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# GMAT Tip of the Week: 99 Problems But Probability Ain't One

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Math Expert
Joined: 02 Sep 2009
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GMAT Tip of the Week: 99 Problems But Probability Ain't One  [#permalink]

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22 Apr 2015, 03:12
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 FROM Veritas Prep Blog: GMAT Tip of the Week: 99 Problems But Probability Ain't One Some of the GMAT’s hardest Problem Solving problems can be made exponentially easier by keeping a famous Jay-Z lyric in the back of your mind. When you hear the phrase:If you’re having girl problems, I feel bad for you son?What immediately springs to mind?I got 99 problems but a b**** ain’t one.Now, what’s the GMAT genius in Hova’s lyric? He didn’t tell you what his problems WERE, he just told you what they WEREN’T. Explaining 99 problems would take way more than the two minutes you’d have for a quant problem or the ~3 minutes that Jay wants to spend on a track. And, like Jay-Z, you want to be Mr. One Take on GMAT problems, doing things the efficient way and getting to the answer much more quickly. So heed his advice when you see a problem like:Solange takes four roundhouse swings at her brother-in-law. If she is just as likely to connect on any one punch as she is to not connect on that punch, what is the probability that she connects on at least one punch?Now, there are plenty of sequences in which she can connect:Hit, Miss, Hit, MissMiss, Miss, Miss, HitHit, Hit, Hit, Hit (ouch!)etc.Trying to list out all the different ways in which she can land a punch is almost as time-consuming as listing all of one’s 99 problems. But think of it this way – which of the sequences available “ain’t one”; which ways does she NOT land a punch. There’s only one:Miss, Miss, Miss, MissAnd so if we’re calculating the probability among the 16 total sequences (each of two things can happen at each of four points, so the total number of sequences is 2^4 = 16), then if one doesn’t work the other 15 must work. So the probability is 15/16. And the “formula” to use on this essentially derives straight from Jay-Z’s lyrics about what “ain’t one”:For complementary events (when the probability of A + the probability of B = 100%), the probability of A = (1 – “not A”). And most strategically, this can be used as:The probability of “At least one” = (1 – probability of “none”)So if you’re calculating the probability of an outcome that has many different paths, see if it’s a cleaner calculation to determine the number of paths that “ain’t one” of your desired outcomes, and then just subtract those from one.Note that this ideology doesn’t just extend to probability. In many problems, calculating all the outcomes that “are” desired is a whole lot harder than calculating the outcomes that “ain’t one” of the desired. Consider this problem from this week’s G-MATT Mondays session:Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?A) 66B) 67C) 68D) 69E) 70Here look at the answer choices – they’re all very, very high numbers for the range (1-70) in question. So if your goal is to try to come up with all the possible coin combinations that work, you’ll be there a while. But what about the combinations that “ain’t one” of the possibilities? Since the maximum is 70, if you find the combinations that don’t work you’re doing this much more efficiently…and the answer choices tell you that at maximum only four won’t work so your job just became a lot easier.With 2 and 5 cent coins as your options, you can’t get to 1 and you can’t get to 3, so those are two “ain’t one” possibilities. And then “100% minus… comes back into play” – Notice too that 70¢ is the maximum possible sum (that would use all the coins), so 70¢ – 1¢, or 69¢, and 70¢ – 3¢, or 67¢ are impossible too. So the answer is 66, but the takeaway is bigger: when calculating all the possibilities looks to be far too time-consuming, you often have the opportunity to calculate the possibilities that “ain’t one.” You’ve got a lot of problems to tackle on test day; hopefully this strategy allows you to make one question much less of one.Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!By Brian Galvin
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Math Expert
Joined: 02 Sep 2009
Posts: 61344
Re: GMAT Tip of the Week: 99 Problems But Probability Ain't One  [#permalink]

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22 Apr 2015, 03:17
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##### General Discussion
Manager
Joined: 21 Feb 2017
Posts: 143
Re: GMAT Tip of the Week: 99 Problems But Probability Ain't One  [#permalink]

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22 Dec 2019, 00:09
Bunuel wrote:
 FROM Veritas Prep Blog: GMAT Tip of the Week: 99 Problems But Probability Ain't One Some of the GMAT’s hardest Problem Solving problems can be made exponentially easier by keeping a famous Jay-Z lyric in the back of your mind. When you hear the phrase:If you’re having girl problems, I feel bad for you son?What immediately springs to mind?I got 99 problems but a b**** ain’t one.Now, what’s the GMAT genius in Hova’s lyric? He didn’t tell you what his problems WERE, he just told you what they WEREN’T. Explaining 99 problems would take way more than the two minutes you’d have for a quant problem or the ~3 minutes that Jay wants to spend on a track. And, like Jay-Z, you want to be Mr. One Take on GMAT problems, doing things the efficient way and getting to the answer much more quickly. So heed his advice when you see a problem like:Solange takes four roundhouse swings at her brother-in-law. If she is just as likely to connect on any one punch as she is to not connect on that punch, what is the probability that she connects on at least one punch?Now, there are plenty of sequences in which she can connect:Hit, Miss, Hit, MissMiss, Miss, Miss, HitHit, Hit, Hit, Hit (ouch!)etc.Trying to list out all the different ways in which she can land a punch is almost as time-consuming as listing all of one’s 99 problems. But think of it this way – which of the sequences available “ain’t one”; which ways does she NOT land a punch. There’s only one:Miss, Miss, Miss, MissAnd so if we’re calculating the probability among the 16 total sequences (each of two things can happen at each of four points, so the total number of sequences is 2^4 = 16), then if one doesn’t work the other 15 must work. So the probability is 15/16. And the “formula” to use on this essentially derives straight from Jay-Z’s lyrics about what “ain’t one”:For complementary events (when the probability of A + the probability of B = 100%), the probability of A = (1 – “not A”). And most strategically, this can be used as:The probability of “At least one” = (1 – probability of “none”)So if you’re calculating the probability of an outcome that has many different paths, see if it’s a cleaner calculation to determine the number of paths that “ain’t one” of your desired outcomes, and then just subtract those from one.Note that this ideology doesn’t just extend to probability. In many problems, calculating all the outcomes that “are” desired is a whole lot harder than calculating the outcomes that “ain’t one” of the desired. Consider this problem from this week’s G-MATT Mondays session:Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?A) 66B) 67C) 68D) 69E) 70Here look at the answer choices – they’re all very, very high numbers for the range (1-70) in question. So if your goal is to try to come up with all the possible coin combinations that work, you’ll be there a while. But what about the combinations that “ain’t one” of the possibilities? Since the maximum is 70, if you find the combinations that don’t work you’re doing this much more efficiently…and the answer choices tell you that at maximum only four won’t work so your job just became a lot easier.With 2 and 5 cent coins as your options, you can’t get to 1 and you can’t get to 3, so those are two “ain’t one” possibilities. And then “100% minus… comes back into play” – Notice too that 70¢ is the maximum possible sum (that would use all the coins), so 70¢ – 1¢, or 69¢, and 70¢ – 3¢, or 67¢ are impossible too. So the answer is 66, but the takeaway is bigger: when calculating all the possibilities looks to be far too time-consuming, you often have the opportunity to calculate the possibilities that “ain’t one.” You’ve got a lot of problems to tackle on test day; hopefully this strategy allows you to make one question much less of one.Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!By Brian Galvin
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

