer could be anything from 00 to 99 - so there are 100 "fillers" for each of our pairs of primes.

16 * 100 = 1600... choose (e).