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Which of the following numbers has the greatest number of unique digit

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Which of the following numbers has the greatest number of unique digit [#permalink]

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New post 24 Sep 2017, 11:14
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A
B
C
D
E

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Question Stats:

78% (00:31) correct 22% (00:43) wrong based on 37 sessions

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Which of the following numbers has the greatest number of unique digits?

A 1/6
B 1/4
C 1/3
D 3/4
E 5/7
[Reveal] Spoiler: OA

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Re: Which of the following numbers has the greatest number of unique digit [#permalink]

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New post 24 Sep 2017, 12:42
SajjadAhmad wrote:
Which of the following numbers has the greatest number of unique digits?

A 1/6
B 1/4
C 1/3
D 3/4
E 5/7


This can be determined by actual division, which is easiest approach here.

A 0.16....
B 0.52
C 0.3....
D 0.75
E 0.7142....

Hence E is the answer.
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Re: Which of the following numbers has the greatest number of unique digit [#permalink]

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New post 24 Sep 2017, 15:14
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I think the question needs some additional wording to indicate that we're talking about the DECIMAL EQUIVALENT of each fraction.
As it stands, each FRACTION has exactly 2 unique digits.
For example, 1/4 has a 1 and a 4
1/3 has a 1 and a 3
etc

Here's one way to word the original question....

SajjadAhmad wrote:
Which of the following fractions has the greatest number of unique digits in its decimal equivalent?

A 1/6
B 1/4
C 1/3
D 3/4
E 5/7


Interestingly enough, we don't even need to convert answer choice E to a decimal.
Here's why:

A 1/6 = 0.1666666... (2 unique digits)
B 1/4 = 0.25 (2 unique digits)
C 1/3 = 0.3333333... (1 unique digit)
D 3/4 = 0.75 (2 unique digits)

At this point, we know that the decimal equivalent of E (5/7) cannot have just 1 unique digit, since answer choices A, B and D would then be TIED for having the greatest number of unique digits
Likewise, the decimal equivalent of E (5/7) cannot have 2 unique digits, because that would mean answer choices A, B, D and E would then be TIED for having the greatest number of unique digits.
So, we can safely conclude that answer choice E must have the greatest number of unique digits

Cheers,
Brent
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Re: Which of the following numbers has the greatest number of unique digit   [#permalink] 24 Sep 2017, 15:14
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