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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number

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simondahlfors

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Information given:
- Total gym members: 180

Question:
- Is the number of members who attend yoga sessions greater than the number who attend strength training sessions?

Solution:
- Statement 1: Every member who attends yoga sessions also attends at least one other type of session
- Therefore, no one only attends yoga sessions
- However, one other type of session can include strength training, but also any other type of session (e.g. cardio)
- Therefore, statement 1 is insufficient

- Statement 2: Every member who attends yoga sessions also attends strength training sessions
- Everyone who does yoga, also does strength training
- It is therefore impossible that the number of members who attend yoga sessions is greater than the number who attend strength training sessions
- The number of members who attend yoga sessions could be equal to, or less than, the number of members who attend strength training sessions
- Therefore, statement 2 is sufficient

Answer: B, statement 2 alone is sufficient

Bunuel

Out of 180 gym members, is the number of members who attend yoga sessions greater than the number who attend strength training sessions?

(1) Every member who attends yoga sessions also attends at least one other type of session.
(2) Every member who attends yoga sessions also attends strength training sessions.

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Bunuel

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(1) Every member who attends yoga sessions also attends at least one other type of session.

We don't know the number of sessions that the gym has.

The gym has only two sessions, yoga and strength training. We can have a scenario when all yoga members are attending strength training as well. In that case, the number is equal.

If the gym has more than two sessions, we can have the split created in a manner in which more members attend Yoga and let's say some other session and fewer members are attending the strength training sessions. In that case yoga > strength training.

As there could be an ambguity, statement 1 is not sufficient.

(2) Every member who attends yoga sessions also attends strength training sessions.

There is a complete overlap. In this case, yoga cannot be more than strength training, because every member who attends yoga also attends strength training. The number of people attending yoga can be less or equal to the number of people attending strength training. Hence, the answer is always no.

This statement is sufficient to answer the question asked.

Option B

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Bunuel

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The statement is sufficient

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01 Jul 2025, 08:38

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Statement two alone is sufficient information to determine the answer to this question.

1) Just because they attend at least one other type of session doesn't really tell us anything, it could be strength but it could also be something else, and if it is a majority strength, we don't know any specific numbers for sure and we don't know if there is a large number of people taking strength training sessions but not yoga.

2) If every member who attends a yoga session attends a strength training session that can mean a couple different things. We also need to recognize that the total gym members is an even number. The number who attend yoga COULD be equal to the number who attend strength training 90:90 in which case the answer would be no the number of yoga sessions is not greater. BUT we could have even just 89:91 for yoga sessions to strength training sessions in this case we would know for sure that the number of strength training sessions is higher.

Now it is important to note that the questions specifically asks if the number of yoga sessions is greater than the number who attend strength training sessions. In the second statement we prove that there are two possible scenarios but in both scenarios the number who attend yoga sessions CANNOT be higher.

The answer is B

Bunuel

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This is a Yes/No question. Our goal is to determine whether we have enough information to answer it with certainty.
[hr]
Statement (1):
Every member who attends yoga sessions also attends at least one other type of session.
This tells us that no one attends only yoga. Every yoga attendee does something else too (maybe strength training, cardio, etc.).
However, this does not give us any information about the number of members who attend strength training. We can’t compare yoga to strength training based on this.
→ Statement (1) is NOT sufficient.
[hr]
Statement (2):
Every member who attends yoga sessions also attends strength training sessions.
This means the set of yoga attendees is a subset of strength training attendees. So, the number of people who attend yoga is less than or equal to the number who attend strength training.
Therefore, the number of yoga attendees cannot be greater than strength training attendees. The answer to the question is definitely “No.”
→ Statement (2) IS sufficient.

Bunuel

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The prompt tells us we have 180 gym members and we want to know whether y > s

Using statement (1):
y > s IF yoga and strength training are the only to classes the gym offers. Because we don't know whether this is the case, statement (1) alone is not sufficient.

Using statement (2):
y > s IF there are more people that attend yoga. For example, if the gym offers only y and s, and lets say 100 people attend s and 80 attend y, then s > y. But if its the other way round and 100 people attend y, then y > s. Thus, statement (2) alone is not sufficient.

Using both statements:
From using each statement alone I know that I need info on how many classes they offer or whether more people attend yoga than strength training. Neither statement provides this so we can conclude that both statements together are not sufficient.

