Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1223
Concentration: Strategy, General Management

Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
22 Jul 2010, 04:04
Question Stats:
73% (02:56) correct 27% (03:12) wrong based on 337 sessions
HideShow timer Statistics
Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology? A. 30 B. 90 C. 120 D. 172 E. 188
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings



SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1856
Concentration: General Management, Nonprofit

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
22 Jul 2010, 07:11
Okay, here's my take on this. This is mildly tricky. Let's first draw a Venn Diagram. Attachment: File comment: Venn Diagram
c73058.jpg [ 19.75 KiB  Viewed 5857 times ]
According to the diagram we need to find z. So we are given the following: \(x+y+z+a+b+c+p=400\) (Totally there are 400 students) \(a+c+x+p = \frac{56}{100}*400 = 224\) (Total number of Sociology students) \(a+b+y+p = \frac{44}{100}*400 = 176\) (Total number of Math students) \(b+c+z+p = \frac{40}{100}*400 = 160\) (Total number of Biology students) \(a+p = \frac{30}{100}*400 = 120\) (Total number of students studying both Math and Sociology) Adding the first three statements: \(x+y+z+2(a+b+c)+3p=224+176+120 = 560\) Substituting the first equation into this (\(x+y+z+a+b+c+p=400\))\((a+b+c)+2p=560400=160\) Substituting \(a+p=120\) in this equation, we get:\(b+c+p=160120=40\) So, now we know that the total number of biology students = \(b+c+z+p = 160\). So to get z, we just plug in \(b+c+p=40\) to get \(z = 120\) Hope this helps. Try drawing a Venn Diagram and start simplifying it in terms of what's given and you'll hit the answer really soon most of the time.



Intern
Joined: 22 Jun 2010
Posts: 49

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
22 Jul 2010, 08:15
whiplash2411 wrote: \(a+c+x+p = \frac{56}{100}*400 = 224\) (Total number of Sociology students)
\(a+b+y+p = \frac{44}{100}*400 = 176\) (Total number of Math students)
whiplash2411 wrote: I can't see anything in red, can you please let me know what's wrong? Thanks. Think You mixed up X and Y there thats all! (colors apparently don't work in the [ m ] notation: a+c+ x+p = 224 (should be y) a+b+ y+p = 176 (should be x)



Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1223
Concentration: Strategy, General Management

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
22 Jul 2010, 08:54
whiplash2411 wrote: I can't see anything in red, can you please let me know what's wrong? Thanks. Actually, the problem is in b & c when you wrote the equations of sociology & Maths b & c should replace each other in these eqations. a + c + x + p There is no problem with x & y.
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 18 Jun 2010
Posts: 270
Schools: Chicago Booth Class of 2013

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
16 Oct 2010, 09:31
Lady's way is elegant but timeconsuming. Too many digits and variables... Can not we apply an overlapping sets formula to fix it more easy?



Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1223
Concentration: Strategy, General Management

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
16 Oct 2010, 09:35
Financier wrote: Lady's way is elegant but timeconsuming. Too many digits and variables... Can not we apply an overlapping sets formula to fix it more easy? Check Bunuel's post in this thread formulaefor3overlappingsets69014.html
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 11 Jul 2010
Posts: 200

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
16 Oct 2010, 09:59
i kind of ended up guessing c with the following method:
3 sets theory formula
400 = 224 (S) +176 (M) +160 (B)  2 * All 3  SM  SB  MB
[Formula  Total = A + B + C  2 ABC  AB  BC  CA + None]
2 All 3 + SB +MB = 160  120 [coz SM is 120]
2 All 3 + SB + MB = 40
Now 160 people do B
This includes people who do only B (what we need) + MB + SB + Do all 3
So only B, I did = 160  40 = 120
But according to the formula 2 All 3 + SB + MB = 40... so I am wondering why do I have "2 All 3" giving me the right answer?? Can someone explain this using the set theory formula? Thanks.



