4 digit numbers

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kartikshah: Master | Next Rank: 500 Posts; Posts: 156; Joined: Sun Jul 15, 2012 12:03 pm; Location: New York, USA; Thanked: 34 times; Followed by:1 members

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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Source: Beat The GMAT — Problem Solving | Fri Jul 20, 2012 8:19 am

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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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