This Data Sufficiency question, from Session 4, Extra Practice HW 3 (Sets and Rates), has stumped 50% of Knewton students so far. How would you tackle it?

Give it a shot, then share your answers, questions, and thought processes in the comments below. If you’re in our GMAT class now, don’t forget to add your teacher name and session (e.g., Zwelling, MW 1:30)!

7/8 of the students at Edgemont High play a sport in the fall semester. What fraction of the students play a sport in neither the fall nor the spring semester?

1. 280 students play a sport in the spring semester.
2. 2/7 of the students who do not play a sport in the fall semester do not play a sport in the spring semester.

[A] Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
[B] Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
[C] BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
[D] EACH statement ALONE is sufficient.
[E] Statements (1) and (2) TOGETHER are NOT sufficient.

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  • Philip Cho

    (Brigidette, Sunday 6-9 pm)

    Wow, this is tricky- well, there seem to be four groups:

    Total (T)= all the kids in school
    Fall (F)= sports in fall
    Spring (S) = sports in spring
    Both (B) = sports in fall and spring
    Neither (N) = no sports

    So, T = N + F + S – B. Right?

    Statement 1 says that F = 7T/8, which means you can sub in ONE of those variables, but there are still four, so that seems like a non-suff.

    Statement 2- I might be wrong about this- says that 2/7 (N+S-B) = (N+F-B). (N+S-B) should be “those who DON’T play in fall” because its those who don’t play at all plus spring athletes minus spring+fall athletes. Same with the other side.

    That’s where I get pretty lost. That second equation also seems to yield four variables, and I don’t know how to combine the two statements….

    • Vish_GMAT

      T = N + F + S – 2B (because people who play sports all year are counted twice)

  • Philip Cho

    (Brigidette, Sunday 6-9 pm)

    Wow, this is tricky- well, there seem to be four groups:

    Total (T)= all the kids in school
    Fall (F)= sports in fall
    Spring (S) = sports in spring
    Both (B) = sports in fall and spring
    Neither (N) = no sports

    So, T = N + F + S – B. Right?

    Statement 1 says that F = 7T/8, which means you can sub in ONE of those variables, but there are still four, so that seems like a non-suff.

    Statement 2- I might be wrong about this- says that 2/7 (N+S-B) = (N+F-B). (N+S-B) should be “those who DON’T play in fall” because its those who don’t play at all plus spring athletes minus spring+fall athletes. Same with the other side.

    That’s where I get pretty lost. That second equation also seems to yield four variables, and I don’t know how to combine the two statements….

    • Vish_GMAT

      T = N + F + S – 2B (because people who play sports all year are counted twice)

  • Philip Cho

    (Brigidette, Sunday 6-9 pm)

    Wow, this is tricky- well, there seem to be four groups:

    Total (T)= all the kids in school
    Fall (F)= sports in fall
    Spring (S) = sports in spring
    Both (B) = sports in fall and spring
    Neither (N) = no sports

    So, T = N + F + S – B. Right?

    Statement 1 says that F = 7T/8, which means you can sub in ONE of those variables, but there are still four, so that seems like a non-suff.

    Statement 2- I might be wrong about this- says that 2/7 (N+S-B) = (N+F-B). (N+S-B) should be “those who DON’T play in fall” because its those who don’t play at all plus spring athletes minus spring+fall athletes. Same with the other side.

    That’s where I get pretty lost. That second equation also seems to yield four variables, and I don’t know how to combine the two statements….

  • Lkmen

    I think the answer is B, statement 2 alone is sufficient. Let the number of total student be X, so students who do not play a sport in Fall is 1/7 X (1-7/8), then follow the statement 2, we get (1/7)(2/7)X. so the fraction is 2/49?

  • Lkmen

    I think the answer is B, statement 2 alone is sufficient. Let the number of total student be X, so students who do not play a sport in Fall is 1/7 X (1-7/8), then follow the statement 2, we get (1/7)(2/7)X. so the fraction is 2/49?

  • Sutapa Chatterjee

    the answer is B. Hint – Use Venn Diagrams to solve it.

  • Sutapa Chatterjee

    the answer is B. Hint – Use Venn Diagrams to solve it.

  • Ashok Kadam

    a= only fall semester.
    b= both in fall semester and in spring semester.
    c= only in spring semester.
    d= neither in fall semester nor in spring semester.

    d/(a+b+c+d)=?

    stmt#1:
    b+c = 280. ——(1)
    we cannot calculate d.

