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805+ (Hard)|   Overlapping Sets|   Word Problems|         
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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 00:14
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1 yes1 nototal
2 yesab
2 nocd
totalT

we need a+b+c+d = total

given= c+b+2d = 144

S-1

a= 60
not sufficient.

S-2
a= d
not sufficient.

S- 1& 2
a= d
a=d = 60

c+b = 24

60+24+60 = 144

T= 144

Choice C
Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


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Let, who use only interface 1= A ; use both= B ; use only interface 2= C ; use neither= N
T= A+B+C+N
Total number of not use responses = slow loading+ confusing navigation = 96+48=144
Total number of would not responses = A+C+2N=144
To find : Total number of users who tested the two interfaces.

1) B=60
T=A+60+C+N= A+C+2N+60-N = 144+60-N =204-N
It is not sufficient

2) N=B
T= A+C+2N=144
It is sufficient

B. Statement B alone is sufficient to answer the question.
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Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


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total users = both + neither + any 1 interface. would not use - both(0), neither(2), any 1(1). thus, 144 = 2N+I.
T = B + I + N.
from 1 --> T = B + I + N.... we don't know N so 1 alone is not sufficient.
from 2 --> T = N + I + N = 2N+I = 144. Therefore 2 alone is sufficient.Option B
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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 01:43
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B = users who would use both interfaces
I1 = users who would use only Interface 1
I2 = users who would use only Interface 2
N = users who would use neither interface

Given:
Slow loading = 96
Confusing navigation = 48

Total "would not use" responses = 96 + 48 = 144

Use both -- 0 "would not use" responses
Use only one -- 1 "would not use" response
Use neither -- 2 "would not use" responses

Therefore, I1 + I2 + 2N = 144

Total users T = B + I1 + I2 + N

Statement I: B = 60

We still do not know I1, I2, or N.

Not sufficient.

Statement II: N = B

Substitute into the total users equation:

T = B + I1 + I2 + N
----> I1 + I2 + 2N

From the given equation:

I1 + I2 + 2N = 144

Therefore, T = 144

Statement II alone is sufficient.

Answer: B
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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 02:34
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Users who won't use for both apps =
slow loading + confusing nav = 96 + 48 = 144

Question: total users tested both apps?

(1) 60 users said they would use both interfaces.

total users tested both apps = users who wont use both apps + users who use both apps - users who use either apps = 144 + 60 - x
It is insufficient since we don't know x.

(2) # of users who wont use neither the apps = # of users who would use both apps = y
x = users who would use either app

Total users: y + y - x = 2y - x = ?
So, it is Insufficient.

If combine (1)+(2)

144+60 - x =2y - x
2y=204
y=102
x=? still cannot calculated

So (1)+(2) is still insufficient. So, the answer is E.


Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


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The correct answer is C. Both statements together are sufficient.


Now lets look at what is given in the question.
96 complaints for slowing down.
48 complaints about confusing navigation
total= 144 complaints.

Here, for people who loved both the apps, 0 complaints
for someone who loved 1 app- 1 complaint
and for someone who hated both the apps- 2 complaints.

Evaluating statement 1
It says 60 people liked the apps, so 0 complaints.
We don't see any mention of the other people who hated 1 app and both apps.
Hence, the statement is not sufficient.

Evaluating statement 2
It states that people who hated both apps are equal to those who liked both apps.
We do not have any clear number here. Hence, it does not tell us the number of people.


When we combine both the statements.
1. People who hated both the apps= 60 = people who liked both apps.
2. 2 complaints*60= 120 complaints.
3. Remaining complaints = 144- 120= 24
4. 24 people hated 1 app.

Hence the total number of people= 60+60 +24= 144.

So, both the statements are needed to get the answer.
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N be total no. Of testers.
No. Of "would not use" responses = 96+48 = 144
No. Of "would use" responses = N + N - 144 = 2N - 144

x be no. Of users to use both interfaces
y be no. Of users to use exactly one interface
y be no. Of users to use none of them

So, x+y+z = N

Group x includes 2 "would use" responses 0 "would not use" response
Group y includes 1 "would use" response 1 "would not use" response
Group z includes 0 "would use" response 2 "would not use" responses

Hence, y+2z = 144
We need to find N = x+y+z

Given statement 1,
x = 60
N = 60 + 144 - z = 204-z
Hence, not sufficient

Given statement 2,
This gives z = x
N = x+y+z = y+2z = 144
Hence, sufficient alone.

