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Can someone please explain in detail how both the statements are not sufficient to answer the question?

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

1) There are no students studying all of the three subjects. 2) None of those who study math study chemistry.

Can someone please explain in detail how both the statements are not sufficient to answer the question?

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

1) There are no students studying all of the three subjects. 2) None of those who study math study chemistry.

just draw the overlapping venn diagram and things become clearer. even after the above 2 pieces of information, we still dont know how many study physics and chemistry or physics and maths and hence we cannot figure out how many are not taking any one of the above 3 subjects.

There is a formula for these but i cant remember it now. basically u have to get sum up the number of students who are studying physics only +chem only + math only + all 3 + any 2 (3 combinations) and then subtract by 20....for final answer!

Given - Students - 20 Math - 5 Physics - 10 Chemistry - 6

Total - P + M + C + PC + PM + MC + PCM (Where P = Physics only, M = Maths Only, C = Chemistry only, PC = Physics and Chemistry only, MC = Maths and Chemistry only, PM = Physics and Maths only, PCM = Physics, Chemistry and Maths)

From this Total = X + Y, hence students who do not study any of the above-mentioned subjects = 0

sufficient

Statement 2 -

Not sufficient

Hence answer - A

Please point where I'm going wrong. I know the methodology I have followed sounds stupid, but this is what I got when solved. I need to improve my Venn diagram problems, and these are the ones that are taking out on my score

the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total . and we are asked about variable "exactly 2" ? am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total . and we are asked about variable "exactly 2" ? am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

anybody ? thanks

20 is the total number of students.

We have three variables here (with both statements in consideration), a, b and x. 5-a+6-b+10 + x = 20 21+x-a-b = 20 1 + x = a+b x = a+b-1

the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total . and we are asked about variable "exactly 2" ? am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

anybody ? thanks

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

First of all note that total # of students is 20. Next:

Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:

20 = 5 + 10 + 6 - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups};

So: {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1.

Question: is {people in none of the groups} > 0? --> is {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1 > 0

(1) There are no students studying all of the three subjects --> {people in exactly 3 groups} = 0 --> question becomes is {people in none of the groups} = {people in exactly 2 groups} - 1 > 0. Now, if {people in exactly 2 groups} = 1 then the answer will be NO (for example if there is only one student who study exactly two subjects: math and physics and all other students study only one subject) but if {people in exactly 2 groups} = 2 then the answer will be YES (for example if there are two students who study exactly two subjects: math and physics and all other students study only one subject). Not sufficient.

(2) None of those who study math study chemistry. Clearly insufficient.

(1)+(2) Examples from (1) are still valid, thus we have both YES and NO answers. Not sufficient.

the formula mention above is total= set 1+ set 2+ set3 -2(All) - (exactly 2)

however since we are informed that Among 20 students , 20 is not total . and we are asked about variable "exactly 2" ? am i right? actually i was not able to discenr what basically is asked. can someone draw a diagram/matrix?

anybody ? thanks

If among 20 students in a group, 5 study math, 10 study physics, and 6 study chemistry, are there any students who do not study any of the above-mentioned subjects?

First of all note that total # of students is 20. Next:

Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:

20 = 5 + 10 + 6 - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups};

So: {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1.

Question: is {people in none of the groups} > 0? --> is {people in none of the groups} = {people in exactly 2 groups} + 2*{people in exactly 3 groups} - 1 > 0

(1) There are no students studying all of the three subjects --> {people in exactly 3 groups} = 0 --> question becomes is {people in none of the groups} = {people in exactly 2 groups} - 1 > 0. Now, if {people in exactly 2 groups} = 1 then the answer will be NO (for example if there is only one student who study exactly two subjects: math and physics and all other students study only one subject) but if {people in exactly 2 groups} = 2 then the answer will be YES (for example if there are two students who study exactly two subjects: math and physics and all other students study only one subject). Not sufficient.

(2) None of those who study math study chemistry. Clearly insufficient.

(1)+(2) Examples from (1) are still valid, thus we have both YES and NO answers. Not sufficient.

None of those who study math study chemistry >> Can someone explain what it is exactly, probably rephrase it? or put it on venn diagram?

That means that there are no students who study both math and chemistry. On diagram it would be so that the circles of math and chemistry do not intersect. _________________

Straight E. We need info on the two other intersections, videlicet: (students who study both chem and physics, and those study maths and physics) in order to determine how many do not study any of the three subjects.