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# A list of 2018 positive integers has a unique mode, which occurs exact

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Senior Manager
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Joined: 02 Nov 2018
Posts: 280
A list of 2018 positive integers has a unique mode, which occurs exact  [#permalink]

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18 Mar 2019, 10:01
5
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:48) correct 44% (01:44) wrong based on 34 sessions

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A list of 2018 positive integers has a unique mode, which occurs exactly 10 times. What is the least number of distinct values that can occur in the list?

(A) 202
(B) 223
(C) 224
(D) 225
(E) 234
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Joined: 05 Jan 2018
Posts: 8
Re: A list of 2018 positive integers has a unique mode, which occurs exact  [#permalink]

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19 Mar 2019, 00:37
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A list of 2018 positive integers has a unique mode, which occurs exactly 10 times. What is the least number of distinct values that can occur in the list?

the mode occurs 10 times. So remaining digits = 2018-10 = 2008.
For least number of distinct digits, other digits should repeat maximum times but less than 10.
So, 2008/9 = 223 and 1 remainder
=> 223 digits can each repeat 9 times and we will have 1 more distinct digit
=224 total remaining digits
Thus, total unique digits in the list = 224 + 1 (the mode that repeats 10 times) = 225
Re: A list of 2018 positive integers has a unique mode, which occurs exact   [#permalink] 19 Mar 2019, 00:37
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