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GMAT Club World Cup 2026 (Day 7): A weekend training program had 75

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Bunuel

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Bunuel

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GMAT Club Official Solution:

A weekend training program had 75 participants, each assigned to exactly one of two tracks: the morning track or the afternoon track, with at least one participant assigned to each track. If 30 of the 75 participants registered for the data-visualization session, what percentage of the afternoon-track participants did not register for the data-visualization session?

Of the 75 participants, 30 registered for the data-visualization session, so the overall fraction who registered was:

30/75 = 2/5

The question asks what percentage of the afternoon-track participants did not register.

(1) Of the morning-track participants, 2/5 registered for the data-visualization session.

The overall fraction who registered was 2/5. (1) says that the fraction of morning-track participants who registered was also 2/5.

Since the overall fraction is a weighted average of the morning-track fraction and the afternoon-track fraction, the afternoon-track fraction who registered must also be 2/5. So the fraction of afternoon-track participants who did not register was:

1 - 2/5 = 3/5

Sufficient.

(2) Among the afternoon-track participants, the number who registered for the data-visualization session was 2/3 of the number who did not register for it.

So among afternoon-track participants:

registered : did not register = 2 : 3

Therefore, the fraction who did not register was:

3/(2 + 3) = 3/5

Sufficient.

Answer: D.

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A weekend training program had 75 participants, each assigned to exactly one of two tracks: the morning track or the afternoon track, with at least one participant assigned to each track. If 30 of the 75 participants registered for the data-visualization session, what percentage of the afternoon-track participants did not register for the data-visualization session?

(1) Of the morning-track participants, 2/5 registered for the data-visualization session.
(2) Among the afternoon-track participants, the number who registered for the data-visualization session was 2/3 of the number who did not register for it.

plot is 2x2 matrix
--------MT---AT----
DV--- ---- -- ---- 30
NDV-- --- N ----- 45
total--- ---- ------ 75

determine value of N
#1

let MT be x
2x/5 have registered for DV
3x/5 have not registered for DV
AT with DV is 30- 2x/5
AT with NDV is 45-3x/5
AT = 75-x
45-3x/5 / 75-x = 60 %
sufficient statement 1

#2
if A NDV is x then A DV is 2x/3
total A participants 5x/ 3
ratio will be
x/ 5/ 3x = 3/5 = 60%
sufficient statement 2

OPTION D is correct

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Answer: D) each statement alone is sufficient

We're looking for aND/a (afternoon No Data divided by afternoon)

Let's set up a matrix
Morning Afternoon. Total
Data course 2m/5 2x/3 30
No Data course 3m/5 x 45
Total m 5x/3 75

From statement (1):
(45 - 3m/5) / (75 - m) = aND/a ->after factoring 3/5 out of the numerator, (75 - m) cancels out and gives us an answer

From statement (2)
If x = the number of people who didn't register for the data course in the afternoon
x/(5x/3) = 3/5 -> the x cancels out and we have an answer

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Total participants = 75

Registered for DV = 30

(30/75)* 100% = 40%

We have to find % of afternoon trackers who didnt register for DV.

Statement 1 = 2/5 of morning registered for DV (2/5) *100% = 40%, Total DV registration = 40%, Morning DV registration 40% so afternoon also has to be 40%, so % of ones who didnt register in afternoon = 100-40 = 60%. SUFFICIENT

Statement 2 = During Afternoon track, DV reg # = 2/5 of non DV

DV = 2/3 NON DV = DV / NON DV = 3/2, Total = 5, % = (3/5)*100% = 60%.

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Total = 75
Registered for data = 30 , Did not Register for data = 45
Ask: No data participant percentage in the afternoon track

S1
Let M be morning track participants
M (Data) = 2M/5 , Therefore, M (No Data) = 3M/5
A (Data) = 30-(2M/5)
A (No Data) = 45-(3M/5)

Total A
[30-(2M/5)]+[45-(3M/5)]=75-M
Since we are able to extract all our values, Sufficient.

S2
A (Data) = 2NA/5
Thus, Total A = NA + (2NA/5) = 5NA/3
Since we are able to extract all our values, Sufficient.

D - Each statement alone is sufficient

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let MT participants be x
AT = 75 - x

Given 30 or 75 are DV

S1 - 2/3x = DV from MT
meaning 3/5x = are non DV
and say "a" percent of DV are from AT
meaning
2/3x + a (75-x) = 30, we are still let with 2 variables, so insufficient

S2 - 2/3 (75-x) = DV from AT meaning 1/3 (75-x) are non DV from AT

so it is 1/3 of AT = 33.33 percent of AT, which is being asked here, so SII is sufficient

Ans - B

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Total Participants = 75
Given that register for Data Session = 30/75

Statement 1:
Let morning Track have x participants then a/q to statement 1, 2x/5 morning track partcipants have registered for Data session.

