5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
700 DS tough question .. really challenging !
-
jayoptimist
- Junior | Next Rank: 30 Posts
- Posts: 19
- Joined: Tue Nov 08, 2011 10:03 pm
- Thanked: 2 times
This can be solved using a Venn diagram. From the provided information we know that there are 15 people who are not vegetarian or students. So to get to our result, all we need is the percentage of vegetarian and student combined.
From statement 1, we can get to 20% both student and vegetarian, 30% only Vegetarian. As the rate is double that of Student, we can get the percentage of student only as well. From here, we can quickly see that we have the rate of student and vegetarian combined without any further calculation. So statement 1 is conclusive.
Statment 2 give us 30% vegetarian only and 20% vegetarian and student. What is missing here is the percentage of student alone. Notice how we can easily get into the trap of using the information carried over from statement 1 (I nearly fell for this). Statement 2 is not sufficient.
Hence the answer is A.
I think this is a great question and represents many of the tricks that we might see in the real test.
From statement 1, we can get to 20% both student and vegetarian, 30% only Vegetarian. As the rate is double that of Student, we can get the percentage of student only as well. From here, we can quickly see that we have the rate of student and vegetarian combined without any further calculation. So statement 1 is conclusive.
Statment 2 give us 30% vegetarian only and 20% vegetarian and student. What is missing here is the percentage of student alone. Notice how we can easily get into the trap of using the information carried over from statement 1 (I nearly fell for this). Statement 2 is not sufficient.
Hence the answer is A.
I think this is a great question and represents many of the tricks that we might see in the real test.
-
parachuter2b
- Newbie | Next Rank: 10 Posts
- Posts: 8
- Joined: Wed Jun 30, 2010 10:51 pm
I know I must be obviously wrong since I'm the only one who's reaching a contradiction with B:Stuart Kovinsky wrote:Hooray for another opportunity to showcase the all-powerful data sufficiency tool, "# of equations vs # of unknowns".meng wrote:Hi everybody, this is actually a 700 level question !I hope that you can solve it within 2 min ! if you did .. I can say that your score gonna be around 700
Guests at a recent party ate a total of fifteen hamburgers. Each guest who was neither a student nor a vegetarian ate exactly one hamburger. No hamburger was eaten by any guest who was a student, a vegetarian, or both. If half of the guests were vegetarians, how many guests attended the party?
(1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.
(2) 30% of the guests were vegetarian non-students.
There are only two groups here, so we can use the basic overlapping sets formula:
True # of objects = total # in group 1 + total # in group + total # in neither group - # in both groups
or, more simply:
Total = G1 + G2 + neither - both
Applying that formula to the question stem, we get:
# Guests = #students + #vegetarians + neither - both
and we know that
#v = 1/2(#g) and neither = 15, so:
G = S + .5G + 15 - both
So, we have 1 equation and 3 unknowns.
(1) gives us two ratios. What can we do with ratios? Turn them into equations! Now, here's the beautiful thing... we don't care what those equations are, as long as they:
- are linear;
- are distinct; and
- don't introduce any new variables.
Going through our checklist, we see that all 3 criteria are upheld. Therefore, we have 3 distinct linear equations for 3 unknowns: we can solve the entire system, sufficient!
(2) gives us one equation that still leaves some variables we don't want in the mix: insufficient.
(1) is sufficient, (2) isn't: choose (A).
so I solved it the same way as you did (ven diagram and equations) and I got that A is sufficient, however, for B this is what I get..please lemme know where I'm wrong?
so before approaching A or B, we get:
S (students) - S conjunction V + 15 = T/2 (same thing as you got)
now B gives me:
V = 30%T, in other words: non-vegeterians = 70%T.
let's call S- (S conjuction V) : a -just for the sake of simplicity. I understand that they are two independent vars.
so what we had from before:
a + 15 = T/2
and B gives us:
a + 15 (all the non-veg)= 70%T
which leads to a contradiction, since 70%T can't be equal to T/2
Please advice,
Thanks
-
parachuter2b
- Newbie | Next Rank: 10 Posts
- Posts: 8
- Joined: Wed Jun 30, 2010 10:51 pm
nvm my post above.. just saw the flaw in my approach: didn't pay attention to the "non student" part in B.
-
pappueshwar
- Master | Next Rank: 500 Posts
- Posts: 234
- Joined: Fri Oct 01, 2010 7:28 pm
- Location: chennai
- Thanked: 5 times
- Followed by:4 members
This is my first post (this is a great website - thanks to all posting) so I am including a little more detail on my thought process.
Given that
Guests = G
Student vegetarian = SV
Student non-vegetarian = SN
Nonstudent vegetarian = NV
Nonstudent non-vegetarian = NN = 15
SV + NV =1/2*G
Eq 1:
SV + SN + NV + NN = G
SV + SN + NV + 15 = G
=> 1/2*G + SN + 15 = G
=> SN + 15 = 1/2*G or G = 2(SN + 15)
From (1)
Eq 2: SV/NV = 2/3
Eq 3: SN/NN = 4/3 (twice the above ratio since (1) says SV/NV = 1/2*SN/NN)
Eq 3: SN = 4/3* NN = 4/3*15 = 20 (NN = 15 from above)
Solving for G:
G = 2*(20 + 15) = 70
(1) Is sufficient
From (2)
NV = 0.3G this is not sufficient to solve for
SV + NV =1/2*G
Eq 1: SV + 3/10*G = 1/2*G
Eq 2: G = 2(SN + 15)
3 variables, 2 equations, (2) is insufficient
The SN/NN is a little tricky (you could either double or halve the SV/NV = 2/3), but regardless of how you interpreted this ratio, (1) is still sufficient to solve.