    INSUFFICIENT

    stmt#2:
    2/7 of the students who do not play a sport in the fall semester do not play a sport in the spring semester.
    2/7(c+d) = a + d ——-(2)

    a+b = 7/8(a+b+c+d) ——(3)

    INSUFFICIENT.

    Combining both statements, we see that we have 3 equations but 4 unknowns

    so INSUFFICIENT and E is the answer.

  • Ashok Kadam

    a= only fall semester.
    b= both in fall semester and in spring semester.
    c= only in spring semester.
    d= neither in fall semester nor in spring semester.

    d/(a+b+c+d)=?

    stmt#1:
    b+c = 280. ——(1)
    we cannot calculate d.

    INSUFFICIENT

    stmt#2:
    2/7 of the students who do not play a sport in the fall semester do not play a sport in the spring semester.
    2/7(c+d) = a + d ——-(2)

    a+b = 7/8(a+b+c+d) ——(3)

    INSUFFICIENT.

    Combining both statements, we see that we have 3 equations but 4 unknowns

    so INSUFFICIENT and E is the answer.

  • http://pulse.yahoo.com/_U6B4MVKDYPK2D54G65ATP4A37A sudhanshu

    Statement E. All we can get is n(NOT(Spring)), n(NOT(Fall)) but there might be some number of students that are common between them, a number we have no idea about.

  • http://pulse.yahoo.com/_U6B4MVKDYPK2D54G65ATP4A37A sudhanshu

    Statement E. All we can get is n(NOT(Spring)), n(NOT(Fall)) but there might be some number of students that are common between them, a number we have no idea about.

  • Nwhaught

    This doesn’t seem too tricky actually…7/8 play a sport in Fall, and since the question is, what percentage play in NEITHER fall NOR Spring, we’re just left with 1/8 of the student population that’s even eligible. Statement 1 is obviously irrelevant since we’re looking for a fraction. Statement 2 says that of the 1/8 that we’re interested in, 2/7 are also sportless in spring. 1/8 x 2/7 = 2/56, Sufficient. B.

  • Nwhaught

    This doesn’t seem too tricky actually…7/8 play a sport in Fall, and since the question is, what percentage play in NEITHER fall NOR Spring, we’re just left with 1/8 of the student population that’s even eligible. Statement 1 is obviously irrelevant since we’re looking for a fraction. Statement 2 says that of the 1/8 that we’re interested in, 2/7 are also sportless in spring. 1/8 x 2/7 = 2/56, Sufficient. B.

  • Nwhaught

    This doesn’t seem too tricky actually…7/8 play a sport in Fall, and since the question is, what percentage play in NEITHER fall NOR Spring, we’re just left with 1/8 of the student population that’s even eligible. Statement 1 is obviously irrelevant since we’re looking for a fraction. Statement 2 says that of the 1/8 that we’re interested in, 2/7 are also sportless in spring. 1/8 x 2/7 = 2/56, Sufficient. B.

  • Silambarasan S

    STMT A : no info about fall sem so insufficient

    B: Since the question asks only fraction we don’t require absolute number as answer so stmt 2 is sufficient

    i think the ans for the question might be 2/7(1/8)

  • Silambarasan S

    STMT A : no info about fall sem so insufficient

    B: Since the question asks only fraction we don’t require absolute number as answer so stmt 2 is sufficient

    i think the ans for the question might be 2/7(1/8)

  • Vincent Ng05

    Even though I got this one wrong initially. I understand that its a LOT easier than originally thought out to be. If you understand the question its a million times easier. Its asking what fraction of students DO NOT play in neither Fall nor Spring?
    S1) the prompt doesn’t tell you how many students are at the school and how many are in the other seasons. there lacks a lot of information
    S2) it states it in a vague and abnormal way but it gives you everything needed. there might be a typo in the second statement as well which makes it a little more confusing than need be.

  • Vincent Ng05

    Even though I got this one wrong initially. I understand that its a LOT easier than originally thought out to be. If you understand the question its a million times easier. Its asking what fraction of students DO NOT play in neither Fall nor Spring?
    S1) the prompt doesn’t tell you how many students are at the school and how many are in the other seasons. there lacks a lot of information
    S2) it states it in a vague and abnormal way but it gives you everything needed. there might be a typo in the second statement as well which makes it a little more confusing than need be.

  • Midmigurl

    I agree that it’s B, that statement 2 is sufficient. Of the total students, 7/8 play sports in the fall…so 1/8 of the total number of students play no sports in the fall. Of those 1/8 that play no sports…2/7 of them also play no spring sports. You’re looking for a fractional answer and that statement is in fractional form…statement 1 is irrelevant because we have no total number of students to work with. So I say B.