Statement 2:
Afternoon track will have 75-x participants, Now a/q to statement 2, 2(75-x)/3 afternoon track particpants have registered for Data Session.

We can see that Both Statements alone can not give the required. But if we use both statements we can find x, Thus we can find the percentage of afternoon people who have not registered for data session that is {(75-x)/3}*100 /75.

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How many afternoon didn't register for Data visualization?
It is mentioned that participant =2/3*non participant
participants +non participants= total afternoon
(1+2/3)*non participants=total afternoon
non participants= 3/5*total afternoon attendees
Statement 2 alone is sufficient.
Statement 1 is not able to answer anything about afternoon participation.

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	Data-visualization	~Data-visualization	Total
Morning track			>0
Afternoon track			>0
Total	30	45	75

(1) Of the morning-track participants, 2/5 registered for the data-visualization session.

	Data Visualization	~Data-visualization	Total
Morning track	2x/5	3x/5	x
Afternoon track	30-2x/5	45 - 3x/5 = 3(75-x)/5	75-x
Total	30	45	75

The percentage of afternoon-track participants who did not register for data-visualization session = = (45-3x/5)/(75-x) *100% = 60%
SUFFICIENT

(2) Among the afternoon-track participants, the number who registered for the data-visualization session was 2/3 of the number who did not register for it.

	Data-visualization	~Data-visualization	Total
Morning track
Afternoon track	2y/3 = 2x/5	y = 3x/5	x
Total	30	45	75

2y/3 + y = x
5y/3 = x
y = 3x/5

The percentage of afternoon track participants who did not register for data visualization session = (3x/5)/x *100% = 60%

SUFFICIENT

IMO D

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IMO B
Each participant is aasigned exactly 1 track & no track is with 0 participant
Let Morning(M) track = x participant
Afternoon track(A) = 75-x
Data vis session registered = 30
Data not registered = 75-30=45
Required %= (n/75-x)*100 where n is the no of participant in A track did not register in D session

ST 1=2x/5 registered of M registered in D session, A registered = 30-2x/5, A not registered = 75-x-(30-2x/5) =45-x+2x/5 =45-3x/5
we dont know x, insufficient
ST2 = 75-x -n= 2n/3 or, 75-x=5n/3
So, Req % = n/(5n/3) *100 = 300/5 = 60% Sufficient
Hence B
Hope this helps!

Bunuel

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Total part=75
total reg=30
total not reg=45

we want-afternoon not reg/afternoon total

stat1 2m/5 can't spilt into afternoon

stat2 afternoon: registered :not =2:3
afternoon not/afternoon total=3/5=60% suff

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i am going with option d
A - 2/5 morning track registered.
m+a=75, m(reg)+a(reg) = 30, substituting statement 1 forces afternoon track to be 40%, 60% didn't register.
B - 2/3 of afternoon non registered
ratio of non registered to total afternoon track - 3/5, 60%.

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IMO, B alone is sufficient.

Given that, total 75 people are there, out of which 30 registered for data-visualization process.
So, 45 people did not register for the process.

We have to find the percentage of people assigned in afternoon track, who did not participate in the data-visualization process.

Statement - 1:
Let "X" be the people who were assigned morning track.
And since, 2/5(X) people participated in the session, 3/5(X) of morning-track did not.

3/5(X) + People of afternoon track who did not participate = 45

But we do not know what is "X". So, we can't find anything from above.
Thus, this statement alone is insufficient.

Statement - 2:
Let "Y" be the people who were assigned afternoon track.
And given that people who registered for the session (Let R) = 2/3 of the people who did not register (Let NR)

And, we know that R + NR = Y
So, R = Y - NR
That is, 2/3(NR) = Y - NR
NR = 3/5(Y) = 60%
So, this is sufficient.

