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What percent of the integers between 100 and 999, inclusive,

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What percent of the integers between 100 and 999, inclusive, [#permalink] New post 24 Mar 2017, 14:21
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What percent of the integers between 100 and 999,
inclusive, have all three digits the same?


(A) 1%
(B) 2%
(C) 3%
(D) 4%
(E) 5%


Anyone willing to solve this problem? Thanks
[Reveal] Spoiler: OA
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GRE Instructor
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Re: What percent of the integers between 100 and 999, inclusive, [#permalink] New post 24 Mar 2017, 15:38
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Expert's post
HarveyKlaus wrote:
What percent of the integers from 100 to 999, inclusive, have all three digits the same?


(A) 1%
(B) 2%
(C) 3%
(D) 4%
(E) 5%



A nice rule says: the number of integers from x to y inclusive equals y - x + 1
999 - 100 + 1 = 900
So, there are 900 integers from 100 to 999, inclusive

Of those 900 integers, the integers with all 3 digits the same are: 111, 222, 333, 444, 555, 666, 777, 888, and 999
So, there are 9 altogether.

So, 9/900 = what percent?
Well, 9/900 = 1/100 = 1%

Answer:
[Reveal] Spoiler:
A


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Re: What percent of the integers between 100 and 999, inclusive, [#permalink] New post 13 May 2018, 16:46
Expert's post
HarveyKlaus wrote:
What percent of the integers between 100 and 999,
inclusive, have all three digits the same?


(A) 1%
(B) 2%
(C) 3%
(D) 4%
(E) 5%


There are 9 possible options to get all the digits the same in the numbers 100 to 999 inclusive:

111, 222, 333, 444, 555, 666, 777, 888, 999

There are 900 numbers from 100 to 999 inclusive.

So the percent is 9/900 = 1/100 = 1%.

Answer: A
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Re: What percent of the integers between 100 and 999, inclusive,   [#permalink] 13 May 2018, 16:46
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