Intern
Joined: 16 Oct 2010
Posts: 2

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
17 Oct 2010, 11:38
gosh... these 3 sets overlapping rules/equations driving me mad! I'd have just done this using simple logic only:
total no of students doing either maths or sociology = 400, but of which we know 120 r doing both, so there are a total 400120 = 280 students doing maths or/and sociology. now, make this as one single entity in the venn diagram. (of course this only works as we don't really care how many r doing bio &/or maths/sociology, we are only concerned with the one doing bio only! so i didn't go for the complex rules and just focus on the bio group as the primary entity  i really hate 3 sets thing and always try to simplify it to two sets only... doesn't work all the time i know...)
then draw another one for your bio group, so u end up with two groups only!
group A = 280(maths or/and sociology), group B = 160 (bio)
obviously together they can't exceed 400 in number so u merge them together to form the overlap.
it hit 400 when the overlap = 40, ie minimum no of ppl doing both groups therefore max no. of students doing bio only = 16040 = 120.
does this makes sense?
(the beauty of this is u don't need to even work out what 56% or 44% is, all u need is to focus is the overlap between the first 2 groups which is nice round no 120 and the totla no of students which is 400!)



Retired Moderator
Joined: 03 Aug 2010
Posts: 210

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
30 Nov 2010, 21:03
pls assess my approach and correct me if i am wrong s=56 and m = 44 , s+m(s n m ) = 56+4430= 70% Now 70% are in either S or M ( not in both ), so 30% of the total students will be in B , which is 120 Pls correct me if my approach is wrong thanks
_________________
http://www.gmatpill.com/gmatpracticetest/
Amazing Platform



Intern
Joined: 26 Oct 2010
Posts: 17

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
30 Nov 2010, 23:21
Hi Dhiren,
I would like to think that since there is a 30% overlap between S and M...S would be 26% and M would be 14% that makes it total of 40% for S or M but not both.
Coming to the question: (S + M + SM(overlap)) ==> 26+14+30 = 70. Now the question mentions 40% study biology, and the largest number of students who can study biology would be 30%(since the rest 10% would be overlap with Sociology and Mathematics..to put it another way 10% would be the least overlap with Sociaology and Mathematics)
==> 30%(400) = 120
Answer C



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8391
Location: Pune, India

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
02 Dec 2010, 11:34
hirendhanak wrote: pls assess my approach and correct me if i am wrong
s=56 and m = 44 , s+m(s n m ) = 56+4430= 70%
Now 70% are in either S or M ( not in both ), so 30% of the total students will be in B , which is 120
Pls correct me if my approach is wrong
thanks Your approach is fine except for one tiny thing: Now 70% are in either S or M ( not in both ),  instead this is 70% are in S or M or both. (When you subtract 30 above, you are doing it to remove double counting ) So we only have 30% left for only B.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 27 Oct 2010
Posts: 29

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
02 Dec 2010, 16:02
My approach is similar to hirendhanak's
Div 400 / 4 to get a easy 100 to work with. Therefore,
Total S = 56 Total M = 44 Total B = 40 [S & M] = 30
Number of Only S or Only M or Only B or [S&M&B] or [B&S] or [B&M] = S + M  (S & M) = 70
Since we want max Only B, we set [S&M&B], [B&S] and [B&M] to 0, so
Only S or Only M or Only B = 70 Only B = 70  Only S  Only M Only B = 70  (56  30)  (44  30) = 30
4 * Only B = 120



Intern
Joined: 02 Jan 2015
Posts: 8

Among 400 students, 56% study sociology, 44% study mathematics a
[#permalink]
Show Tags
03 Apr 2015, 23:06
arjtryarjtry wrote: Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
A. 30 B. 90 C. 120 D. 172 E. 188 This is how i solved this questions: First calculate # of students studying M and S, since the question has given us information about % of students who study both of these. Therefore, # of students studying M: 44% of 400 = 176 # of students studying S: 56% of 400 = 224 # of students studying both M and S: 30% of 400 = 120 Now we can calculate total number of students studying both M and S : 176+224120= 280. Therefore largest number of students studying B would be 400(Total)280 (Studying both M and S)=120 Since the question asked for largest possible number for B and not B only so it was pretty straightforward. Hope this Helps! Thanks



