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'A' is the set of the first 100 positive integers. What is the minimum

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'A' is the set of the first 100 positive integers. What is the minimum  [#permalink]

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New post 21 Aug 2019, 10:36
4
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

33% (02:10) correct 67% (01:26) wrong based on 46 sessions

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'A' is the set of the first 100 positive integers. What is the minimum number of elements that should be picked from 'A' to ensure that at least one pair of numbers whose difference is 10 is picked?

(A) 11

(B) 20

(C) 51

(D) 55

(E) 60
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Concentration: Strategy, International Business
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Re: 'A' is the set of the first 100 positive integers. What is the minimum  [#permalink]

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New post 22 Aug 2019, 17:28
by picking the first 9 numbers (1-9), we have to skip the following 9 (10-19)
then pick (20-29), skip (30-39), pick (40-49), skip (50-59), pick (60-69), skip (70-79), pick (80-89), skip (90-99), pick (100)

so the number of picked ones = 9+10+10+10+10+1 = 50
by picking any further number (51th), its difference from at least another number must be 10
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Re: 'A' is the set of the first 100 positive integers. What is the minimum   [#permalink] 22 Aug 2019, 17:28
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'A' is the set of the first 100 positive integers. What is the minimum

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