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What is the largest multiple of 24 that can be written using

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by Max@Math Revolution » Mon Apr 15, 2019 12:14 am

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[GMAT math practice question]

What is the largest multiple of 24 that can be written using each of the digits 0, 1, 2, ... , 9 exactly once?

A. 9876543210
B. 9876543120
C. 987654102
D. 1234567890
E. 1234567980
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by Max@Math Revolution » Wed Apr 17, 2019 12:16 am
=>

A number is a multiple of 24 precisely when it is a multiple of both 3 and 8.
The sum of 0, 1, 2, ... , 9, "0 + 1 + 2 + ... + 9 = 45" is a multiple of 3. Thus, a number which uses each of the digits 0, 1, 2, ... , 9 exactly once is a multiple of 3.
In order for a number to be a multiple of 8, the last three digits of the number must be a multiple of 8. And the smallest multiple of 8 that can be formed using three of the digits 0, 1, 2, ... , 9 is 120.
Thus, the biggest possible multiple of 24 is 9876543120.

Therefore, B is the answer.
Answer: B
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