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4 digit numbers

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4 digit numbers

by kartikshah » Fri Jul 20, 2012 8:19 am
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?

A 20
B 150
C 225
D 300
E 320

OA is D

Please explain
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by Anurag@Gurome » Fri Jul 20, 2012 8:32 am
kartikshah wrote: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?
Number of possible digits for 1st digit : 2, 4, 6, and 8 --> 4 possibilities
Number of possible digits for 2nd digit : 1, 3, 5, 7, and 9 --> 5 possibilities
Number of possible digits for 3rd digit : 2, 3, 5, and 7 --> 4 possibilities
Number of possible digits for 4th digit : 0, 3, 6, and 9 --> 4 possibilities

Hence, a total of 4*5*4*4 = 320 integers

Among these 320 integers, there will be some integers in which the digit 2 have been used more than once. Number of such integers = 1*5*1*4 = 20

Hence, the number of 4-digit integers that satisfy all the criteria = (320 - 20) = 300

The correct answer is D.
Anurag Mairal, Ph.D., MBA
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