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10 Jul 2026, 08:00
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A
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Difficulty:
25%
(medium)
Question Stats:
88% (01:55) correct
12%
(02:58)
wrong
based on 280
sessions
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A recreation center surveyed 420 members about two activities: swimming and cardio-machine workouts. Of the members surveyed, 160 met a 2-hour-per-week mark for both activities, 80 met the mark for cardio-machine workouts but not for swimming, and for every member who met the mark for neither activity, 5 met the mark for swimming but not for cardio-machine workouts. How many of the 420 members met the 2-hour-per-week mark for neither activity?
A. 30
B. 80
C. 150
D. 180
E. 260
A. 30
B. 80
C. 150
D. 180
E. 260
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M46-40
10 Jul 2026, 09:00
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GMAT Club Official Solution:
A recreation center surveyed 420 members about two activities: swimming and cardio-machine workouts. Of the members surveyed, 160 met a 2-hour-per-week mark for both activities, 80 met the mark for cardio-machine workouts but not for swimming, and for every member who met the mark for neither activity, 5 met the mark for swimming but not for cardio-machine workouts. How many of the 420 members met the 2-hour-per-week mark for neither activity?
A. 30
B. 80
C. 150
D. 180
E. 260
Let x be the number of members who met the 2-hour-per-week mark for neither activity.
Then the number of members who met the mark for swimming but not for cardio-machine workouts, that is, swimming only, is 5x.
The 420 members are split into four groups:
Both activities: 160
Cardio-machine workouts only: 80
Swimming only: 5x
Neither activity: x
So:
160 + 80 + 5x + x = 420
6x = 180
x = 30
Therefore, 30 members met the 2-hour-per-week mark for neither activity.
Answer: A.
A recreation center surveyed 420 members about two activities: swimming and cardio-machine workouts. Of the members surveyed, 160 met a 2-hour-per-week mark for both activities, 80 met the mark for cardio-machine workouts but not for swimming, and for every member who met the mark for neither activity, 5 met the mark for swimming but not for cardio-machine workouts. How many of the 420 members met the 2-hour-per-week mark for neither activity?
A. 30
B. 80
C. 150
D. 180
E. 260
Let x be the number of members who met the 2-hour-per-week mark for neither activity.
Then the number of members who met the mark for swimming but not for cardio-machine workouts, that is, swimming only, is 5x.
The 420 members are split into four groups:
Both activities: 160
Cardio-machine workouts only: 80
Swimming only: 5x
Neither activity: x
So:
160 + 80 + 5x + x = 420
6x = 180
x = 30
Therefore, 30 members met the 2-hour-per-week mark for neither activity.
Answer: A.
General Discussion
10 Jul 2026, 08:08
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Answer: A
This is a double overlapping set question. The two main approaches are a venn diagram or a double set matrix, I personally prefer to solve with double set matrix as that is what I am most used to.
Set up:
Both = 160, Cardio but not swimming = 80, so total Cardio = 240. Therefore, total who did not hit the mark for Cardio = 180.
The second part of the question provides a ratio between the neither group and the swimming but not cardio group. The sum of these two groups will be 180, aka the total who did not hit the mark for cardio This allows us to set up the equation x + 5x = 180, or 6x = 180.
Therefore, x = 30.
This is a double overlapping set question. The two main approaches are a venn diagram or a double set matrix, I personally prefer to solve with double set matrix as that is what I am most used to.
Set up:
Both = 160, Cardio but not swimming = 80, so total Cardio = 240. Therefore, total who did not hit the mark for Cardio = 180.
The second part of the question provides a ratio between the neither group and the swimming but not cardio group. The sum of these two groups will be 180, aka the total who did not hit the mark for cardio This allows us to set up the equation x + 5x = 180, or 6x = 180.
Therefore, x = 30.