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2066

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
18 Apr 2015, 05:40
Dear Neha Your solution was quite elegant! This was a good way of solving the question methodically, without having to dabble with too many variables in one go (which, as someone pointed out above, can get tedious). I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 120 Using your analysis: nehawadhawan wrote: First calculate # of students studying M and S, since the question has given us information about % of students who study both of these. Therefore, # of students studying M: 44% of 400 = 176 # of students studying S: 56% of 400 = 224 # of students studying both M and S: 30% of 400 = 120
We see that the total number of students who study either Maths or Sociology = 176 + 224  120 = 280 So, in the image we know that the number of students in the zone with the black boundary = 280 Let's assume the number of students who study only biology to be b (this is the number that we have to maximize) And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space = wSince the total number of students = 400, we can write: 280 + b + w = 400 Or, b + w = 400  280 = 120 That is, b = 120  w So, the maximum value of b will happen for w = 0 This is how we get, the maximum value of b = 120 I wanted to explicitly draw out the attention of the students to w. Because, a few of the older solutions above have not even taken w into account. They could still get the right answer because the question here was asking about the maximum value of b (for which, as we saw, w = 0). But in another question, this nonconsideration of w (the number of students who study none of the 3 subjects) could lead to a wrong answer. Hope this helped.  Japinder
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Board of Directors
Joined: 17 Jul 2014
Posts: 2655
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
09 May 2016, 19:05
Hussain15 wrote: Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
A. 30 B. 90 C. 120 D. 172 E. 188 I think the question is more of a logic than equation based only... we are told from the beginning that 40% students study biology. that's 160 students. we have 30% (120 students) who study both math and sociology. if 120 students study all 3 subjects, then 40 of the students study biology only. if 120 students study only math and sociology, then the maximum # of students to study only biology is 160. since we do not have 160 here, let's narrow down to what we have. we know that 40<=# we are looking for<=160 A, D, and E are right away eliminated. between B and D. suppose 40 students study all 3 subjects. then 80 study only sociology and math. therefore, we might have 0 who study sociology and biology, and 0 who study math and biology. in this case, sociology only = 104, and math only = 56. we are then left with biology only = 120. since C is possible, and is definitely greater than B, then C must be the answer.



Board of Directors
Joined: 17 Jul 2014
Posts: 2655
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
26 Oct 2016, 07:10
Solved it, after few months, in a different way...though it takes longer I believe... 3 venn diagram... A is in the center B is Sociology and Biology C is Sociology and Math D is Math and Biology E is biology only F is sociology only G is math only
we are then told: (1) A+B+C+F = 224 (2) A+C+D+G=176 (3) A+B+D+E=160 (4) A+C=120
(5) A+B+C+D+E+F+G=400 from (5), subtract (1) we are left with: D+E+G=176 but this is equal to A+C+D+G D+E+G=A+C+D+G > E=A+C but we know for sure that A+C = 120! answer is 120!



Intern
Status: preparing
Joined: 30 Dec 2013
Posts: 40
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35 GMAT 2: 640 Q49 V28 GMAT 3: 640 Q49 V28 GMAT 4: 640 Q49 V28 GMAT 5: 640 Q49 V28
GPA: 2.84
WE: General Management (Consumer Products)

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
23 Jun 2017, 03:20
total is 100 (100%)
s=56 m=44 and b=40 s & m = 30
s+m+b= 56+44+40 =140
total  (s+m+b) = 140  100 = 40 40% is the total that will be common among s,m,b
40  s&m = 40 30 = 10 %
so 10% from b will be shared with either s or m or both.
so b10 = 4010 =30 %
30% 400 = 120
ans C
Kudos if it helps



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
26 Jun 2017, 18:00
Hussain15 wrote: Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
A. 30 B. 90 C. 120 D. 172 E. 188 We can let S denote sociology, M denote mathematics, and B denote biology. Since %(S or M) = %(S) + %(M)  %(S and M), we have: %(S or M) = 56 + 44  30 = 70 Thus, 70% of the students study sociology or mathematics or both. If we add this percentage to the 40% who study biology, we have 110%, which is not possible since it’s over 100%. So, we must have (at least) 10% of the students who study biology and also study either mathematics or sociology or both. However, we can exclude that 10% of the students and say that the remaining 40%  10% = 30% of the students study biology only. Thus, the largest possible number of students who study biology but do not study either mathematics or sociology is 0.3 x 400 = 120. Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 8451

Re: Among 400 students, 56% study sociology, 44% study mathematics and 40%
[#permalink]
Show Tags
21 Sep 2018, 05:05
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: Among 400 students, 56% study sociology, 44% study mathematics and 40% &nbs
[#permalink]
21 Sep 2018, 05:05