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A weekend training program had 75 participants, each assigned to exactly one of two tracks: the morning track or the afternoon track, with at least one participant assigned to each track. If 30 of the 75 participants registered for the data-visualization session, what percentage of the afternoon-track participants did not register for the data-visualization session?
Let, morning registered= a and morning not registered= b
Afternoon registered= c and afternoon not registered= d
e= Total morning = a+b
f= Total afternoon= c+d
Total morning+Total afternoon= 75
a+b+c+d= 75
a+c=30 and b+d=45

(1) Of the morning-track participants, 2/5 registered for the data-visualization session.
a= 2/5 e
a=30-c and e=75-f
(30-c)=(2/5)(75-f)
c=2/5 f
d= f-c = f-2/5 f = 3/5 f
Percentage= d/f= (3/5)100= 60%
Sufficient
(2) Among the afternoon-track participants, the number who registered for the data-visualization session was 2/3 of the number who did not register for it.
c=2/3 d
f=c+d =(2/3)d+d
f=5/3 d
Percentage= d/f = (3/5)100= 60%
Sufficient

D

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Let M = Morning participants and A = Afternoon participants

Then M + A = 75 and total registered = 30

We are looking for the % of participants who did not register.

S1 -> Morning registrations = 2M/5, so:
Afternoon registrations = 30 - 2M/5
Afternoon non-registrants = (75-M) - ((30- (2M/5)) = 45 - 3M/5

% of afternoon non-registrants: ((45 - (3M/5))/(75 - M) = 3/5 = 60%
The variable M cancels out, so the answer is fixed.

S1 - Sufficient

S2 -> Among afternoon participants, the ratio of registered : not registered = 2 : 3

So, the % of not registeres is: 3 / (2+3) = 3/5 = 60%

S2 - Sufficient

Answer: (D) - Each statement alone is sufficient.

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Registered R =30
Not Registered R'=45
Afternoon Not Registered=??

1. Morning =x
Morning Registered = 2x/5
No afternoon info..NOT SUFFICIENT

2.Afternoon not registered =y
Afternoon registration=2y/3
total afternoon=y+2y/3 = 5y/3

%=3y/5y=60...SUFFICIENT

Ans B

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There are total 75 participants and out of which total 30 participants have registered for the data-visualization session.

Question asked is : what % of the afternoon-track participants did not register for the data visualization session ?

Thinking : We need to understand How many of the participants are there in afternoon session and how many of them have registered and how many of them have not registered. If we don't have exact values then also fine we need just relative proportion.

In afternoon-track : registered + Not registered = Ra+Na = ?
In morning track : registered + Not registered = Rm+Nm = ?

We need to find Na/(Ra+Na)

Statement 1 : Rm/Nm = (2/5)/(1-2/5) = 2/3. No data available which can link this value to afternoon participants. Not sufficient alone.

Statement 2 : Ra/Na = 2/3 i.e. Na/Ra = 3/2 Then Na/(Ra+Na) = 3/5 = Required percentage. Statement 2 alone is sufficient.

Bunuel

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This is a overlapping sets problem. I used the 2x2 matrix method. Info given in the stem is:
75 participants each took exactly Morning or Afternoon batches.
30 participants took the Data Visualization course (DV). THus the 2x2 matrix can be formed as follows

	Morning	Afternoon	Total
Data Visualization	a	x	30
No Data Visualization	b	y	45
Total	c	z	75

I assigned the variables a, b, c, x, y and z to all information unknown so far. What we want to find is the (y/z)*100

Let's get into the statements:
Statement 1: Of the morning participants, 2/5 took data visualization
This translates to
a = (2/5)*c OR c = (5/2)*a_____(1)

Now since we need y/z, let's see if we can get any relation/ratios in x/z, x/y or y/z

Now we also know
c+z = 75_______(2)

From (1)
c = (5/2)*a
But a = 30-x
Thus, c = (30-x)*5/2

Thus (2) can be expressed as (30-x)*5/2 + z = 75
Simplifying this, we get,
150- 5x + 2z = 150
Or 2z = 5x OR x = (2/5)*z______(3)

We also know that x+y = z_______(4)
Thus, from (3) and (4),
we get y = (3/5)*z
or y/z = 3/5

Thus, we can find the percentage. Hence this statement is enough. We can eliminate (B), (C) and (E)

Statement 2: Among the afternoon participants, the number who registered for data vsualization was 2/3 of the number who did not register for it.
This translates to:
x = (2/3)y

We know that x+y = z
Thus,
(2/3)y + y = z
Thus, (5/3)*y = z
Thus, y/z = 3/5
Hence, we can calculate the percentage. Thus this statement is also sufficient.

We can go for choice (D)

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14 Jul 2026, 10:45

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We are asked for Afternoon non workshop divided by Afternoon total %age
A alone does not give anything
B alone is really simple and gives direct ratio of what`s needed
So B

Bunuel

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