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# A number of people each wrote down one of the first 30

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A number of people each wrote down one of the first 30 [#permalink]

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06 Dec 2012, 07:17
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A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people?

(1) The number of people who wrote down an integer was greater than 40.
(2) The number of people who wrote down an integer was less than 70.
[Reveal] Spoiler: OA
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Re: A number of people each wrote down one of the first 30 [#permalink]

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27 Apr 2015, 15:17
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Hi All,

This DS questions is a great example of how you can "rewrite" the question to find "the question behind the question."

We're told that an unknown number of people EACH wrote down one of the first 30 positive integers (1-30, inclusive). We're asked if ANY of the integers were written down by MORE than one person. This is a YES/NO question.

Given the 'restrictions' in this question, IF there are MORE than 30 people, then at least one of the numbers would be repeated. If there are 30 or LESS, then it's possible that a number was repeated, BUT it's also possible that NONE of the numbers were repeated. So the question is really asking...."Were there more than 30 people?"

Fact 1: The number of people....was greater than 40

This GUARANTEES that at least 1 of the numbers was written more than once, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: The number of people....was less than 70

IF....
The total number of people was greater than 30, then the answer to the question is YES.

IF...
The total number of people is 30 or LESS, then the answer to the question COULD be YES, but it COULD be NO.
Fact 2 is INSUFFICIENT.