Ans. B, Statement 2 alone is sufficient.
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Statement 2 alone is sufficient , but statement 1 alone is not sufficient

Sol
N= total numbers of users
N = 2n = use + not use

Not use = 96 +48 = 144
Use = 2N - 144

Now N = both + neither interface + exactly one
N = x +y +z

Use responses = 2x + z = 2n - 144
Not use = 2y+ z= 144


Subtracting both equations = x-y= N - 144

Statement 1 , x= 60

Y = N- 204

we cannot find the value of N neither Y so statement one is insufficient

Statement 2
y =x , Both interface = neither interface

y-y = N-144
N= 144
Statement 2 alone is sufficient
Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 03:53
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Interface -1 Interface-2
___________|______________ ________|___________________
|YES-1 _________NO|_______ |YES-2 _________NO|_________
| | | |
Confusion nav -1 Slow load -1 Confusion nav-2 slow load-2

Given confusion nav-1 + confusion nav -2 = 48 and slow load-1 + slow load-2 = 96.
Hence inorder to find out the total users we need to find out the no. of people who said YES to the interfaces( Yes-1+Yes-2) and then divide the total sum ( Yes + confus nav+slow load) of both interfaces by 2.

Statement-1 : 60 users said yes to both. But this doesn't give Yes-1+ Yes-2 infor. This only gives Yes-1 intersection Yes-2.
Hence statement-1 alone not sufficient.

Statement-2: no. of users who said neither = no. of users who said both.
We will not get total YES people from this. Hence 2 alone not sufficient.

Using both.
No. of users who said neither= no. of users who said both= 60.

We know that total no. of users who said no are 48+96 = 144.
Of these 60 people said No twice. Hence need to remove them once.
Hence total no. of people who said No = 144 - 60 = 84.( this is the sum of no. of people who said no to I Only nterface-1 + Only Interface-2 + Both)

We know that no. of people who said no to both = 60. Hence no. of people who said no to only either of them is 84-60 = 24.

Hence these 24 people said No to one of the interfaces and said Yes to the other.

Now total no. of responses = No. of people who said (Yes to only I1+ Yes to only I2)+Yes to both + (No to only I1 + No to Only I2)+ No to both = (24)+60+24+(60) = 168.

Hence both statements together are sufficient.

Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


This question was provided by GMAT Club
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answer is b-only statement 2 works. lets take a=doesnt use b=uses only 1 and c =uses 2 features so b+2c=144. statement 1 -gives many values so insufficient but statement 2 gives c=a so b=144-2a so neither=2a+(144-2a)=144 which gives us unique value hence b is sufficent
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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 04:07
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not use
96 sL = a
48 cn =b
calculate
n(a u b) = n(A) + n (b) - n (a inter b)
stmt 1
only have 60 users use both , no not use data

smt2


no of user using neither = no of users using both , quantity not given

stmt 1 +2

96+ 48 - 60 = 74 not using 1 of app interfaces

total users tested= non users + users (for both )

= 134 + 60 = 194
option C
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The answer is B because each user gives two answer(one per interface). “No” answers total 96+48=144.
Let a= would use both(0 no’s), b= exactly one(1 no), c= neither(2 no’s).
No’s: b+2c=144
Users: n=a+b+c
(1) a=60=> still don’t know b, c. Insufficient
(2) c=a=>b=144-2a, so n=a+(144-2a)+a=144. The a’s cancel. Sufficient


Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


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UseNot useNot useTotal
SlowConfusing
I1
I2
Total9648

.: Total number of people chose not use= 96+48=144

Considering, Statement 1 alone,
total both use=60
.: Total people tested=60+144
.: Statement 1 alone is sufficient.
.: we can eliminate option B,C & E. left with A & D.

Considering statement 2 alone.
We do not know how many people chose neither of the interfaces. We know the total no of people who chose 'would not use' for either of them & both of them.
.: statement 2 is insufficient.

