November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 177

A number of people each wrote down one of the first 30
[#permalink]
Show Tags
06 Dec 2012, 06:17
Question Stats:
83% (00:42) correct 17% (00:56) wrong based on 617 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 50711

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
06 Dec 2012, 06:23



Manager
Joined: 22 Mar 2011
Posts: 52

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
06 May 2013, 23:18
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: 50711

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
06 May 2013, 23:22
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?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 22 Mar 2011
Posts: 52

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
07 May 2013, 00:56
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: 50711

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
07 May 2013, 01:10



Manager
Joined: 22 Mar 2011
Posts: 52

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
07 May 2013, 01:25
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



Intern
Joined: 21 Jun 2014
Posts: 4

A number of people each wrote down one of the first 30
[#permalink]
Show Tags
05 Dec 2014, 15:36
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: 20

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
26 Apr 2015, 12:00
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



Retired Moderator
Joined: 06 Jul 2014
Posts: 1241
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

A number of people each wrote down one of the first 30
[#permalink]
Show Tags
26 Apr 2015, 12:10
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.
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



Intern
Joined: 18 Apr 2015
Posts: 20

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
26 Apr 2015, 12:48
Following the same logic,both the statements should have been insufficient right?



Retired Moderator
Joined: 06 Jul 2014
Posts: 1241
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
26 Apr 2015, 12:52
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.
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12891
Location: United States (CA)

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
27 Apr 2015, 14:17
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 (130, 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. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 18 Apr 2015
Posts: 20

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
28 Apr 2015, 19:26
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



Retired Moderator
Joined: 06 Jul 2014
Posts: 1241
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
28 Apr 2015, 22:35
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 kirtivardhanYou 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.
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12891
Location: United States (CA)

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
29 Apr 2015, 10:03
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Senior Manager
Joined: 11 Nov 2014
Posts: 334
Location: India
Concentration: Finance, International Business
WE: Project Management (Telecommunications)

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
24 Jul 2016, 04:07
first 30 integers pre think  if we know the number of people is greater than 30  for sure, we will have atleast one repetitive number 1 wrote only 1 30 only 30 but if 31 wrote 30 & 1 for sure the person matches 1 & 30 (1) The number of people who wrote down an integer was greater than 40. Suff (2) The number of people who wrote down an integer was less than 70. number of people can be 2 or 69 diff answers hence A



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 484

Re: A number of people each wrote down one of the first 30
[#permalink]
Show Tags
26 Sep 2018, 11:47
Walkabout 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.
(simplified wording) FOCUS: Was at least one number "chosen" more than once (among the 30 numbers available)? (1) Sufficient: if each person (among P people) would choose a different number, it would be needed at least P numbers. We have 30 numbers to be chosen among P > 40 people. There are at least two people who will choose the same number. (*) (2) Insufficient: we could have only 2 people, say A and B. > If A chose 1 and B chose 2, the answer would be NO. > If A chose 1 and B also chose 1, the answer would be YES. This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. (*) The Pigeon Principle : https://en.wikipedia.org/wiki/Pigeonhole_principle
_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12questions Mock included) to gain a 50% discount!




Re: A number of people each wrote down one of the first 30 &nbs
[#permalink]
26 Sep 2018, 11:47