Given that
Guests = G
Student vegetarian = SV
Student non-vegetarian = SN
Nonstudent vegetarian = NV
Nonstudent non-vegetarian = NN = 15
SV + NV =1/2*G
Eq 1:
SV + SN + NV + NN = G
SV + SN + NV + 15 = G
=> 1/2*G + SN + 15 = G
=> SN + 15 = 1/2*G or G = 2(SN + 15)
From (1)
Eq 2: SV/NV = 2/3
Eq 3: SN/NN = 4/3 (twice the above ratio since (1) says SV/NV = 1/2*SN/NN)
Eq 3: SN = 4/3* NN = 4/3*15 = 20 (NN = 15 from above)
Solving for G:
G = 2*(20 + 15) = 70
(1) Is sufficient
From (2)
NV = 0.3G this is not sufficient to solve for
SV + NV =1/2*G
Eq 1: SV + 3/10*G = 1/2*G
Eq 2: G = 2(SN + 15)
3 variables, 2 equations, (2) is insufficient
The SN/NN is a little tricky (you could either double or halve the SV/NV = 2/3), but regardless of how you interpreted this ratio, (1) is still sufficient to solve.
did a mistake in making the table. -
rajeshsinghgmat
- Master | Next Rank: 500 Posts
- Posts: 171
- Joined: Tue Jan 08, 2013 7:24 am
- Thanked: 1 times
-
confusedSoul730
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Sat Apr 27, 2013 8:44 am
student Non-student Total
Vegetarians 2x 3x 35
Non-vegetarians y 15[frm ques] 35
total 70
Ratio of vegetarian student:non-student given in stmt(1)
Now we know 2x/3x = ½ of non-vegetarians. So non-veg = 4x:3x which is equal to y/15 from the table above. So y=20. Total non-veg=35.
Veg ppl are 50% so they too are 35. So you get total guests as 70.
(2) 30% guests are veg non-students.
Assume that total guests are 2g. We get the below data but we have no way of finding the value of g. hence 2 is not sufficient.
student Non-student Total
Vegetarians 0.4g 0.3*2g g
Non-vegetarians g-15 15[frm ques] g
total 2g
Vegetarians 2x 3x 35
Non-vegetarians y 15[frm ques] 35
total 70
Ratio of vegetarian student:non-student given in stmt(1)
Now we know 2x/3x = ½ of non-vegetarians. So non-veg = 4x:3x which is equal to y/15 from the table above. So y=20. Total non-veg=35.
Veg ppl are 50% so they too are 35. So you get total guests as 70.
(2) 30% guests are veg non-students.
Assume that total guests are 2g. We get the below data but we have no way of finding the value of g. hence 2 is not sufficient.
student Non-student Total
Vegetarians 0.4g 0.3*2g g
Non-vegetarians g-15 15[frm ques] g
total 2g
-
Mathsbuddy
- Master | Next Rank: 500 Posts
- Posts: 447
- Joined: Fri Nov 08, 2013 7:25 am
- Thanked: 25 times
- Followed by:1 members
Using a Venn diagram, this is very fast to solve, giving an answer of 40 people altogether.
Hand drawn in circles this is easier to visualise, but these parentheses should suffice:
[] = s = students set
() = v = vegetarian set
{} = s' = non-student set
[5(8]0{12)15} = 40 total
This was found following these steps:
If h = (number of hamburgers eaten)/(number of people)
then the h values in each set are:
[0(0]0{0)1}
As we know that 15 people ate hamburgers, we can enter the number of people in each set instead:
[?(?]?{?)15}
Next we know that 30% are {V and S'):
[?(?]?{0.3n)15} where n = total number of people
Also, ratios tell us:
[5(0.2n]?{0.3n)15}
Also, as half the population are V (and 0.2n + 0.3n = 0.5n satisfies this criteria), then:
[5(0.2n]0{0.3n)15}
Adding this all up, we get the total, n
5 + 0.2n + 0 + 0.3n + 15 = n
rearranged gives:
20 + 0.5n = n
so n = 40.
Therefore the total number of people = 40.
Hand drawn in circles this is easier to visualise, but these parentheses should suffice:
[] = s = students set
() = v = vegetarian set
{} = s' = non-student set
[5(8]0{12)15} = 40 total
This was found following these steps:
If h = (number of hamburgers eaten)/(number of people)
then the h values in each set are:
[0(0]0{0)1}
As we know that 15 people ate hamburgers, we can enter the number of people in each set instead:
[?(?]?{?)15}
Next we know that 30% are {V and S'):
[?(?]?{0.3n)15} where n = total number of people
Also, ratios tell us:
[5(0.2n]?{0.3n)15}
Also, as half the population are V (and 0.2n + 0.3n = 0.5n satisfies this criteria), then:
[5(0.2n]0{0.3n)15}
Adding this all up, we get the total, n
5 + 0.2n + 0 + 0.3n + 15 = n
rearranged gives:
20 + 0.5n = n
so n = 40.
Therefore the total number of people = 40.
-
jaspreetsra
- Master | Next Rank: 500 Posts
- Posts: 164
- Joined: Sat Sep 20, 2014 10:26 pm
- Thanked: 1 times
