Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44600

In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 04:21
Question Stats:
61% (01:29) correct 39% (01:34) wrong based on 187 sessions
HideShow timer Statistics



Manager
Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04012015
GPA: 3.98

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 04:35
Total = 232 Geometry = 144 Biology = 119 What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology? Greatest Possible Number taken both should be 144 (As it is maximum for One) Smallest Possible Number taken both should be given by Total  Neither = A + B  Both Both = A+B+Neither  Total (Neither must be 0 to minimize the both) So 144 + 119 + 0  232 = 31 Greatest  Smallest is 14431 = 113 So answer must be C. 113
_________________
Click +1 KUDOS , You can make me happy with just one click! Thanks



Intern
Joined: 01 Jan 2015
Posts: 17

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 06:16
3
This post received KUDOS
1
This post was BOOKMARKED
cutegirlsimran wrote: Total = 232 Geometry = 144 Biology = 119
What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total  Neither = A + B  Both
Both = A+B+Neither  Total (Neither must be 0 to minimize the both) So 144 + 119 + 0  232 = 31
Greatest  Smallest is 14431 = 113
So answer must be C. 113 Since no of students who took Biology =119 ,greatest = 119 greatest  smallest = 11931 = 88 Hence D



Senior Manager
Joined: 28 Feb 2014
Posts: 295
Location: United States
Concentration: Strategy, General Management

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 08:04
1
This post received KUDOS
The max number of students who took both bio and geometry is 119 because we can have 0 students who had bio but no geometry, and 0 students who had geometry but not bio.
the smallest number of students who took both bio and geometry is 31 because we can have 88 students who took bio and no geometry. (To minimize the students who took bio and geo, maximize students who took bio but no geo). 11988=31
11931=88
Answer: D



Manager
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 11:12
1
This post received KUDOS
Greatest possible # = 119 (as all the bio will be studies by 144 geo students) Least possible #= 31 (119+144232) Therefore Difference between greatest and lease possible #= 11931=88 Hence answer is D
Thanks,



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11496
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 17:40
Hi cutegirlsimran, You have to be careful with how you set up your work on this question. Since there are 144 students who took Geometry and 119 who took Biology, there cannot be any more than 119 who took BOTH. If you swap that number into your calculation, you'll end up with the correct 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: 22 Mar 2015
Posts: 3

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 19:56
1
This post received KUDOS
1
This post was BOOKMARKED
Smallest Possible Number taken both should be given by
Total  Neither = A + B  Both
The greatest is between 144 and 119 is: 119. The Smallest can be calculated by the formula Both = A+B+Neither  Total (Neither must be 0 to minimize the both) So 144 + 119 + 0  232 = 31
Greatest  Smallest is 11931 = 88 So the answer is D



Manager
Joined: 21 Jan 2015
Posts: 149
Location: India
Concentration: Strategy, Marketing
WE: Marketing (Consumer Products)

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 22:24
1
This post received KUDOS
Bunuel wrote: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A. 144 B. 119 C. 113 D. 88 E. 31
Ans: D Solution: This can be done with or without Venn Diagram total is 232 Maximum common can be 119 for both G ad B minimum common can be 144+119= 263, 263232=31 so the difference is 11931=88
_________________
 The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks



Manager
Joined: 22 Feb 2015
Posts: 56
Location: United States
Concentration: Finance, Operations
GMAT Date: 04012015
GPA: 3.98

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
13 May 2015, 22:49
Yes I got it Now I Swapped the Numbers to calculate the both
_________________
Click +1 KUDOS , You can make me happy with just one click! Thanks



Senior Manager
Joined: 02 Mar 2012
Posts: 344

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
14 May 2015, 08:40
1
This post received KUDOS
D88
highest number can come to 119(both g and biology is max) and lowest to 31(when students studying geometry adn not biology is max)
hope it helps



Math Expert
Joined: 02 Sep 2009
Posts: 44600

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
18 May 2015, 07:55
Bunuel wrote: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A. 144 B. 119 C. 113 D. 88 E. 31
Kudos for a correct solution. OFFICIAL SOLUTION:First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119. {Total} = {geometry} + {biology}  {both} + {neither}; 232 = 144 + 119  {both} + {neither}; {both} = 31 + {neither}. {both} is minimized when {neither} is 0. In this case {both} = 31. The greatest possible number of students that could have taken both geometry and biology, is 119. Thus, the answer is 119  31 = 88. Answer: D.
_________________
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



