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Integer quest

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Senior | Next Rank: 100 Posts
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by jawad » Tue Sep 09, 2008 12:44 pm
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
Jawad Shah
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Re: Integer quest

by Stuart@KaplanGMAT » Tue Sep 09, 2008 1:39 pm
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).
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