  • Midmigurl

    I agree that it’s B, that statement 2 is sufficient. Of the total students, 7/8 play sports in the fall…so 1/8 of the total number of students play no sports in the fall. Of those 1/8 that play no sports…2/7 of them also play no spring sports. You’re looking for a fractional answer and that statement is in fractional form…statement 1 is irrelevant because we have no total number of students to work with. So I say B.

  • Brian S.

    It has to be E.

    Given: 1/8 do not play sport in fall.

    Stmt 1: 280 play sport in spring. Tells us nothing of fall, nor what fraction of total population 280 is.

    Stmt 2: 2/7 of those who do not play in fall do not play in spring. So 1/28 of the students overlap. But we do not know what fraction that is of the 280 who play.

    E.

  • Brian S.

    It has to be E.

    Given: 1/8 do not play sport in fall.

    Stmt 1: 280 play sport in spring. Tells us nothing of fall, nor what fraction of total population 280 is.

    Stmt 2: 2/7 of those who do not play in fall do not play in spring. So 1/28 of the students overlap. But we do not know what fraction that is of the 280 who play.

    E.

  • http://twitter.com/Knewton_Alex Alex Sarlin

    Great work on this, everyone. For those of you who chose E… try to push the statements a little bit further.

    You can certainly do this without Venn diagrams, but, as Sutapa notes, using them is a great approach that can really make things clearer. Midmigurl also makes a smart move in noticing that if 7/8 play a sport in the fall, that means 1/8 DON’T play a sport in the fall. That’s a key step.

    Feel free to post additional thoughts and questions, too, even if you don’t have a solution, to start a dialog and learn how to approach this question.

  • http://twitter.com/Knewton_Alex Alex Sarlin

    Great work on this, everyone. For those of you who chose E… try to push the statements a little bit further.

    You can certainly do this without Venn diagrams, but, as Sutapa notes, using them is a great approach that can really make things clearer. Midmigurl also makes a smart move in noticing that if 7/8 play a sport in the fall, that means 1/8 DON’T play a sport in the fall. That’s a key step.

    Feel free to post additional thoughts and questions, too, even if you don’t have a solution, to start a dialog and learn how to approach this question.

  • Harish

    Statement 2 is suffficient.

    Given that statement 1 contains a value (280) but the question stem has everthing in relative terms, it wont be useful in calculating a relative term (fraction of total number of students that dont play…).

    Statement 2 directly tells us that 2/7(1/8) is the fraction we are looking for.

    I used a matrix to verify this – horizontal columns were ‘play’ and ‘dont play’, while vertical columns were ‘Fall’, ‘Spring’, ‘Both’. Used 560 as my value for the total number of students (since 560 is divisible by both 7 and 8) and filled up this matrix first using data from statement 1, then from statement 2.

    Data provided by statement 1 did not lead me to the required answer, while that in statement 2 did.

  • sandeep

    Answer B
    statement 1.Insufficient coz it gives no idea about the spring students play..

    statement 2.Sufficient form the question i have 1/8 who do not play in Spring now from statement 2 i can see that 2/7 of 1/8 dont play in spring so i can get the fraction…..

    (BRIGIDETTE CROWE M 9:00 am)

  • Jess N (Knewton)

    Hey everyone,

    Jess from Knewton here! Awesome job discussing this question so far, as Alex said. It’s definitely trickier than first meets the eye.

    For all you Knewton students out there, we will be going over this problem in this week’s live Office Hours sessions. It’s a great chance to discuss this question with a Knewton teacher, ask any questions you still have, and share your work with other students.

    I hope to see you there!

  • Timtinny

    I did spend a minute here. But this is actually a simple question. The trick is to understand that we need people who don’t play in fall as well as in spring.

    You have been given the fraction of ppl who did not play in fall. Now, the maximum fraction for the ppl who did not play in both fall and spring has to be 1/8 (s), it cant be more than that. So, the answer should be fraction of this 1/8 (s) or 1/8 (s) itself. Prompt 2) clearly gives what fraction did not play in spring from the 1/8 (s), that is what we are trying to find here :)

  • Gautam

    (Brigidette)

    Let total students in Edgemont High be = E
    Therefore from the question stem : 7/8 E students play a sport in the fall sem. This implies (1-1/8) E = 1/8 E students do not play a sport in the fall sem.
    Now Statement 1 tell 280 students play a sport in the spring sem — we have no idea about the number of students playing in the fall sem and we do not have the total number of students. Hence insufficient.