Retired Moderator
Joined: 29 Apr 2015
Posts: 874
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
19 May 2015, 04:52
EMPOWERgmatRichC wrote: Hi cutegirlsimran,
You have to be careful with how you set up your work on this question.
Since there are 144 students who took Geometry and 119 who took Biology, there cannot be any more than 119 who took BOTH. If you swap that number into your calculation, you'll end up with the correct answer.
GMAT assassins aren't born, they're made, Rich Dear Rich Why is that so "natural" that no more than 119 can take BOTH of the classes? The question is in a very conditional form and does not come with any constrains. It seems that I don't understand this concept ... Total 233 in the Class, which means, they're all allowed and able to visit both courses right? Thank you
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Math Expert
Joined: 02 Sep 2009
Posts: 44600

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
19 May 2015, 05:41
reto wrote: EMPOWERgmatRichC wrote: Hi cutegirlsimran,
You have to be careful with how you set up your work on this question.
Since there are 144 students who took Geometry and 119 who took Biology, there cannot be any more than 119 who took BOTH. If you swap that number into your calculation, you'll end up with the correct answer.
GMAT assassins aren't born, they're made, Rich Dear Rich Why is that so "natural" that no more than 119 can take BOTH of the classes? The question is in a very conditional form and does not come with any constrains. It seems that I don't understand this concept ... Total 233 in the Class, which means, they're all allowed and able to visit both courses right? Thank you There can be students who took both classes but there cannot be more than 119 students who took both. We are told that 144 took geometry and 119 took biology. How can then the number of students who took both geometry and biology be more than 119?
_________________
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



Retired Moderator
Joined: 29 Apr 2015
Posts: 874
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
19 May 2015, 07:33
Bunuel wrote: reto wrote: EMPOWERgmatRichC wrote: Hi cutegirlsimran,
You have to be careful with how you set up your work on this question.
Since there are 144 students who took Geometry and 119 who took Biology, there cannot be any more than 119 who took BOTH. If you swap that number into your calculation, you'll end up with the correct answer.
GMAT assassins aren't born, they're made, Rich Dear Rich Why is that so "natural" that no more than 119 can take BOTH of the classes? The question is in a very conditional form and does not come with any constrains. It seems that I don't understand this concept ... Total 233 in the Class, which means, they're all allowed and able to visit both courses right? Thank you There can be students who took both classes but there cannot be more than 119 students who took both. We are told that 144 took geometry and 119 took biology. How can then the number of students who took both geometry and biology be more than 119? I understand that BUT, the question virtually asks "... that COULD have taken both geometry and biology". Since this is conditional, my thoughts go back to the roots where we have 232 students and none of them have chosen biology or geometry yet, so 232 COULD have taken both geometry and biology. Again, I guess it's my english which makes me misunderstanding the question here ...
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11496
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
20 May 2015, 00:06
Hi reto, In real basic terms, you have to use ALL of the information that is given to get to the correct answer. You're told 3 different facts about the group of students, but your 'deduction' is based on just the first of those facts. THAT is why the answer is NOT 232 (and since that answer doesn't appear among the 5 choices, you KNOW that it cannot be correct). And for what it's worth, your English "skills" seem to be just fine. 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!***********************



SVP
Joined: 08 Jul 2010
Posts: 2067
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
08 Oct 2016, 22:24
Bunuel wrote: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A. 144 B. 119 C. 113 D. 88 E. 31
Kudos for a correct solution. Greatest Number of students who took both Geometry and Biology = 119 (Smaller of the two numbers) Smallest Number of students who took both Geometry and Biology = x Let Then total people = (144x) + x + (119x) = 232 (Given) i.e. 263x = 232 i.e. x = 31 The required difference = 119  31 = 88 Answer: Option D
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



NonHuman User
Joined: 09 Sep 2013
Posts: 6647

Re: In a graduating class of 232 students, 144 took geometry and 119 took [#permalink]
Show Tags
12 Apr 2018, 03:41
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In a graduating class of 232 students, 144 took geometry and 119 took
[#permalink]
12 Apr 2018, 03:41