Answer: E)

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lets consider, total number of gym members, T = 180.
Y = number of members who attend yoga sessions.
S = number of members who attend strength training sessions.

we have to check if Y greater than S.

Statement (1): Every member who attends yoga sessions also attends at least one other type of session.
This statement tells us that the group of members who attend yoga sessions (Y) is a subset of members who attend other sessions. It doesn't give us a direct relationship or number for Y or S, nor does it compare Y and S.
For example:
Case 1: Y = 50. All 50 attend some other session. S = 40. (Y is greater than S)
Case 2: Y = 50. All 50 attend some other session. S = 60. (Y is less than S)
Since we can get different answers, Statement (1) is not sufficient.

Statement (2): Every member who attends yoga sessions also attends strength training sessions.
This means that all members in the yoga group are also in the strength training group.
If Y is a subset of S, it implies that the number of members in Y cannot be greater than the number of members in S, i.e.,Y is less than or equal to S.

The question asks: Is Y greater than S?
Based on Statement (2), we know that Y must be less than or equal to S. Therefore, Y > S is definitively false.
Since we can definitively answer the question (the answer is "No"), Statement (2) is sufficient.

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Ans: B (Statement 2 is sufficient

Out of 180 gym members, is the number of members who attend yoga sessions greater than the number who attend strength training sessions?
We are seeking is Y > ST ??

(1) Every member who attends yoga sessions also attends at least one other type of session.
any one with Y atleast attend one other type of sessoion. we do not know how many type of sessions are there and any other info which can relate Y with ST.
Not Sufficient

(2) Every member who attends yoga sessions also attends strength training sessions.
each who attend Y also attend ST
meaning ST >= Y
and from this we know that Y is not greater than ST [Sufficient]

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Looking at the statement B - Y(yoga) is either subset of S (Strength) or perfect overlap.
Hence,
Y<=S ; It's sufficient to say that Y is not greater than S.

Ansr - B

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Statement (1):

This tells me that yoga attendees don't attend yoga exclusively - they all attend at least one other session type
But we don't know how many attend yoga or strength training.
So this doesn’t tell us how many attend either — it only tells us about overlap.
We can’t compare Y and S
Statement (1) alone is not sufficient.

Statement (2):

This means Y ⊆ S (the yoga group is a subset of the strength training group)
Every member who attends yoga sessions also attends strength training sessions
If every yoga attendee also attends strength training, then: Y ≤ S
This directly answers the question: No, Y cannot be greater than S
Statement (2) alone is sufficient.

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Neither statement alone or both together prove that yoga attendance exceeds strength training:

Mentions nothing about strength training numbers.
Says yoga ⊆ strength training, so strength ≥ yoga. This rules out yoga > strength.

Both of them together also not sufficient.

Answer: E (Not sufficient).

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Statement 1:Every member who attends yoga sessions also attends at least one other type of session.

Here, since we don't know whether that other session is strength or not, we won't be able to answer the question. Not sufficient.

Statement 2: Every member who attends yoga sessions also attends strength training sessions.

We know for sure that Y = S if not less than S by the statement above because anyone who is attending yoga is definitely attending strength.
Therefore, Y <= S but will not be greater than S in anycase.
Hence, Statement 2 is sufficient.

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Bunuel

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Lets consider the number of members who attend yoga sessions is y, and strength training is s.

We need to prove y>s.

Stmt 1 : Every member who attends yoga sessions also attends at least one other type of session
But we don't know about the other type of session, It can be strength or something else.

If strength.
y<=s, We can prove y>s as false,

But If there are other sessions we cannot say y<=s, Hence this can be true.

So stmt 1 is insufficient.

Stmt 2: Every member who attends yoga sessions also attends strength training sessions.
If the given statement is true, then y<=s is always true and y>s is always false.

Hence stmt 2 is sufficient

IMO B

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Statement 1: Let's say 50 members attend yoga sessions. Statement 1 says that these 50 are attending at least one other type of session, this could mean the following of things:

1. That all of these 50 are attending strength training - meaning NO, the number of members who attend yoga is not greater than the one who attend strength training.
2. Say 30 (and these 30 only) are doing strength training, while the rest 20 are doing some other type of session - meaning YES, the number of members who attend yoga is not greater than the one who attend strength training.
3. Say even if there's no overlap between yoga attendees and strength training attendees - what if the strength training attendees is more than 50? - meaning NO, the number of members who attend yoga is not greater than the one who attend strength training.

