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GMAT Club World Cup 2026 (Day 5): A recreation center surveyed 420 mem

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PulkitSaran

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11 Jul 2026, 01:16

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Bunuel

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

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Translating the given information into a 2x2 matrix, we get:

	Swimming	No Swimming	Total
Cardio-machine	160	80	240
No Cardio-machine	5x	x	180
			420

We need to find out the value of x:
5x + x = 180, which implies x = 30. Hence, answer is A.

noerd23

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11 Jul 2026, 01:22

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Both Swimming and Cardio = 160, Cardio only = 80, Swimming only = x, Neither = y

We know given:
For every member who met neither 5 met the mark for swimming only. So we can say that

-----> Swimming only : Neither = 5 : 1
----> x/y=5/1
-----> x = 5y

Now using the total number of members:
160 + 80 + x + y = 420

Substituting x = 5y:

160 + 80 + 5y + y = 420

-----> 240 + 6y = 420

-----> 6y = 180

-----> y = 30

Answer: A) 30

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11 Jul 2026, 01:48

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The correct answer is A.

Given in the question,
Both= 160
only cardio= 80
only swimming= 5x
neither= x
total= 420

Putting the same in the equation below;
Total= both+ only cardio+ only swimming+ neither
420=160+80+5x+x
420=240+6x
180=6x
x=30

A. 30.

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11 Jul 2026, 01:54

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Let:
$T$ = total members
$S$ = only swimming
$C$ = only cardio
$SC$ = both swimming and cardio
$N$ = no activities

We have:
$T = 420$
$C= 80$
$SC = 160$

We also know that the ratio $N:S = 1:5$, which means that $\frac{N}{S}=\frac{1}{5}$ and so: $S = 5N$.

The total number of members is given by the sum of all the categories:

$T = S+C+SC+N$

$420 = 5N + 80 + N +160$

$6N = 180$

$N=30$

Answer: A

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11 Jul 2026, 02:42

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Total Members surveyed = 420

Members who did not meet neither swimming nor cardio (A) = x
Members who met swimming but not for cardio(B) = 5x
Members who met both cardio and swimming(C) = 160
Members who met mark for cardio machines(D) = 80

Total no. of members =420 = A + B +C +D = x +5x +160 +80
6x=180

x=30 = Answer

Bunuel

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11 Jul 2026, 03:14

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The answer is A) 30.
Let neither be x , only swim is 160 and only cardio is 80 and both is 160 as per the stem
Total= swim + cardio-both + neither
420= swim+ 5x + 80+160-160+ x
x=30

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11 Jul 2026, 03:29

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Bunuel

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Given data-
Total members- 420:- Both activities- 160; Only Cardio- 80
Assume that members doing neither activities- x then only Swimming- 5x
Therefore, 420=160+80+x+5x
On solving, x=30. Option- A

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11 Jul 2026, 03:50

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I have solved this using a Venn Diagram.

As per the question, it has been given to us that there are 420 member surveyed, among which
Some do neither activity
some do swimming
some do cardio
& some do both

We are also given that 160 do both, 80 do swimming.
We are also given that for every one person who does neither activity, there are 5 people who do swimming. So, there is a ratio of 1:5 for people who do neither activity and who do swimming.
That means we can write them as x and 5x respectively.

Now, Total Participants= Participants who do neither + participants who do do both + participants who do swimming + participants who do cardio

420= 160+80+ x+5x
420=240+6x
180=6x
x=30
That is our answer because it indicates people who do neither activity.

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11 Jul 2026, 04:06

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The answer is A.30 because
Let neither swim=x, swim-only=5x
160+80+5x+x=420
=> x=30

Bunuel

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11 Jul 2026, 04:47

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Car machine but not swimming =80
Swimming but not cardiac machine= 5x (say) and neither=x
Both=160
.: 80+160+5x+x=420 (Since total participants=420)
.: 6x=180
.: x=30
The answer is B.