Hi in the Matt problem. 68 is possible too? (70-2). Is that not so? Am i missing something?
Math Expert
Joined: 02 Sep 2009
Posts: 61344
Re: GMAT Tip of the Week: 99 Problems But Probability Ain't One  [#permalink]

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22 Dec 2019, 01:39
1
1
Kritisood wrote:
Bunuel wrote:
 FROM Veritas Prep Blog: GMAT Tip of the Week: 99 Problems But Probability Ain't One Some of the GMAT’s hardest Problem Solving problems can be made exponentially easier by keeping a famous Jay-Z lyric in the back of your mind. When you hear the phrase:If you’re having girl problems, I feel bad for you son?What immediately springs to mind?I got 99 problems but a b**** ain’t one.Now, what’s the GMAT genius in Hova’s lyric? He didn’t tell you what his problems WERE, he just told you what they WEREN’T. Explaining 99 problems would take way more than the two minutes you’d have for a quant problem or the ~3 minutes that Jay wants to spend on a track. And, like Jay-Z, you want to be Mr. One Take on GMAT problems, doing things the efficient way and getting to the answer much more quickly. So heed his advice when you see a problem like:Solange takes four roundhouse swings at her brother-in-law. If she is just as likely to connect on any one punch as she is to not connect on that punch, what is the probability that she connects on at least one punch?Now, there are plenty of sequences in which she can connect:Hit, Miss, Hit, MissMiss, Miss, Miss, HitHit, Hit, Hit, Hit (ouch!)etc.Trying to list out all the different ways in which she can land a punch is almost as time-consuming as listing all of one’s 99 problems. But think of it this way – which of the sequences available “ain’t one”; which ways does she NOT land a punch. There’s only one:Miss, Miss, Miss, MissAnd so if we’re calculating the probability among the 16 total sequences (each of two things can happen at each of four points, so the total number of sequences is 2^4 = 16), then if one doesn’t work the other 15 must work. So the probability is 15/16. And the “formula” to use on this essentially derives straight from Jay-Z’s lyrics about what “ain’t one”:For complementary events (when the probability of A + the probability of B = 100%), the probability of A = (1 – “not A”). And most strategically, this can be used as:The probability of “At least one” = (1 – probability of “none”)So if you’re calculating the probability of an outcome that has many different paths, see if it’s a cleaner calculation to determine the number of paths that “ain’t one” of your desired outcomes, and then just subtract those from one.Note that this ideology doesn’t just extend to probability. In many problems, calculating all the outcomes that “are” desired is a whole lot harder than calculating the outcomes that “ain’t one” of the desired. Consider this problem from this week’s G-MATT Mondays session:Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?A) 66B) 67C) 68D) 69E) 70Here look at the answer choices – they’re all very, very high numbers for the range (1-70) in question. So if your goal is to try to come up with all the possible coin combinations that work, you’ll be there a while. But what about the combinations that “ain’t one” of the possibilities? Since the maximum is 70, if you find the combinations that don’t work you’re doing this much more efficiently…and the answer choices tell you that at maximum only four won’t work so your job just became a lot easier.With 2 and 5 cent coins as your options, you can’t get to 1 and you can’t get to 3, so those are two “ain’t one” possibilities. And then “100% minus… comes back into play” – Notice too that 70¢ is the maximum possible sum (that would use all the coins), so 70¢ – 1¢, or 69¢, and 70¢ – 3¢, or 67¢ are impossible too. So the answer is 66, but the takeaway is bigger: when calculating all the possibilities looks to be far too time-consuming, you often have the opportunity to calculate the possibilities that “ain’t one.” You’ve got a lot of problems to tackle on test day; hopefully this strategy allows you to make one question much less of one.Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!By Brian Galvin
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

Hi in the Matt problem. 68 is possible too? (70-2). Is that not so? Am i missing something?

That question is discussed here: https://gmatclub.com/forum/matt-is-tour ... 75202.html Hope it helps.
_________________
Re: GMAT Tip of the Week: 99 Problems But Probability Ain't One   [#permalink] 22 Dec 2019, 01:39
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