So, Statement 1 is not sufficient.

Now, statement addresses the first point we noted. That there are at least 50 people attending strength training sessions. So, we can say for sure that the number of members who attend yoga is not greater than the one who attend strength training.

Therefore, statement 2 is sufficient. Hence, Ans. B.

Bunuel

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(1) Every member who attends yoga sessions also attends at least one other type of session.
We can't get a definitive answer from this statement. So not sufficient.
Eliminate A & D.
(2) Every member who attends yoga sessions also attends strength training sessions.
This means that number of members who attend yoga is either equal to or less that no of people who attend strength training sessions. Although we don't know which one is the case, we can be sure that number of members who attend yoga sessions is not greater than the number who attend strength training sessions.
Sufficient

ANS- B

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We are asked whether the number of gym members who attend yoga is greater than those who attend strength training. Statement (1) tells us that every yoga attendee also attends at least one other session, but it doesn’t specify which—so we can’t compare the numbers of yoga and strength attendees, making it insufficient. Statement (2) says every yoga attendee also attends strength training, meaning yoga is a subset of strength; thus, the number attending yoga can never be greater than those attending strength training, and the answer to the question is definitively “no,” making this statement sufficient. Therefore, only statement (2) is sufficient to answer the question. The correct answer is B.

Bunuel

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Let’s denote:

Y = number of members who attend yoga

S = number of members who attend strength training

We’re being asked: Is Y > S?

Now let’s analyze the two statements.

Statement (1):
Every member who attends yoga also attends at least one other type of session.

This tells us that no one does yoga alone — every yoga attendee also does something else.

But it doesn't tell us how many do yoga or strength training. For example:

Maybe 50 people do yoga + cardio, and 10 people do strength training.

Or 50 do yoga + cardio + strength training, and 100 do only strength training.

We have no comparison of Y vs S from this.
So, Statement (1) alone is not sufficient.

Statement (2):
Every member who attends yoga also attends strength training.

This means:
Yoga attendees are a subset of strength training attendees
-> So: Y ≤ S

But we are asked: Is Y > S?
If Y ≤ S, then Y is not greater than S.

So, the answer is No based on this statement.
Therefore, Statement (2) alone is sufficient to answer the question.

Combined?
No need. Statement (2) alone answers the question definitively.

Final Answer:
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

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This is a trap question.

total = 180 ( This detail is not useful for the question, but just quoting.)
y = No. of person who attended the yoga session. s = No who attended Strength Sessions.
Question: is y>s?
Statement 1:
Every member who attends yoga sessions also attends at least one other type of session. We don't know what all type of sessions are there and no detail about no. who attended strength sessions, it could be more or less, y>s or y<=s. SO, Insufficient.

Statement 2:
Every member who attends yoga sessions also attends at least one other type of session. This means atleast y = s. But strength session attendees could be more since no data about the strength session attendees. But the question is whether y>s. But we know now, that it y<=s. So No. So sufficient.

Hence Statement 2 alone is enough, so B.

Bunuel

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Answer - B
Statement (1) is NOT sufficient: Knowing that yoga members attend other sessions doesn't tell us if there are more yoga members than strength training members. For example, 50 yoga/other members vs. 40 strength training (Yes), or 40 yoga/other members vs. 50 strength training (No).

Statement (2) IS sufficient: If every member who attends yoga also attends strength training, it is impossible for the number of yoga attendees to be greater than the number of strength training attendees. The number of yoga attendees must be less than or equal to the number of strength training attendees. Mathematically, N(Y)≤N(S). Since N(Y) can never be greater than N(S) based on this statement, the answer to the question "Is N(Y)>N(S)?" is No.

Bunuel

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We need to check if Y>S( where Y is yoga and S is Strength)

In the second option,it says Y is equal to S,so its sufficient to answer the question is Y>S
In the first option, it says those who attended yoga sessions also attend some other session,but the problem here is there could be many other different sessions like hockey for example.So this option is not sufficient to answer is Y>S

Hence B is the answer

Bunuel

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