.: A is the correct choice.
Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 05:24
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lets use variables ABCD
A=use both
B= only interface 1
C=only interface 2
D= neither

Remember, D will hold twice the count, B and C only 1 count, A will hold 0.
Count of what? of the # of would not responses

Total =A+B+C+D
=B+C+2D=96+48=144

This much we have been given

Statement 1
A=60
But this doesnt help us with B+C+2D=144
So not sufficient

Statement 2
A=D
We have Total=B+C+2D
But hey earlier we saw B+C+2D=144
Thuse total =144
Sufficient

IMO B
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So lets say we have n users. n = ?
We have n users using 2 apps and giving feedback => 2n feedback (will use or not use with a reason)

2n = satisfied + not satisfied

Given => not satisfied = 96 + 48

S1 => 60 satisfied with both => satisfied count subset is 120
But we still don't know about the rest they would have like one and not liked another so insufficient

S2 => use both count = not use both
But we just know the count of non satisfied feedbacks => if we somehow knew people satisfied or unsatisfied with both apps count we could determine n. But we don't know that so insufficient

S1 + S2 combine => This gives us the info we need

120 satisfied feedbacks + (96+48) non satisfied feedback (in this 120 feedbacks are from the same person - who are not satisfied by both)

n = 60 + 60 + (96+48-120) (The last term is the count of people unsatisfied with one of the app)

Ans C - Both statements together are sufficient
Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


This question was provided by GMAT Club
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Use both - 60
Don't use both - 60 (120 reasons)

Given reasons - 96+48=144

Pending reasons = 144-120 = 24

So 24 would not use one of it.

So total 144 people, we can answer with both the statements combined
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Each person has 2 unique responses. If neither, either of the two gets selected but overall 2 NO response noted. For only 1, only 1 NO response was noted.

Reqd Total= both yes+ only 1 yes+ neither

only 1 + 2*neither=96+48

Total=both yes+96+48-neither

1. Total=60+96+48-neither.....NOT SUFFICIENT
2. neither=both
Total=both+96+48-both=96+48...SUFFICIENT

Ans B
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x = number of users who would use both interfaces
y = number of users who would use only one interface
z = number of users who would use neither interface

users = x + y + z ?

"would not use" responses means:
+ each user in x group contributes with 0 responses
+ each user in y group contributes with 1 responses
+ each user in z group contributes with 2 responses

y + 2z = 96 + 48 = 144 -> y = 144 - 2z

users = x + 144 - 2z + z = x - z + 144

(1)
x = 60

users = 60 - z + 144 = 204 - z

It depends on the unknown z.

Insufficient

(2)
x = z

users = z - z + 144 = 144

Sufficient

IMO B
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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 06:31
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In the given question it is mentioned that the software company has launched 2 new app interfaces. After testing the interfaces the users were given an option to continue using the interface or not to continue by giving a reason for the same.

All the users who opted for not to continue using the interface gave 2 responses - either " Confusing navigation" - 48 Times or "slow loading" - 96 Times = 144 times

We are asked how many total users tested the 2 interfaces.

So the total users who tested the interfaces = Total users who continued using both the interface + Total who continued using first interface + Total who continued using second interface + those who used none of the interface
= x + y + z + a

So basis this we also have 1 more equation = y+z+2a = 144 ( since the count of total users who rejected for both will be 2)

Statement 1 - 60 users said they would use both the interfaces - So we have value of x - but we don't have value of a and to arrive at total we need a - hence this statement is not sufficient

Statement 2 - The number of users who said that they would use neither interface was equal to the number of users who said they would use both interface
Over here = we have an equation which will help us find the total value as under:
x = a
So x+ y + z + a = x + 144- 2x + x = 144
Accordingly, this statement is sufficient. Hence answer is option B
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GMAT Club World Cup 2026 (Day 5): A software company asked a group of 11 Jul 2026, 06:32
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Bunuel
A software company asked a group of users to test two new app interfaces. Each user tested both interfaces and, for each interface, said whether he or she would use that interface. If a user said that he or she would not use an interface, the user selected exactly one of two reasons: confusing navigation or slow loading. Across all such “would not use” responses, slow loading was selected as the reason 96 times, and confusing navigation was selected as the reason 48 times. How many users tested the two interfaces?

(1) 60 users said that they would use both interfaces.
(2) The number of users who said that they would use neither interface was equal to the number of users who said that they would use both interfaces.

 


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Assume users who voted for both = B
users who voted for only one = O
user who voted for neither = N

Question : B + O + N

Given
O + 2N = 144

1) B = 60

O = 144 - 2N

As N is not known, the statement alone is not sufficient.

2) B = N

B + O + N = N + O + N = 2N + O

This value is given to us.

2N + O = 144

Sufficient

Option B
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