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21 Aug 2019, 10:36
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
49% (02:09) correct
51%
(01:38)
wrong
based on 157
sessions
History
Date
Time
Result
Not Attempted Yet
'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
(A) 11
(B) 20
(C) 51
(D) 55
(E) 60
22 Aug 2019, 17:28
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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
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
General Discussion
04 Sep 2020, 06:25
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Given
To Find
Approach and Working Out
- 'A' is the set of the first 100 positive integers.
To Find
- • 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.
Approach and Working Out
- • I can pick 1 to 10 but then can’t pick 11 to 20 and then again can pick 21 to 30 and so on.
- o So without any possible pairs, we can pick 50 numbers.
• We need the 51st number to be able to have a pair with a difference of 10.
