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14 Mar 2019, 23:57
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (02:31) correct
53%
(02:26)
wrong
based on 115
sessions
History
Date
Time
Result
Not Attempted Yet
A drawer in a darkened room contains 100 red socks, 80 green socks, 60 blue socks and 40 black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at least 10 pairs? (A pair of socks is two socks of the same color. No sock may be counted in more than one pair).
(A) 21
(B) 23
(C) 24
(D) 30
(E) 50
(A) 21
(B) 23
(C) 24
(D) 30
(E) 50
Archit3110
16 Mar 2019, 01:53
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Bunuel
so as to get 1 pair of socks we would require to pick atleast 5 socks ;similarly to get 2 pairs of socks 7 socks are required to be removed
for 3 pairs of socks 9 socks are required to be removed...
if we observe there is a pattern of 2p+3 ; p is no of desired pairs ; so here p = 10
we get 23
IMO B
General Discussion
15 Mar 2019, 01:46
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My logic may be wrong. Luckily the question asks for 10 pairs (and not 10 pairs of the same colour). We just need the one combination which might disprove an answer. We can consider each answer in turn applying pretty much the same logic (each letter represents the colour of the sock and Bl. represents black socks):
A. He can pick out 19Bl., 1R and 1G. That's 9.5 pairs and short of the 10 pairs. At this point the youngster may consider turning the lights on, looking at the socks he is picking out or asking for help.
B. Same logic applies as above: 19Bl., 1R, 1G, 1B and the final one has to be any of Bl, B, R or G, making 10 pairs. It is necessary to think of mathematical counter-arguments: he could've equally have picked out 5G, 5B, 5R, 8Bl giving 10 pairs! Other combos? 6G, 6B, 6R and 2Bl giving 10 pairs. What if the first few socks were all of different colours then 1G, 1R, 1B, 20 Bl. 10 Pairs. I think it help picking out the extremes.
C. Again, same logic so as to test out the B. 1G, 1R, 1B and 21Bl works and at this point we probably would have exhausted most of our time on the question.
A. He can pick out 19Bl., 1R and 1G. That's 9.5 pairs and short of the 10 pairs. At this point the youngster may consider turning the lights on, looking at the socks he is picking out or asking for help.
B. Same logic applies as above: 19Bl., 1R, 1G, 1B and the final one has to be any of Bl, B, R or G, making 10 pairs. It is necessary to think of mathematical counter-arguments: he could've equally have picked out 5G, 5B, 5R, 8Bl giving 10 pairs! Other combos? 6G, 6B, 6R and 2Bl giving 10 pairs. What if the first few socks were all of different colours then 1G, 1R, 1B, 20 Bl. 10 Pairs. I think it help picking out the extremes.
C. Again, same logic so as to test out the B. 1G, 1R, 1B and 21Bl works and at this point we probably would have exhausted most of our time on the question.
