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John has 10 pairs of matched socks. If he loses 7 individual
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11 Sep 2012, 04:41
Question Stats:
87% (00:37) correct 13% (00:44) wrong based on 1291 sessions
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John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left? (A) 7 (B) 6 (C) 5 (D) 4 (E) 3 Practice Questions Question: 39 Page: 157 Difficulty: 600
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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11 Sep 2012, 04:42
SOLUTIONJohn has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?(A) 7 (B) 6 (C) 5 (D) 4 (E) 3 General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others. The lowest number of pairs we can make from 7 individual socks is 3 pairs and one sock from a fourth pair. Hence, the greatest number of pairs of matched socks John can have left is 10  4 = 6. Answer: B.
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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12 Sep 2012, 12:32
John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left? (A) 7 (B) 6 (C) 5 (D) 4 (E) 3 Because we have to maximize the pair of matched socks, we will remove 3 pairs(6 socks) out of 10 pairs & 1 sock from the 4th pair. Thus the no of matching socks pair remaining = 10 4 = 6 Answer B If we were asked minimum no of pairs of matched socks, we would have removed all the 7 socks from 7 different pairs out of 10 pairs. Thus the no of matching socks pair remaining = 10 7 = 3 Answer E Hope it helps
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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11 Sep 2012, 09:28
Since question is asking the Greatest number of pairs left after John loses 7 socks, it is better to count the socks in pairs. In total 7 socks are lost, which can be counted as 3 pairs of socks (3x2) + 1 single socks. So in total 4 pairs are lost as 1 single sock can not be counted in a pair. So, 10  4 = 6 pairs of socks. B
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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14 Sep 2012, 05:50
SOLUTIONJohn has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?(A) 7 (B) 6 (C) 5 (D) 4 (E) 3 General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others. The lowest number of pairs we can make from 7 individual socks is 3 pairs and one sock from a fourth pair. Hence, the greatest number of pairs of matched socks John can have left is 10  4 = 6. Answer: B. Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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17 Sep 2012, 10:46
I'm thinking that if he has 10 pairs, that is 20 socks. If he loses 7 individual socks, then the greatest number of socks he could have left is:
207= 13 > 6 pairs, since 13/2 is not an integer.
Hence, the answer is B.



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Re: John has 10 pairs of matched socks. If he loses 7 individual
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26 Nov 2012, 14:01
Hi there This might sound silly but when I read this question I initially drew out aa bb cc etc as his socks and crossed out one letter of each 7 pairs which left me with 3 pairs left, could someone explain how clearly this is a wrong approach? How do I know that his socks are all the same. Thank u



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Re: John has 10 pairs of matched socks. If he loses 7 individual
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30 Jun 2015, 22:22
If he loses 7 socks, to maximise the number of pairs of matching socks we should assume that he lost 3 pairs of socks and 1 sock from a different pair, so that rules out 4 pairs. maximum possible pairs he is left with is 6.
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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27 May 2016, 07:19
Bunuel wrote: John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?
(A) 7 (B) 6 (C) 5 (D) 4 (E) 3 Let’s label each pair of socks with letters. AA = pair 1 BB = pair 2 CC = pair 3 DD = pair 4 EE = pair 5 FF = pair 6 GG = pair 7 HH = pair 8 JJ = pair 9 KK = pair 10 We are given that he loses 7 individual socks and need to find the greatest number of pairs of matched socks he can have left. Strategically, this means that if we lose one sock from a particular pair of socks, we also want to lose the other sock from that same pair. So, for instance, John could lose the following: A, A, B, B, C, C, D The pairs of socks John has left are as follows: EE, FF, GG, HH, JJ, and KK. Thus, the greatest number of pairs of matched socks John could have left is 6 pairs. The answer is B.
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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28 Jul 2017, 07:57
I used the answer choices to help me get to the answer A. 7 Pairs left. Means initially he has 7*2+7 = 21 Socks. Not possible, since he had total of 10 pairs (20 Socks) B. 6 Pairs left. Means initially he has 6*2+7 = 19 Socks. Possible. Rest all options will decrease the pair of Socks. Since the MAX pair possible is asked, the right answer has to be B.
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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10 Jan 2018, 16:20
Bunuel niks18 VeritasPrepKarishmaIs below approach correct: Total no of socks: 20 No of socks lost: 7 No. of socks remaining: 13 Out of 13 socks, I can make only 6 matched pairs at max.
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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10 Jan 2018, 20:30
adkikani wrote: Bunuel niks18 VeritasPrepKarishmaIs below approach correct: Total no of socks: 20 No of socks lost: 7 No. of socks remaining: 13 Out of 13 socks, I can make only 6 matched pairs at max. _____________________ Yes.
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Re: John has 10 pairs of matched socks. If he loses 7 individual
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01 Jul 2019, 10:51
Individual socks lost = 7 3 pairs are lost and 1 socks but a pair is not completed with only 1 sock. Hence, maximum number of pairs of matched socks he can have left = 10  4 = 6 pairs So, Answer choice is (B).




Re: John has 10 pairs of matched socks. If he loses 7 individual
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