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How many five digit numbers can be formed using digits 0,1,2

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Anaira Mitch Master | Next Rank: 500 Posts
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How many five digit numbers can be formed using digits 0,1,2

Post Thu Nov 09, 2017 5:55 am
How many five- digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 3, without any of the digits repeating?

A. 15
B. 96
C. 120
D. 181
E. 216

OA:E

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GMAT/MBA Expert

Post Thu Nov 09, 2017 6:04 am
Anaira Mitch wrote:
How many five- digit numbers can be formed using digits 0,1,2,3,4,5, Which are divisible by 3, without any of the digits repeating?

A. 15
B. 96
C. 120
D. 181
E. 216
If the sum of the digits of integer N is a multiple of 3, then N itself is a multiple of 3.

Adding 5 of the digits above, there are 2 ways to get a sum that is a multiple of 3 if no digit is repeated:
1+2+3+4+5 = 15 and 0+1+2+4+5 = 12.

Number of ways to arrange 1,2,3,4,5 = 5! = 120.

Number of 5-digit integers composed of 0,1,2,4,5:
Ten-thousands digit can be 1,2,4,5 = 4 choices.
Number of ways to arrange the remaining 4 digits = 4! = 24.
Combining our choices for the digits, we get:
Number of possible integers = 4*24 = 96.

Thus, total possible integers = 120+96 = 216.

The correct answer is E.

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