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

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Vivek1707

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10 Jul 2026, 10:07

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Two set approach can help solve this quickly

Let S be swimming and C be cardio machine

As per the question

	S	~S	T
C	160	80	240
~C	5x	x	180
			420

Hence 5x + x = 180 i.e 6x = 180 i.e x = 30 Answer A

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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10 Jul 2026, 10:13

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total-T=420
both-B=160
cardio only-C=80
neither-N=x
swimming only-S

for everyone who met neither (x), 5 met swim only so 5x

total=both+C+S+N
420=160+80+5x+x
420=240+6x
420-240=6x
180=6x
180/6=6x/6
x=30
Ans:A, 30

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Needs to focus on the statement: For every member who met neither activity, 5 met swimming only.
Which means, is the total number of member who met neither is X, then 5x met only swimming and not cardio

so equation becomes: 420 = 160 + 80 + 5x + x --> x = 30

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Total Members: 420
Both activities: 160
Only Cardio: 80
Neither: Only Swimming
1 : 5
The remaining is 180, so 180/6= 30
30: 150

The answer for neither is 30

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Total members = 420

There are two groups in these 420 people: One who met the mark for at least one activity and one who did not meet the mark for any

Now, we can make a venn diagram for the group that meets the mark for at least one activity:

Both = 160
Cardio but not S = 80

Now, its given for every member who does not meet the mark for any activity, 5 meet the mark for swimming but not cardio machine

So, if neither is x, then those who meet mark for S but not C = 5x

Now, we can just add them all- 240 + 6x = 420

x = 30

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10 Jul 2026, 10:47

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BOTH SWIMMING AND CARDIO(A)=160
CARDIO ONLY(B)=80

LET X AS NEIETHER
THEN ONLY SWIMMING=5X

SO TOTAL- 160+80+5X+X= 240+6X

GIVEN THIS AS 420

MEANS 420=240+6X
6X=180
X=30

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both S and C = 160
only C = 80
neither = x
only S=5x
160+80+x+5x=420
x=30 Answer A

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So there are 4 parts which equals to 420. One part of those who met the 2 hr mark for both activities. One part for cardio only, one for swimming only and one for the members who met neither. If we consider the number of members for neither, lets say its x, it will make the number of members who met the mark for swimming only, as 5x.

Which will make the equation-

160+80+5x+x=420. Eventually making x as 30.

Thus it will be option A

Bunuel

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Let number of people meeting neither activity be X
Number of people meeting swimming but not cardio requirement is 5x

From the question, total people = 420, Number meeting both cardio and swimming = 240, number meeting cardio but not swimming = 80.

total swimming = (Swimming and Cardio) + (Swimming but not cardio) = 160 + 5x
total not swimming = (Cardio but not swimming ) + (neither cardio nor swimming) = 80 + x

Total people = 420 = 160 +5x + 80 + x = 240 + 6x.

Solving for x = 30

Answer A

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Bunuel

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given total :420
both activities : 160
cardio only : 80
if we consider n be the no of members who did neither activity,
given that 5n be the no of members who did swimming only
we can write, Total = Swimming only + cardio only + both +neither
420 = 5n + 80+ 160 + n
6n = 180
n = 30
So, No of members who met the 2 hr per week mark for neither activity is 30
A

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Let the no. who met the mark for neither activity be x
Then the no. who met the mark for swimming only is 5x

Using the total:
160(both) + 80(cardio only) + 5x(swimming only) + x(neither) = 420
240 + 6x = 420
6x = 180
x = 30

Ans : A

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10 Jul 2026, 11:09

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Let the people who meet only Swimming activity's 2 hour mark = a
the people who meet only cardio's mark = b
the people who meet both = C and those who meet neither's = d

Question says c = 160, b = 80 and a=5d. Question is asking for the value of d.

We know a+b+c+d = 420, a+80+160+d = 420, a+d = 180, 5d+d = 180, 6d = 180 and d=30.

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10 Jul 2026, 11:14

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2hr/week both + only swimming + none + only cardio = 420
160+80+5+5x = 420
x = 30

Bunuel

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IMO A
Let no of member who met mark for neither activity =x
Then no of member who met mark for swimming but not cardio =5x
Then as per Q, Total members = members not met mark + members in cardio-swimming+ members in swimming-cardio + members in both
420 = x+80+5x+160
or , x= 30 Ans

Bunuel

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Bunuel

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Members who meet the mark for swimming ONLY = S
Members who meet the mark for cardio ONLY = C
420 members = S + C + Both (S &C) + neither (S and C)
420 = S + 80 + 160 + neither
S + neither = 180

We have been given that for every member who met the amrk for neither- 5 met the mark only for swimming
thus S = 5*neither
Substitute,
6*neither = 180

neither = 30
Answer - (A)

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Easiest way would be to make a table:
swim no swim
Cardio 160 80 240
No cardio 5x x 6x
420
6x = 420 -240
x = 30
Answer A

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10 Jul 2026, 12:06

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Only Swimming + Only Cardio + Both + None = 420.
Let None be x.
Swimming will be 5x.

5x + 80 + 160 + x = 420
6x = 180
x = 30
Ans A IMO.

Bunuel

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My answer is a.) 30

Let member who did neither of the activities= x
Then, members who did only Swimming= 5x

Only Cardio + Only swimming + Both + Neither = 420
80 + 5x + 160 + x = 420
x = 30

Bunuel

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Using the overlapping method,
420=80+5X+160+X
180=6X
X=30, we need this as this is what is asked.
Hence A, is our answer.

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total - 420
both - 160
only cardio - 80
let neither be x
then only swimming - 5x

We need to solve for x
160 + 80 + x + 5x = 420
240 + 6x = 420
6x = 180
x = 30

Hence, A. 30 is the correct answer

Bunuel

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