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

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feistygirl

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10 Jul 2026, 08:45

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i am going with option c.
it accurately represents 5:1 ratio for the remaining members
remaining members: (420-160-80) = 180
ratio: 180 members into 6 parts (5x swimming only: 1x neither)
1 part = 180/6 = 30
swimming only group gets 5 parts - 5x30=150
a incorrect - gives value of neither group than of swimming
b and e incorrect - values from mixing up overlapping groups
d incorrect - it gives total remaining pool 6x before applying ratio.

DachauerDon

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10 Jul 2026, 08:46

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Answer: A) 30

x = members who met the mark for neither
y = members who met the mark for swimming but not for cardio

420 = 80 + 160 + x + y
y = 5x
180 = 6x, x = 30

rockstar09rulez

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10 Jul 2026, 08:48

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		S	S
		2h	not2h
C	2h	160	80
C	not 2h	5x	x

Now sum of everything in the table should be 420
gives 240+6x = 420
6x = 180
x = 30 A)

VenkataSai

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10 Jul 2026, 08:55

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Let S be the no. of people who met only swimming, C be only cardio, I be both and N be for none.

Now total = 420= S+C+I+N.
Given, B= 160, C=80. and I=5N.( for every 5 people who met mark for only swimming there is 1 person who met neither.)

substituting these values in the above equation, we get N=30.

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

This question was provided by GMAT Club
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⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.

JayBKK

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There are 4 cases in this universe.
1. Only swimming: we're given 5x
2. Only cardio: we're given 80
3. Both cardio and swimming: we're given 160
4. Neither: we're given x

So, from the total 420 = 5x+80+160+x
180 = 6x
x = 30

Choice A

Saurav1408

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10 Jul 2026, 08:56

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This question is from 2 set Venn Diagram. Just understand the question carefully and write what is given. The abbreviations used are: Swimming - 's' and Cardio-machine workout: 'cmw'
2-hour-per week mark - it is the mark on which both the activities are assessed.
The values as per given information in the 2 set Venn Diagram would be:
Total members = 420
Both(intersection of both s and cmw) = 160
Only cmw = 80
None = suppose 'x'
Only s = if none is considered 'x' then the members included in only swimming would be '5x' as given.

Now solve:

only s + only cmw + both(s and cmw) + none = 420
5x + 80 + 160 + x = 420

And after solving we get x = 30. Since none was considered 'x' so
the answer would be 30

MakB

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I usually work by matrix method so little difficult to explain without table but here it goes.
Total doing swimming and cardio = 160
Total doing only cardio, not swimming = 80
Hence, total swimming = 160 + 80 = 240
If 420 is total members, and total people doing swimming is 240
Then 420- 240 = 180
Let no. of people doing neither be x
then no. of people doing only swimming, not cardio = 5x
Now equating,
5x + x = 180
6x = 180
x =30
Hence, A

harshitaa45

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10 Jul 2026, 09:00

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420 people in total
Both cardio and Swimming=160
Only cardio=80
None=x
Only swimming =5x

420= 160+80+6x
6x=180 x=30
Answer:30

ischiragkapoor

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10 Jul 2026, 09:04

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420 Members

	Cardio	No Cardio	Total
Swim	160	$5x$
No Swim	80	$x$
Total	240	$6x$	420
		420-240=180

$\\
6x = 180\\
x = 30\\
\\
$

IMO Answer (A) = 30

Dawoodgmat

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10 Jul 2026, 09:05

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both=160
cardio only =80
swim= 5y
nither= y

5y+80+160+y=420
6y=180
y=30

RahulSax

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10 Jul 2026, 09:06

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This is how I solved it using the sets method, and taking the unknown variables in terms of x
Hence, answer comes out to be 30

Attachments

IMG_20260710_212035067.jpg [ 1.47 MiB | Viewed 146 times ]

GamePine

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There are 420 members of which 160 met the goal for both swimming and cycling and 80 met it for only cycling.

The equation I set up is 420 = 80 +160 + swimming only + did not meet any goal, so

swimming (set as S)+ did not meet any goal (Set as N) = 180

For every 1 that did not meet the goal, 5 only met it in swimming so I sub s for 5n

5n + n = 180
6n = 180
n = 30.

The answer is A 30

c404

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10 Jul 2026, 09:17

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use the grid method
given

	met swim	not met swim	total
met cardio	160	80	240
not met cardio	5A	A	B
total			420

we can solve 240+B=420 so B=180
and then 5A+A=B=180 or A=30

RDM42

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10 Jul 2026, 09:24

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Of the 420 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?

Total members= 420
Both activities= 160
Cardio only = 80
Swimming only = 5x
Neither= x
We need to find x.
160+80+5x+x=420
240+6x =420
6x=420-240=180
x=180/6= 30

30

metrogloomin

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10 Jul 2026, 09:32

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Let us assume two overlapping sets S and C, and n(neither S or C) be x.
n(both)=160
n(only C)=80
n(only S)=5x

Adding all:
n(neither S or C)+n(only S)+n(both)+n(only C)=420
x+5x+160+80=420
6x=180
x=30

SS990

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10 Jul 2026, 09:36

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	s	ns	t
c	160	80	=240
nc	5x	x=?	=180
t			480

6x=180

x=30

onlyPlanA

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I am not sure but I did this.

Total people surveyed = 420
People who met the two hour mark in both activities = 160
People who met the mark in only cardio but not swimming (let C) = 80
People who met the mark in only swimming but not cardio = S
So, we have the equation:

420 = C + S - Both + Neither
420 = 80 + S - 160 + Neither
S + Neither = 180 ------------------eq (1)

But it says, for every person who met the mark in neither activity, there are 5 who met the mark in swimming but not cardio.
So, S = 5 * Neither -------> (Am I right?)

So, from eq (1):
Neither = 30

IMO, the answer is A.

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10 Jul 2026, 09:52

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We know:
Number of members for both the activities: 160
Number of members for cardio only: 80
Let the number of members who met the mark for neither activity be x.

Since for every member who met the mark for neither activity, 5 met the mark for swimming only:
Swimming only : Neither = 5 : 1

Use the total: 160 + 80 + 5x + x = 420
x = 30

Hence, the correct answer is Option A - 30.

Hope this helps!

Desberia

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Total =420
C=cardio, S=swimming
x= neither
5x swimming only

5x+160+80+x=420
solving for x=30
Ans A

princesskitt

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Total number of members: 420
There are 2 activities: Swimming (S) and Cardio (C).

According to the question:
both S and C = 160
C = 80
Let the number of members who did not meet the 2-hour-per-week criteria of either activity be n
Therefore, according to the information provided, S = 5n

The venn diagramm pertaining to all of the above given information can be constructed as follows: (Image attached)

Therefore, the total number of members can be written as S + C + both S and C + neither S nor C = 5n + 80 + 160 + n = 240 + 6n
We also know that the total number of members who signed up was 420.
Therefore, 240 + 6n = 420 or 6n = 180 which implies n = 30.
Hence, the number of members who met the criteria for neither activity is 30.
Final answer: A. 30

P.S. I used excalidraw to draw the venn diagram in the image attached.

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Screenshot 2026-07-10 at 10.22.47 PM.png [ 59.35 KiB | Viewed 126 times ]