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What is the smallest positive multiple of 15 that has only 0

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by Max@Math Revolution » Sun Apr 21, 2019 11:52 pm

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[GMAT math practice question]

What is the smallest positive multiple of 15 that has only 0 and 1 as digits?

A. 15
B. 30
C. 110
D. 1110
E. 111000
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by Max@Math Revolution » Wed Apr 24, 2019 12:18 am
=>

A multiple of 15 is a number divisible by both 3 and 5.
Since it is divisible by 5, its units digit must be 0 or 5.
Since it is divisible by 3, the sum of its digits must be a multiple of 3.
1110 is the smallest number with only 0 and 1 as its digits that has a units digit of 0 or 5 and the sum of its digits a multiple of 3.

Therefore, D is the answer.
Answer: D
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by Scott@TargetTestPrep » Thu Apr 25, 2019 5:50 pm
Max@Math Revolution wrote:[GMAT math practice question]

What is the smallest positive multiple of 15 that has only 0 and 1 as digits?

A. 15
B. 30
C. 110
D. 1110
E. 111000
Notice that 15 is divisible by 3 and 5, so any multiple of 15 would be also divisible by 3 and 5. Let's now analyze the given answer choices. We can eliminate choices A and B since they don't have only 0 and 1 as digits. As for choice C, 110, it is not a multiple of 15 since it's not divisible by 3. Now, let's examine D. 1110 is divisible by 3 since the the sum of its digits is divisible by 3. Furthermore, it's divisible by 5 since the last digit is 0. Therefore, 1110 is the smallest positive multiple of 15 that has only 0 and 1 as digits.

Answer: D.

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