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24 Apr 2026, 16:37
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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:
95%
(hard)
Question Stats:
32% (02:42) correct
68%
(02:15)
wrong
based on 31
sessions
History
Date
Time
Result
Not Attempted Yet
A drawer in a Anton’s room contains 10 pairs of socks of each of three colors. Anton takes out socks one at a time from the drawer at random but does not notice the color of the socks drawn. What is the smallest number of socks that he must take out so that they form at least 10 pairs of color-matched socks?
A. 20
B. 21
C. 22
D. 23
E. 24
A. 20
B. 21
C. 22
D. 23
E. 24
kevincan
A drawer in a Anton’s room contains 10 pairs of socks, each of three colors.
So each pair is available in three colours. Let the three colours be B,G,R.
So there are a total of \(60\) socks.
To ensure we get at least \(10\) pairs, we have to check the worst case scenario.
B,G,R
B,G,R
B,G,R
B,G,R
B,G,R
B,G,R
B,G,R
Till now we have \(9\) pairs of each colour. Whatever colour we pick next, we will get \(10\) pairs of a single colour.
\(7*3+1 = 22\) socks. Hence \(22\) socks are required in the worst case scenario.
Ans C
Hope it helped.
25 Apr 2026, 11:57
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This is a classic Min-Max / Pigeonhole problem. The 43% accuracy rate on GMAT Club for this one tells you it trips people up.
The question: you have 30 pairs of socks (10 pairs each of 3 colors = 60 individual socks). You're pulling socks blindly. What's the minimum number to guarantee at least 10 color-matched pairs?
Worst case thinking is the key here. To answer "minimum to guarantee X," you always ask: what's the maximum you could pull and still NOT have X? Then add 1.
So: what's the maximum socks you could pull while having fewer than 10 matched pairs?
Work backwards. You want to keep matched pairs under 10, so at most 9 complete matched pairs. That's 18 socks forming 9 pairs. Then to delay the 10th pair as long as possible, you draw one extra sock of each remaining color as unmatched singletons. 3 colors = 3 extra socks.
Total so far: 18 + 3 = 21 socks, and you have exactly 9 matched pairs.
The 22nd sock you pull MUST match one of those 3 singletons (there are only 3 colors and you already have a singleton of each), giving you a 10th matched pair.
So the answer is 22. Answer choice C.
The trap that catches people: they try to think about it as "worst case per color" and get confused about distributions. The cleaner move is always to ask "what's the last state before I hit the target?" then add 1 sock.
Stne's answer above is right too, just explained via a slightly different path. Both get to 22.
The question: you have 30 pairs of socks (10 pairs each of 3 colors = 60 individual socks). You're pulling socks blindly. What's the minimum number to guarantee at least 10 color-matched pairs?
Worst case thinking is the key here. To answer "minimum to guarantee X," you always ask: what's the maximum you could pull and still NOT have X? Then add 1.
So: what's the maximum socks you could pull while having fewer than 10 matched pairs?
Work backwards. You want to keep matched pairs under 10, so at most 9 complete matched pairs. That's 18 socks forming 9 pairs. Then to delay the 10th pair as long as possible, you draw one extra sock of each remaining color as unmatched singletons. 3 colors = 3 extra socks.
Total so far: 18 + 3 = 21 socks, and you have exactly 9 matched pairs.
The 22nd sock you pull MUST match one of those 3 singletons (there are only 3 colors and you already have a singleton of each), giving you a 10th matched pair.
So the answer is 22. Answer choice C.
The trap that catches people: they try to think about it as "worst case per color" and get confused about distributions. The cleaner move is always to ask "what's the last state before I hit the target?" then add 1 sock.
Stne's answer above is right too, just explained via a slightly different path. Both get to 22.