Bunuel

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11 Jul 2026, 04:51

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Not 100% sure but some issue in this Question or in my understanding what I should understand by this line "and for every member who met the mark for neither activity" I'm unable to relate how this is related to previous info of 80 met for cardio and not for swimming ... maybe I would be wrong because I'm unable to get correct answer choice so I choice near by answer of 180 option D.

my understanding = > total 420 , Both =160 , C = 80 & S = 5 then neither is 420 - 245 = 175 but didn't find any answer choice so I went with answer choice D 180 some flaw in me I will review this question later once again. Thanks!

Bunuel

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11 Jul 2026, 05:14

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Let x be the number of member who met the mark for neither activity -> this is what the question is asking as well
420 members include: 80 members mark for cardio only, 160 members mark for both, x people mark for none and 5x people for swimming only
We have an equation: x+5x+160+80=420 -> x = 30
--> Choose A

Bunuel

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11 Jul 2026, 05:19

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total 420
Members who did not meet both the mark or just the swimming = 420 - 160 - 80 = 180

Lets assume x people did not meet both mark then it is given that x + 5x = 180 => x = 30

Ans - A

Bunuel

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11 Jul 2026, 05:28

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CD	Not CD
SW	160	x
not SW	80	5x
	240	6x	420

240+6x= 420
X=30

Bunuel

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11 Jul 2026, 05:46

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Overlapping question:
Our formula is (A but not B) + (B but not A) + (Both A and B) + Neither = Total
In other words (Only A) + (Only B) + (Both A and B) + (Neither) = Total
We do not subtract (Both A and B) since the question gives the number for (Only A) as in Cardio but not swimming.
What does the question ask? ------> Number of members that completed NEITHER of the activities:
There is also a slight trick that we be careful: "For every member who met the mark for neither activities, 5 met the mark for swimming but not for cardio" -------> Meaning: If Neither is "N", then "(Only Swimming)"=5N
Lets plug in the numbers:
1. (Only A) Only Swimming = 5N
2. (Only B) Only Cardio= 80
3. (Both A and B) = Cardio and Swimming = 160

So our equation becomes: (5N)+(80)+(160)+(N)=420 --------> 6N + 240 = 420 ------> 6N=180 ------ N=30
Since the question asks for the neither our answer is 30
IMO

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11 Jul 2026, 05:54

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Lets translate all that information into a. table, we get the following-

	Swim yes	Swim No	Total
Cardio yes	160	80	240
Cardio no	5n	n	6n
Total			420

420=6n+240
6n=180
n=30
IMO A

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This question mentions that the recreation center has surveyed Total 420 Members out of which :
a) 160 Members => Both Swimming and Cardio workout for 2 hours
b) 80 Members => Cardio Workout mark met but not swimming
c) Of the balance members - the ratio of members to did not meet any mark to the ratio of members who met the time for swimming but not cardio is 1:5
We are asked what is the total number of members who did not meet the mark for both the activities

So I solved it like this - in the question - there are 2 things which are not given -
d) Number of members who met none of the timing requirements - let it be x
e) number of members who met the mark for Swimming but not cardia - since the ratio is given as 1:5 - this will be 5x

Total members - 420 = 160 +80+ x+ 5x
420-240 = 6x
180 = 6x
x = 30

Accordingly, our answer is Option A = 30.

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11 Jul 2026, 05:56

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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.

Let
a = the no. of people who met the mark for cardio only
b = the no. Of people who met the mark for swimming only
c = no. Of people who met the mark for both
d = no. Of people who met the mark for none

Given, a = 160, c = 80
Say, d = x, then b = 5x

a+b+c+d = 420
240 + 6x = 420
Which gives x = 30 ..Ans. A

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11 Jul 2026, 06:05

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swimming & cardio both = 160
only cardio=80
neither=x
only swimming=5x

5x+160+80+x=420
x=30

Ans A

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11 Jul 2026, 06:13

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Let, total members be T=420, Swimming be S and Cardio C.
so both S & C= 160.
Finally, not both S&C is = 420 - 160= 260 meaning either S only, or C only or neither S nor C.
only C=80, therefore, 260 - 80=180, which is: S only or neither S nor C.

Let neither S nor C be N, so S only is 5N according to the given data.
Finally, 5N+N=260, 6N=180/:6, N=30

My answer is (A)

Bunuel

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