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655-705 (Hard)|   Overlapping Sets|         
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:00
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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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B
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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.

This tells us that no one attends only yoga, but it doesn’t specify which other session is attended. So:

Suppose 10 members attend yoga, and all of them also attend cardio. Strength training has 5 members. Then yoga > strength, so the answer is Yes.

Suppose 10 members attend yoga, and all of them also attend cardio. Strength training has 50 members. Then yoga < strength, so the answer is No.

Not sufficient.

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

This means the entire yoga group is included in the strength training group. So yoga cannot be greater than strength, giving a definite No answer to the question. Sufficient.

Answer: B.
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:10
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The question is: Is the number of yoga members (Y) greater than the number of strength training members (S)?

(1) Every member who attends yoga sessions also attends at least one other type of session.
This "other session" could be anything (cardio, swimming, etc.), not necessarily strength training. It doesn't establish a clear relationship between Y and S. We can't determine if Y > S. This statement is INSUFFICIENT.

(2) Every member who attends yoga sessions also attends strength training sessions.
This means the group of yoga members is a subset of the strength training members. Therefore, the number of yoga members must be less than or equal to the number of strength training members (Y <= S).
This gives a definite "No" to the question "Is Y > S?".
This statement is SUFFICIENT.

The correct answer is (B).
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:14
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T=180
Y>ST?

S1
Every member who attends yoga sessions also attends at least one other type of session.
We don't know if the other session is just strength training or something else
Insufficient

S2
Every member who attends yoga sessions also attends strength training sessions.
This suggests that Y<=ST
Sufficient

Answer B
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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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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:15
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Answer
(B) Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.

Explanation

The Question: Is the number of yoga members (Y) greater than the number of strength members (S)? In short: Is Y > S?

Statement (1): "Every member who attends yoga sessions also attends at least one other type of session."
  • This tells us there are no "yoga-only" members. The "other session" could be strength training, or it could be something else like cardio.
  • We can't compare the size of Y and S. Maybe Y = 100 and S = 50 (Answer: Yes). Or maybe Y = 50 and S = 100 (Answer: No).
  • Since we can get both a "Yes" and a "No", this statement is INSUFFICIENT.

Statement (2): "Every member who attends yoga sessions also attends strength training sessions."
  • This is the key. It means that the entire group of yoga members is contained inside the group of strength training members. The yoga group is a subset of the strength group.
  • This means the number of yoga members can, at most, be equal to the number of strength members, but it can never be greater (Y ≤ S).
  • Therefore, the answer to the question "Is Y > S?" is a definite NO.
  • Since we have a definite answer, this statement is SUFFICIENT.
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:19
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B) Statement (2) alone is sufficient, but statement (1) alone is not.

Explanation
Let Y be the number of members who attend yoga sessions, and S be the number of members who attend strength training sessions. The question is: Is Y > S?

Statement (1): Every member who attends yoga sessions also attends at least one other type of session.
This statement tells us that anyone in the yoga group also participates in another activity (like strength training, cardio, etc.). However, it doesn't establish a direct relationship between the total number of yoga members and the total number of strength training members.

Scenario 1: There could be 50 yoga members who all attend strength training, and 100 members in total attend strength training. Here, Y = 50 and S = 100. The answer to "Is Y > S?" is No.

Scenario 2: There could be 100 yoga members who all attend cardio sessions, and only 50 members attend strength training. Here, Y = 100 and S = 50. The answer to "Is Y > S?" is Yes.

Since we can get both a "Yes" and a "No" answer, Statement (1) is not sufficient.

Statement (2): Every member who attends yoga sessions also attends strength training sessions.
This statement means that the group of people who attend yoga is a subset of the group of people who attend strength training. If you are in the yoga group, you are automatically in the strength training group.

This means that the number of yoga members (Y) can, at most, be equal to the number of strength training members (S), but it can never be greater. Mathematically, Y ≤ S.

Therefore, the answer to the question "Is Y > S?" is a definitive No.

Since this statement provides a conclusive answer, Statement (2) is sufficient.
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:20
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We have to know whether Y > S (where number of people who attended Yoga is Y and Strength training is S)
Statement A) it says Y also attends some other session, it could be any session other than strength training, as it is not mentioned how many other sessions are there in total, so A is insufficient.

it could be B,C or D

Statement B) Clearly it states Y also attends S, so Y<=S, so this statement would be sufficient.

So it is B.
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:21
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The ans is B.

St1 : we don't know total how many sessions and what type of sessions are there. so, yoga can be greater or less than strength train. sessions.

St2: the no of people in strength training sessions can be more or equal to people in yoga sessions but it will never be less. So, ans is B
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:21
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1) We do not know how many other types of sessions there are and can not determine on its own
2)We know that every yoga member attends strength. So we know that yoga could be qual to or less than strength. Thus we know it is not greater than strength - So 2 is sufficient.


