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a: number of users who said yes to both
b: number of users who said no to both
c: number of users who said yes to first & no to second
d: number of users who said no to first & yes to second
total users: n = a+b+c+d?

given: total no responses = 96+48=144
2b+c+d = 144

I) a = 60
n = 60+b+c+d
cannot substitute for b+c+d hence insufficient.

II) b = a
n = b+b+c+d = 2b+c+d
we know this is equal to 144 hence n = 144 sufficient
answer B
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We have no. of users who would not use any interface i.e., (no of users with Slow loading reason)+(no of users with confusing navigation reason) since the user has to select whether he or she will use it or not, and on selecting "Will not use", he or she has to select exactly one reason, so no overlapping of no of users. Now adding those nos will give us a figure for users who will not use. So, to calculate the Total no. of users, we need the no. of users who will use the interface. Evaluation of both statements given below;
Statement -1 - This directly gives the no of users who would use both interfaces ( It means they will use the interface) without depending on other statements
Statement -2 - This also gives the number of Use interface = No of user not use the interface without depending on others.
So both statements alone 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.

 


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The question says the responses mentioning Slow loading as the rejection reason are 96 and those mentioning navigation as rejection reason are 48. So it is telling us the number of responses that mentioned No to either of the interfaces because of whatever reason as 96+48=144. In terms of the attached screenshot, the question is telling us the value of A+2C+D = 144.

Question is asking the value of A+B+C+D

St1: This tells us the value of B=60. I know A+2C+D = 144. I cannot derive A+B+C+D from this. INSUFFICIENT

St2: This tells us B=C. Thus the asked datapoint becomes A+B+C+D = A+C+C+D = A+2C+D and question has already told us the value of this as 144. Hence SUFFICIENT.

Final answer is B.
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Let :
B = users who would use both interfaces
O = users who would use exactly one interface
N = users who would use neither interface

Each "would not use" response contributes one reason
A user is O contributes 1 response
A user in N contributes 2 responses

Since there were 96+48 = 144 "would not use" responses, O + 2N = 144

We need the total no. of users: B + O + N

1) B = 60
Total = 60 + O +N, but O+2N = 144 has multiple solutions
Insufficient

2) N=B
Total = B + O + N => O+2N => 144
Sufficient

Ans : B
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IMO C

As per Q stem, every user tested 2 interface
Possiblity: User likes both, User likes either one, User hates both
For hate: user gives exactly 1 feedback for each interface
Total responses for not liking = 96+48, but we dont know which user gave 1 feedback (if he/she likes either one) or 2 feedback(if he/she dislikes both)

Statement 1: Both like = 60, but how many users dislike both? Not sufficient
Statement 2: Users liking both = Users disliking both = x, insufficient

Combining 1 & 2: X=60, so, users disliking both gave 60*2 =120 response, remaning = 96+48-120=24 resposne from user liking either one
Hence total users = 24+60+60, hence sufficient!
Hope this helps!
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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So take
x = users would use both
y = exactly one use
z = neither interface use

There are total of 96+48 = 144 total would NOT user responses

A user in y would give one not use response whereas a user in z would give 2 responses. So total not use
144 = y +2z

Total users is T = x + y +z
y = 144-2z
rearrage and you get T = 144+x-z

Option 1: x = 60, we then get T = 204- z,
nt sufficient

Option 2: x=z
T = 144+x-z = 144
total determined so statement 2 alone is sufficient
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My answer is C.) Both statements together are sufficient. But correct ans. is B)

There can be 4 type of users-
Interface1 Interface 2
Yes (A)Yes
Yes (B)No
No (B)Yes
No (C)No

We know total No = 96+48 = 144
A+B+C=Total
B+2C=144

1) Users who say yes to both= 60 (type 1).
60+B+C= Total- two missing variables
Still we don't know about other 3 types of users- INSUFFICIENT

2) Type 1 users = type 4 users , nothing about number of users- INSUFFICIENT.

Type 1 + Type 4 = A+C = 2C
A+B+C= B+2C=144
(B= who said NO to one and YES to another hence contributing to 1 NO each user)
Total users= 144 - 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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B is the correct answer because, in case of A, we get T=b+o+n, where T is total, B is both, O means one, and n means neither. Once you plug in numbers, you get 204-N=T. Notice, that we dont know N hence T is not determined. Now moving to second, use O+2B=144, T=B+(144-2B) +B=144. Hence we get a unique number. I feel this question is not in the syllabus.
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given:- total 144 users provided NO for 1, 2 or both the interfaces.