    Statement 2 tells that 2/7 of students who do not play in the fall sem do not play in the spring semester, i.e. 2/7 x 1/8 E (since 1/8 E do not play in the fall) hence this statement alone is sufficient because from it we can get the fraction of students who do not play a sport in neither the fall nor in the spring… 2/7 x 1/8 E = 1/28 E
    Hence the answer is B

  • Gautam

    (Brigidette)

    Let total students in Edgemont High be = E
    Therefore from the question stem : 7/8 E students play a sport in the fall sem. This implies (1-7/8) E = 1/8 E students do not play a sport in the fall sem.
    Now Statement 1 tell 280 students play a sport in the spring sem — we have no idea about the number of students playing in the fall sem and we do not have the total number of students. Hence insufficient.

    Statement 2 tells that 2/7 of students who do not play in the fall sem do not play in the spring semester, i.e. 2/7 x 1/8 E (since 1/8 E do not play in the fall) hence this statement alone is sufficient because from it we can get the fraction of students who do not play a sport in neither the fall nor in the spring… 2/7 x 1/8 E = 1/28 E
    Hence the answer is B

  • Gautam

    (Brigidette)

    Let total students in Edgemont High be = E
    Therefore from the question stem : 7/8 E students play a sport in the fall sem. This implies (1-7/8) E = 1/8 E students do not play a sport in the fall sem.
    Now Statement 1 tell 280 students play a sport in the spring sem — we have no idea about the number of students playing in the fall sem and we do not have the total number of students. Hence insufficient.

    Statement 2 tells that 2/7 of students who do not play in the fall sem do not play in the spring semester, i.e. 2/7 x 1/8 E (since 1/8 E do not play in the fall) hence this statement alone is sufficient because from it we can get the fraction of students who do not play a sport in neither the fall nor in the spring… 2/7 x 1/8 E = 1/28 E
    Hence the answer is B

  • Rajit

    Lets say 8x students in the school.

    Then, 7x students play sport in fall while x students dont play in fall.

    If we draw a table,
    a – students playing sports in fall as well as spring
    b – Spring but not in fall
    c – Fall but not spring
    d – neither fall nor spring

    Then, a+c = 7x ——–eq1
    and b+d = x ——–eq2

    Here we need to find out fraction of students who play a sport in neither fall nor spring.
    i.e. d/8x … basically we need an equation stating d in terms of x.

    Statement1: a+b = 280 …eq3 … 3 eqns, 4 unknown.. not helpful
    Statement2:
    Students not playing a sport in fall: b+d
    Given: d = 2/7 * (b+d) …. this gives us b in terms of d…and if we use eqn2, we can get b in terms of x…which would suffice…

    So 1 insufficient but 2 sufficient … ans B.

    Isn’t it?

  • Blah

    1. by itself is useless.
    2. 2/7*1/8 =1/28
    1/28 of students in spring do not play a sport….27/28 of students play a sport in spring…27/28 of x=280 play a sport.. x=290…which is the total number.

    2/7*1/8*290= students who do not play in fall dont play in spring.
    Therefore C is the right answer.. we need both.

  • Blah

    1. by itself is useless.
    2. 2/7*1/8 =1/28
    1/28 of students in spring do not play a sport….27/28 of students play a sport in spring…27/28 of x=280 play a sport.. x=290…which is the total number.

    2/7*1/8*290= students who do not play in fall dont play in spring.
    Therefore C is the right answer.. we need both.

  • Elaheh

    C….both statment together are sufficient

  • http://www.knewton.com Vishnu Patil:

    1/8 not play sport in fall, so we cant say about spring semester. Also 280 students play sport in spring dosn’t provide any fraction who paly in fall out of all number of students in Edgemont High play sport. So it has to be E.

  • http://Knewton George Zeidan

    Both statments together are sufficient ,
    The question is asking us for students who play sports in neither the Fall nor the spring. So the students who didnt play sports in the fall are 1/8o of the total. we have now to figure out the students who didnt play in Spring, the total of the students who played tennis in the spring is 280( from statment 1) and we know that 2/7 of the 1/8 of who didnt play sport in fall didnt play sport in spring, so the euqtion for the students who played in the spring is 7/8total+5/56total ( 5/7*1/8)=280 so we come up with x=290, therefore the total of the students were 290 were 280 played sports so we are left with 10 who didnt, so 10/290+1/8 is the answer.