[Reveal] Spoiler:
A

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# Rich Cohen

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Math Expert Joined: 02 Sep 2009 Posts: 35266 Followers: 6632 Kudos [?]: 85454 [0], given: 10236 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 06 Dec 2012, 07:23 Expert's post 2 This post was BOOKMARKED A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people? There are 30 integers from 1 to 30, inclusive, thus the maximum number of people possible all of them to write different integers is 30. If there are more than 30 people, then at least one of the integers has to be written by more than one person. (1) The number of people who wrote down an integer was greater than 40 --> at least one of the integers has to be written by more than one person. Sufficient. (2) The number of people who wrote down an integer was less than 70. Not sufficient. Answer: A. _________________ Manager Joined: 22 Mar 2011 Posts: 67 Followers: 1 Kudos [?]: 13 [0], given: 10 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 07 May 2013, 00:18 Bunuel wrote: A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people? There are 30 integers from 1 to 30, inclusive, thus the maximum number of people possible all of them to write different integers is 30. If there are more than 30 people, then at least one of the integers has to be written by more than one person. (1) The number of people who wrote down an integer was greater than 40 --> at least one of the integers has to be written by more than one person. Sufficient. (2) The number of people who wrote down an integer was less than 70. Not sufficient. Answer: A. How can we say that for sure? Its also possible that all the individuals wrote down 1. There is no mention that everyone has to write a unique number. Math Expert Joined: 02 Sep 2009 Posts: 35266 Followers: 6632 Kudos [?]: 85454 [0], given: 10236 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 07 May 2013, 00:22 melguy wrote: Bunuel wrote: A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people? There are 30 integers from 1 to 30, inclusive, thus the maximum number of people possible all of them to write different integers is 30. If there are more than 30 people, then at least one of the integers has to be written by more than one person. (1) The number of people who wrote down an integer was greater than 40 --> at least one of the integers has to be written by more than one person. Sufficient. (2) The number of people who wrote down an integer was less than 70. Not sufficient. Answer: A. How can we say that for sure? Its also possible that all the individuals wrote down 1. There is no mention that everyone has to write a unique number. Say the number of people is 41. Each should write down one of the first 30 positive integers (1, 2, 3, ..., 30). Ask yourself, can each of them write the different integer? _________________ Manager Joined: 22 Mar 2011 Posts: 67 Followers: 1 Kudos [?]: 13 [0], given: 10 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 07 May 2013, 01:56 A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people? (1) The number of people who wrote down an integer was greater than 40. (2) The number of people who wrote down an integer was less than 70. I am not sure what is stopping all 40 people from writing down number 1 on their paper? Why does it has to be a sequence.. All of the 40 can just write a single number (i.e. 1) on their paper. Math Expert Joined: 02 Sep 2009 Posts: 35266 Followers: 6632 Kudos [?]: 85454 [0], given: 10236 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 07 May 2013, 02:10 melguy wrote: A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people? (1) The number of people who wrote down an integer was greater than 40. (2) The number of people who wrote down an integer was less than 70. I am not sure what is stopping all 40 people from writing down number 1 on their paper? Why does it has to be a sequence.. All of the 40 can just write a single number (i.e. 1) on their paper. Yes, and in this case one of the integers (1) will be written down by more than one of the people. Thus the answer to the question will be YES. Does this make sense? _________________ Manager Joined: 22 Mar 2011 Posts: 67 Followers: 1 Kudos [?]: 13 [0], given: 10 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 07 May 2013, 02:25 Ah....I get the problem now. Its an easy problem! Actually I was thinking exactly the opposite in my brain and wondering why am i getting the wrong answer! Time to cut down on careless mistakes Thanks for your patience while my brain was switched off GMAT Club Legend Joined: 09 Sep 2013 Posts: 12189 Followers: 541 Kudos [?]: 151 [0], given: 0 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 02 Aug 2014, 16:48 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 21 Jun 2014 Posts: 2 Followers: 0 Kudos [?]: 0 [0], given: 1 A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 05 Dec 2014, 16:36 This one can be confusing... I made the mistake of not reading the statements properly. The statements are giving the number of people not the sum of the amount of the number that the people wrote down. Statement 1: There at least 10 numbers that are written twice because 30 of the people could write down different numbers but after that the rest of the people have to reuse numbers that were already written down. Statement 2: The number of people could be 30 and each one writing a different number... So we don't know if there are any duplicate numbers. Intern Joined: 18 Apr 2015 Posts: 37 Followers: 0 Kudos [?]: 2 [0], given: 5 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 26 Apr 2015, 13:00 Hi, Consider there are 3 ppl and we are asked to write down any integers from 1 to 30. I could write 2 the next one could write 10 ,the 3rd one could write 2 as well.So does the number of ppl really matter here. By the above logic both the statements have to be correct. Please correct me if i am wrong Math Forum Moderator Joined: 06 Jul 2014 Posts: 1274 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Followers: 135 Kudos [?]: 1639 [0], given: 178 A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 26 Apr 2015, 13:10 kirtivardhan wrote: Hi, Consider there are 3 ppl and we are asked to write down any integers from 1 to 30. I could write 2 the next one could write 10 ,the 3rd one could write 2 as well.So does the number of ppl really matter here. By the above logic both the statements have to be correct. Please correct me if i am wrong In DS questions, statement will be sufficient if answer is definite. In case which you descrive two variants are possbile: Some of this 3 persons could write the same numbers or maybe they are wrote three different numbers. For DS this is insufficient answer. _________________ Intern Joined: 18 Apr 2015 Posts: 37 Followers: 0 Kudos [?]: 2 [0], given: 5 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 26 Apr 2015, 13:48 Following the same logic,both the statements should have been insufficient right? Math Forum Moderator Joined: 06 Jul 2014 Posts: 1274 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Followers: 135 Kudos [?]: 1639 [0], given: 178 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 26 Apr 2015, 13:52 kirtivardhan wrote: Following the same logic,both the statements should have been insufficient right? No, because from first statement you know that numbers will be repeat in ANY case. Because 40 people can't write first 30 numbers and don't repeat them. So it's definite answer and this sufficient. _________________ Intern Joined: 18 Apr 2015 Posts: 37 Followers: 0 Kudos [?]: 2 [0], given: 5 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 28 Apr 2015, 20:26 Hi Bunnel, The thing i am not able to understand is why not 2 ppl write the same number.In that case whether the number of ppl >40 or <70 the number that they write will be repeated. Please assist Math Forum Moderator Joined: 06 Jul 2014 Posts: 1274 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Followers: 135 Kudos [?]: 1639 [0], given: 178 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 28 Apr 2015, 23:35 kirtivardhan wrote: Hi Bunnel, The thing i am not able to understand is why not 2 ppl write the same number.In that case whether the number of ppl >40 or <70 the number that they write will be repeated. Please assist Hello kirtivardhan You understand absolutely right: people from 2 statement will write the same number in any case. And we sure about this and that's why second statement Sufficient. _________________ Intern Joined: 18 Apr 2015 Posts: 37 Followers: 0 Kudos [?]: 2 [0], given: 5 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 28 Apr 2015, 23:38 If so,then the answer would have been both are sufficient Math Expert Joined: 02 Sep 2009 Posts: 35266 Followers: 6632 Kudos [?]: 85454 [0], given: 10236 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 29 Apr 2015, 02:25 kirtivardhan wrote: If so,then the answer would have been both are sufficient Please elaborate your question and make it clear. Thank you. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 7709 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 343 Kudos [?]: 2282 [0], given: 162 Re: A number of people each wrote down one of the first 30 [#permalink] ### Show Tags 29 Apr 2015, 11:03 kirtivardhan wrote: Hi Bunnel, The thing i am not able to understand is why not 2 ppl write the same number.In that case whether the number of ppl >40 or <70 the number that they write will be repeated. Please assist Hi kirtivardhan, The 'tricky' part about this question is that we don't know what number each individual person wrote down. As an example....If there were only 2 people, it's POSSIBLE that they both wrote down the SAME number, but it's ALSO POSSIBLE that they wrote down two DIFFERENT numbers. In Fact 2, we're told that there are fewer than 70 people....so there COULD be just 2 people and the above 2 results are both possible. That's why Fact 2 is INSUFFICIENT. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: A number of people each wrote down one of the first 30 [#permalink]

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23 Jul 2016, 05:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: A number of people each wrote down one of the first 30   [#permalink] 23 Jul 2016, 05:38

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