B - 2 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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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:22
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Let's denote:
Y = number of members who attend yoga sessions
S = number of members who attend strength training sessions
We need to determine whether Y > S.
Statement 1: Every member who attends yoga sessions also attends at least one other type of session.
This tells us that all yoga attendees also attend some other type of session, which could be strength training or something else. However, this doesn't tell us how many members attend yoga or strength training, so we can't determine whether Y > S.
Statement 1 alone is insufficient.
Statement 2: Every member who attends yoga sessions also attends strength training sessions.
This means that all yoga attendees are also strength training attendees. In other words, the set of yoga attendees is a subset of strength training attendees.
This can be represented as Y & S, which means Y s S.
Therefore, Y > S is false, unless Y = S (which would happen if every strength training attendee also attends yoga).
Since we don't know if Y = S or Y < S, we cannot definitively answer whether Y > S.
Statement 2 alone is insufficient.
Combining both statements:
From Statement 2, we know that all yoga attendees also attend strength training (Y C S).
From Statement 1, we know that all yoga attendees also attend at least one other type of session.
Since Statement 2 already accounts for yoga attendees attending strength training, Statement 1 doesn't add any new information that helps us determine whether Y > S.
Therefore, even with both statements combined, we cannot determine whether Y > S.
The answer is E Neither statement is sufficient, even when combined.
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:23
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Total members = 180

Question : is yoga members > strength training members?
is y>s ?

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

Since there are only 2 sessions mentioned, this statement says that one who attend yoga session also attend strength training session
This is insufficient to ans the question

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

This is same as statement 1

Combining both does not give us new info
So its insufficient

Hence E is correct

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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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:25
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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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Analysis: 1 ( Every member who attends yoga sessions also attends at least one other type of session.)

At least means 1 to all, anything; They may have attended all the strength training sessions or may not have attended any strength sessions. The answer could be anything. Not Sufficient.

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

Yoga =< Strength; Here yoga members definitely will not be more than Strength members; Hence Sufficient.
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:25
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Total member = 180

1) all members who attend yoga also attend atleast one other
That might be strength might not be strength,
Other people who dont attend yoga might also attend strength
Not sufficient
2) every member who attends yoga also attends strength
So strength >=yoga
Hence yoga is not greater than strength
Sufficient
Hence B
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:25
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Answer (E)

(1) Every member who attends yoga sessions also attends at least one other type of session- "other type of session". It does not mention strengthening. Not sufficient.
(2) Every member who attends yoga sessions also attends strength training sessions- assume the number of attendees for yoga is 10. Therefore, the number of attendees for strength training will be 10 or more. (because we don't know if everybody who attends strength training attends yoga sessions).




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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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:27
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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.
Since all types of sessions are not known, and it is not mentioned that there are only 2 types of sessions.
NOT SUFFICIENT

(2) Every member who attends yoga sessions also attends strength training sessions.
The number of members attending strength training sessions must be greater than or equal to the number of members attending yoga sessions and the number of members attending yoga session MUST NOT BE greater than who attend strength training sessions.
SUFFICIENT

IMO B
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:28
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total gym members is 180
target 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.
we have no info about strength training member; insufficient
#2
Every member who attends yoga sessions also attends strength training sessions.
it means that same number of members attend yoga & strength training , but not other way around
insufficient
from 1 &2 we cannot determine whether Every member who attends yoga sessions also attends strength training sessions.

OPTION E is correct
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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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:29
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The correct answer is B, below attached is detailed solution
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Statement 1 is vague as it talks about every member of yoga session also attend another session but we don't know if that session is a strength training session.

Statement 2 clearly tell us that all Yoga will do strength which means if X people did yoga then minimum X people would do strength so Yoga is a subset of Strength and it clearly states that no of member is more in strength.

Hence statement 2 is sufficient but 1 alone is not
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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.


 


This question was provided by GMAT Club
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Statement 1 tells us that those who do yoga will do 1 other sport, that could mean all of them do yoga with strength training, or none of them do yoga with strength training. We also dont know how many do yoga vs strength training.

Statement 1 is not sufficient

Statement 2 tells us that since all members of yoga do strength training, the number of people who do yoga will at best match the number who do strength training, otherwise they can only be less people who do yoga.

answer: B , statement 2 alone is suffcient
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GMAT Club Olympics 2025 (Day 2): Out of 180 gym members, is the number 01 Jul 2025, 08:33
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ok We need to find if Y > S (Assume variables as number asked)
Statement 1=>
it say those who attend yoga attend at least one other session
so lets say Y=100 and then they all attend may be football session only so S=100 in this case Y=s => No
now another case say Y=20 and then they but S=10 and F=10 and in this 150 there are 10 then Y>S => Yes
Not Sufficient

Statement 2 =>
This tells us every yoga attende attends strength so Y is subset of S
Y<=S so its always NO
Sufficient

Ans is B
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