    • Darren Meadows

      Statement 2 tells you what portion of those who don’t play in the fall also don’t play in the spring. This is the segment you are looking for, so that makes the question pretty simple. It’s just the fraction who don’t play in the fall multiplied by the fraction who also don’t play in the spring. Hence, 1/8 x 2/7. The answer is B.

  • moni

    c

  • http://www.kujali.org Sydney

    Ok, let me take a swing at this!

    T= total # of students
    N= fraction of students who did not play sports in fall or spring
    F= fraction of students who played sports in fall
    S= fraction of students who played sports in spring

    Given: 7/8 of the total student body played in fall

    Therefore, 1/8T did NOT play in fall.

    Now that we know the fraction of ST who did not play in fall, we have to determine whether or not we can determine (!) the fraction of ST who did NOT play in spring, which seems to be given in statement B: 2/7 OF the number who did not play in the fall (1/8T).

    Therefore:
    N= 1/8T + (2/7)(1/8)T
    N= 1/8T + (2/15)T
    N= 31/120T

    Is it possible to determine the fraction of ST who did not play in the fall or spring?

    I think so. The questions asks for the FRACTION OF TOTAL STUDENTS, not a quantitative value.

    Therefore, I think statement B alone is sufficient.

  • Batychica_rjs

    B!

  • Mubarakozy

    I don’t think there is the need for all these Venn diagrams and ‘scary’ calculations.
    Hi everyone,
    Statement 1 is obviously not sufficient. And this is because all data given are in fractions and we don’t also know the total universe.

    Statement 2 is just too sufficient! It has been answered by slotting in 2/7. The trick is that, the grammar has been ‘twisted’ to confuse people, that’s all!

    Answer= B.

    • Marcatack

      Agreed

  • MG

    The answer is E, the second statement needs to be read couple of times to get the idea … It says, Students who don’t pay in fall (pause), Of those 2/7 do not play in spring. This is not answering the question …

    From the question we know the fraction of students who don’t pay in fall is 1/8. So 2/7 * 1/8 do not play in spring. Well that doesn’t give us all students who don’t play both …

    Statement 1 and Statement 2 will help us solve for total number of students but we still don’t know the following:

    “Students who DO NOT play in Spring and those who do play in Fall”, AND “Students who do not play in Fall but play in Spring”.

    Either of those two if given we can answer this question.

    This Question is tricky!!!

  • Nks_heaven

    Option [B] is my answer

  • Anonymous

    B: 1/8*2/7 = 2/56 = 1/28. 

  • Ksu

    Please write the correct answer. B?

    • http://www.knewton.com Knewton Team

       Hi Ksu,

      B is correct.

      Here’s the explanation:

      The question tells us that 7/8 of the students play a sport in the fall semester, so we know that 1/8 of the students do NOT play a sport in the fall.

      Statement 1 gives us the number of students who play a sport in the
      spring semester, but it tells us nothing about the total number of
      students or the number of students who play a sport in both semesters.
      Thus, we cannot say what fraction of students play a sport in neither
      semester. Statement 1 is NOT sufficient. Eliminate answers choices A and
      D. The correct answer choice must be B, C, or E.

      Statement 2 gives us specific information about the number of
      students who do not play a sport in either semester. In particular, we
      learn that of the students who do not play a sport in the fall (1/8 of the total), 2/7
      do not play a sport in the spring. The fraction of students who play a
      sport in neither season is the product of these two fractions. Statement
      2 gives us enough information to answer the question.

      Answer choice B is correct.

      Although it is not necessary to solve for the exact fraction on the
      exam, we will do so for the purposes of illustration. The fraction of
      students who play a sport in neither semester is 2/7 of 1/8, or (2/7)(1/8)= 2/56 = 1/28.  . Therefore, 1/28 of the students play a sport in neither the fall nor the spring semester.

  • Karan Goyal

    isn’t there a possibility that some of the students that play in the fall do not play in spring?

  • Kris

    Hi, the answer I agree is B. However, the option 2 says 2/7 of the students who do not play a sport in the fall semester do not play a sport in the spring semester. 
    We know that 1/8 of the students do not play in fall. 
    Hence, the fraction of students who do not play in spring is 2/7 of those who did not play in fall= (2/7)*(1/8)
    the total fraction of students who do not play in both seasons= (1/8)*x+(2/56)*x

    This is the way I understand it. Could someone help me with this?

  • Kris

    Oh thanks I got it.