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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Tony owns six unique matched pairs of socks. All twelve sock ##### This topic has 4 expert replies and 0 member replies ### Top Member ## Tony owns six unique matched pairs of socks. All twelve sock ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Tony owns six unique matched pairs of socks. All twelve socks are kept loose and unpaired in a drawer. If Tony pulls socks at random, how many must he pull in order to have better than a 50% chance of getting two socks that match? A) 3 B) 4 C) 5 D) 6 E) 7 OA B Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: Tony owns six unique matched pairs of socks. All twelve socks are kept loose and unpaired in a drawer. If Tony pulls socks at random, how many must he pull in order to have better than a 50% chance of getting two socks that match? A) 3 B) 4 C) 5 D) 6 E) 7 OA B Source: Veritas Prep Determining the number of socks that Tony must pull in order to have a better than 50% chance of having two socks that match is the same as determining the number of socks he must pull in order to have a less than 50% chance that these socks are unmatched. Letâ€™s calculate the latter. For the first sock he pulls, the probability that this sock is unmatched to any other is 1. For the second sock he pulls, the probability that this sock is unmatched to the first one is 10/11 (since there are 11 socks left after the first sock and 10 do not match the first sock). Thus, the probability that the two socks are unmatched is 1 x 10/11 = 10/11. For the third sock he pulls, the probability that this sock does not match either of the first two is 8/10 (since there are 10 socks left after the first two socks and 8 of them do not match). Thus, the probability that the three socks do not match is 1 x 10/11 x 8/10 = 8/11. For the fourth sock he pulls, the probability that this sock does not match the first three is 6/9 (since there are 9 socks left after the first three socks and 6 of them do not match). Thus, the probability that the four socks do not match is 1 x 10/11 x 8/10 x 6/9 = 48/99, which is less than 48/96 or 0.5. Thus, we see that if he pulls 4 socks, the probability that these socks do not match is less than 50%. In other words, the probability that two of them will match must be more than 50%. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: Tony owns six unique matched pairs of socks. All twelve socks are kept loose and unpaired in a drawer. If Tony pulls socks at random, how many must he pull in order to have better than a 50% chance of getting two socks that match? A) 3 B) 4 C) 5 D) 6 E) 7 We can PLUG IN THE ANSWERS, which represent the minimum number of socks that must be pulled. When the correct answer choice is plugged in, the probability of NOT picking a matching pair will be LESS than 1/2 (implying that the probability of picking a matching pair will be MORE than 1/2). Since we need to determine the minimum number of socks that must be pulled, we should start with the SMALLEST answer choice. Note: The first sock pulled can be ANY of the 12 socks and thus is irrelevant. Our only concern is whether any of the SUBSEQUENT socks form a matching pair. A: 3 socks pulled After the 1st sock is pulled: P(2nd sock does not match the 1st) = 10/11. (Of the 11 socks left, 10 do not match the 1st sock.) P(3rd sock does not match the 1st or 2nd) = 8/10. (Of the 10 socks left, 8 do not match the 1st or 2nd.) To combine these probabilities, we multiply: 10/11 * 8/10 = 8/11. Since the resulting probability is not less than 1/2, eliminate A. B: 4 socks pulled After the 1st sock is pulled: P(2nd sock does not match the 1st) = 10/11. (Of the 11 socks left, 10 do not match the 1st sock.) P(3rd sock does not match the 1st or 2nd) = 8/10. (Of the 10 socks left, 8 do not match the 1st or 2nd.) P(4th sock does not match 1st, 2nd, or 3rd) = 6/9. (Of the 9 socks left, 6 do not match the 1st, 2nd or 3rd.) To combine these probabilities, we multiply: 10/11 * 8/10 * 6/9 = 16/33. Success! The resulting probability is less than 1/2. The correct answer is B. The OA implies the following: P(not matching set) = 16/33. P(matching set) = 1 - 16/33 = 17/33. The probability in blue is greater than 50%. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2475 messages Followed by: 350 members Upvotes: 1090 GMAT Score: 780 We can work out the probability he continues to get unmatched socks, and once that probability falls below 1/2, we'll know he has a greater than 1/2 chance of getting at least one pair of matched socks. The first sock he picks doesn't matter. The next sock has a 10/11 chance of not matching the first. Now he has two different socks, so of the 10 that remain, only 8 do not match the first two selections, so an 8/10 probability of having no matched pair. Then he has three that don't match, and only 6 of the 9 remaining do not match, for a 6/9 probability of no match. If we multiply these probabilities: (10/11)(8/10)(6/9) = (1/11)(8/1)(2/3) = 16/33 this probability is less than 1/2, so once he picks four socks, the probability is 17/33 that he has at least one pair of matched socks. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: Tony owns six unique matched pairs of socks. All twelve socks are kept loose and unpaired in a drawer. If Tony pulls socks at random, how many must he pull in order to have better than a 50% chance of getting two socks that match? A) 3 B) 4 C) 5 D) 6 E) 7 We can PLUG IN THE ANSWERS, which represent the minimum number of socks that must be pulled. When the correct answer choice is plugged in, the probability of NOT picking a matching pair will be LESS than 1/2 (implying that the probability of picking a matching pair will be MORE than 1/2). Since we need to determine the minimum number of socks that must be pulled, we should start with the SMALLEST answer choice. Note: The first sock pulled can be ANY of the 12 socks and thus is irrelevant. Our only concern is whether any of the SUBSEQUENT socks form a matching pair. A: 3 socks pulled After the 1st sock is pulled: P(2nd sock does not match the 1st) = 10/11. (Of the 11 socks left, 10 do not match the 1st sock.) P(3rd sock does not match the 1st or 2nd) = 8/10. (Of the 10 socks left, 8 do not match the 1st or 2nd.) To combine these probabilities, we multiply: 10/11 * 8/10 = 8/11. Since the resulting probability is not less than 1/2, eliminate A. B: 4 socks pulled After the 1st sock is pulled: P(2nd sock does not match the 1st) = 10/11. (Of the 11 socks left, 10 do not match the 1st sock.) P(3rd sock does not match the 1st or 2nd) = 8/10. (Of the 10 socks left, 8 do not match the 1st or 2nd.) P(4th sock does not match 1st, 2nd, or 3rd) = 6/9. (Of the 9 socks left, 6 do not match the 1st, 2nd or 3rd.) To combine these probabilities, we multiply: 10/11 * 8/10 * 6/9 = 16/33. Success! The resulting probability is less than 1/2. The correct answer is B. The OA implies the following: P(not matching set) = 16/33. P(matching set) = 1 - 16/33 = 17/33. The probability in blue is greater than 50%. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? 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