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

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Math Revolution GMAT Instructor
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What is the smallest positive multiple of 15 that has only 0 and 1 as  [#permalink]

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New post 22 Apr 2019, 00:51
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

90% (01:15) correct 10% (01:03) wrong based on 21 sessions

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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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Re: What is the smallest positive multiple of 15 that has only 0 and 1 as  [#permalink]

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New post 22 Apr 2019, 01:10
It was tricky, somehow.
I wont bet that on real GMAT, under time pressure, I wont circle C

When you read the stem well and are about to check the answers, the first two options make you come back to the stem and read again,
Yep what da hell those 5 (in A) and 3 (in B) are doing there, we want the answer with only 0s and 1s

Look at C, it satisfies the concerns written above, smash that one, but wait a minute 110 is not a multiple of 15 at all, it's not divisible by 3

choice D consists of 0s and 1s, is divisible by 5 and 3, what else? choice E is much larger, so I've circled D with cautious

Questions like that at the end of GMAT exam reduced my score to 48

IMO
Ans: D
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What is the smallest positive multiple of 15 that has only 0 and 1 as  [#permalink]

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New post 22 Apr 2019, 02:51
1110:15 = 74. Multiple of 15 confirmed. Pick D.
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Re: What is the smallest positive multiple of 15 that has only 0 and 1 as  [#permalink]

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New post 22 Apr 2019, 03:16
1
It is given that 1 & 0 are the only digits
SO Lets prime factorize 15. We gwt 5 & 3.
Apply divisiblity rule for each. If both satisfy it is divisible.

C: 110 not divisble by 3
D: Satisfys for both 5 & 3
E: Satisfys for both 5 & 3

Smallest number needed. Thus D

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Re: What is the smallest positive multiple of 15 that has only 0 and 1 as  [#permalink]

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New post 24 Apr 2019, 01:27
=>

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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Re: What is the smallest positive multiple of 15 that has only 0 and 1 as   [#permalink] 24 Apr 2019, 01:27
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