How many integers?

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

by Vemuri » Tue Mar 17, 2009 6:22 pm

How many integers between 0 and 1570 have a prime tens digit and a prime units digit?

A. 295
B. 252
C. 236
D. 96
E. 76

Is there no easy way to attempt these type of problems? I sometimes find the less lengthy questions more time consuming than the long story telling questions.

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Source: Beat The GMAT — Problem Solving | Tue Mar 17, 2009 6:22 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Tue Mar 17, 2009 7:19 pm

tens and units must be 2,3,5 or 7

I would go with B 252

2 digit numbers = 4*4 = 16

3 digit numbers = 9*4*4 = 144

4 digit number

first digit has to be 1 i.e 1 choice
second digit can be 0,1,2,3,4,5 i.e 6 choices
3 rd digit can be 2,3,5,7 -> 4 choices
4th digit can be 2,3,5,7->4 choices

6*4*4 = 96

16+144+96 = 256

But we would have included 1572,1573,1575,1577 in this

So 256-4 = 252

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

by Vemuri » Tue Mar 17, 2009 11:42 pm

perfecto !!! I like your approach.

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