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form a digit

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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form a digit

by rupsk » Sun Nov 13, 2011 4:11 pm
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

Explain this question
(1)

20


(2)

150

(3)

225

(4)

300

(5)

320
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Source: — Quantitative Reasoning |
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by neelgandham » Sun Nov 13, 2011 4:35 pm
First digit is Even - So the digit should be one among 2,4,6,8
Second digit is Odd - So the digit should be one among 1,3,5,7,9
Third digit is Prime- So the digit should be one among 2,3,5,7
Fourth digit is Odd - So the digit should be one among 3,6,9,0

Case:1 First digit is not 2
Number of ways of forming a Four digit number with the above = 3*5*4*4 = 15*16

Case:2 First digit is 2
Number of ways of forming a Four digit number with the above = 1*5*3*4 = 15*4

Total = 15*16 + 15*4 = 15*20 = 300

IMO D
Last edited by neelgandham on Sun Nov 13, 2011 5:28 pm, edited 1 time in total.
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by rupsk » Sun Nov 13, 2011 5:23 pm
this is not correct answer.
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by neelgandham » Sun Nov 13, 2011 5:31 pm
rupsk wrote:this is not correct answer.
My Bad! I have edited the post. Can you check and let me know if I am correct !
I haven't included 0 in this condition.
Fourth digit is Odd - So the digit should be one among 3,6,9,0
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by rupsk » Sun Nov 13, 2011 7:03 pm
i had written same answer but they say it is 320 but no solution was given.
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