Statement 1: total = 60 + 144 - no. of users said no to both interface
not sufficient

Statement 2: Number of users said No to both interface= 60
Not sufficient

Statement 1& 2 together: total = 60 + 60 + (144-2*60)= 144 users

hence Both are sufficient together.
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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for the GMAT World Cup Competition

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Let A = users who would use both interfaces
B = users who would use only A
C = users who would use only B
D = users who would use neither

Total Users --> N = A + B + C +D

Since there are 96+48 = 144 "would not use" responses:
B + C + 2D = 144

We need to find N

S1 -> A = 60 - Insufficent

-------------
S2 -> D = A

Then -> B + C = 144 - 2D
-> B + C = 144 - 2A

N = A + B + C + D
N = A + 144 - 2A + A
N = 144

--> S2 is sufficient

Answer B
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Both uses interface = B; exactly one uses interface = O; and neither uses interface = N
Total users = B + O + N (We have to find out this)
Since 2 types of users would not use,
O + 2N = 48 + 96
O + 2N = 144

S1: Both uses interface, B = 60
T = 60 + O + N
Lets test for O and N
If N = 0, then O = 144, so T = 60+144+0 = 204
If N = 20, then 0 = 104, so T = 60+104+20 = 184
Different totals are possible. Not Sufficient.

S2: B = N
Now, T = B + O + N; T = 2B + O or, 2N + O; T = 144. Sufficient

Answer (B) Statement 2 is alone sufficient.
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The company is testing 2 products, A and B.

That means there are 4 cases,
1. Likes both A and B.
2. Likes A, not B.
3. Likes B, not A.
4. Dislikes both A and B.

We're interested in how many people tested this product. So, the total number of people, 96 + 48 = 144, who provided feedback means they dislike either
1. ONLY A
2. ONLY B
3. Both A and B

Which overcounts the case when they dislike both. We'll need to subtract this group later.

Now, consider each piece of information.
1. 60 people would use both; that means we're given people who like both A and B.
But we still don't know how many of them dislike both. -> INSUFFICIENT

2. There are 60 people who dislike both.
This alone is INSUFFICIENT as well, because we don't know how many of them like both.

But, taken together, our picture is complete.
Like both + Like A not B + Like B not A + Dislike both = 60 + 144 - 60 = 144. So, choice C.
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The information provided tells us that there were 96 would not use responses categorized as slow and 48 that were confusing giving us 144 would not use responses.

We need to find how many people tested the interfaces which I found easiest to seperate into the categories of people who use both(B), people who would onle use One(O) and people who would use neither.

Those who gave would not use responses would either use neither or one, so I got the formula

2N +O =144, I used 2*N because each person that would use neither would submit 2 would not use responses, one for each interface.

Total responses = B + N + O

Statement 1 gives us that B = 60 but doesn't tell us about N or O which leaves us two unknowns in the first equation ( N and O) and three in the second ( N, O, and Total responses) So we cannot use a system of equations. This is not sufficient

Statement two tells us N = B, but we still don't know the actual values, so the statement is not sufficient on it's own.

Together knowing B =60 and B = N, we can plug this information into our equations.

2(60) + O = 144 -> O =24

Total responses = 60 + 60 + 24 = 144.

Statements are sufficient together so the answer is C.
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B

Total would not use responses = 96 + 48 = 144. Sort users by how many interfaces the would decline, 0, 1, or 2. Users declining exactly one give 1 response each, users declining both give 2 each, so decline one + 2 decline both = 144

Total users = (decline non) + (decline one) + (decline both)

1 - decline none = 60, still leaves (decline one) + 2(decline both) = 144

2 - decline both = (decline none) = b. Then users = b + decline one + b = decline one + 2b which is users = 144 - This works
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This question could be solved by using a flow diagram of the given information.
Key points to note: 2 interfaces ( Int1, Int2), 2 choice (Use, Not use) and 2 choices out of which exactly one is chosen(that means no overlap) for not use case(Confusing Navigation and Slow Loading)

Now fill the information given:

Int1:
- use = Suppose 'u1'
- not use = Slow loading (suppose 's1')
- not use = Confusing Nav (suppose 'cn1')

Int2:
-use = suppose 'u2'
-not use = slow loading (suppose 's2')
- not use = Confusing Nav (suppose 'cn2')

Statement 1: We have been given, value of (u1 + u2) = 60
Since in the 2 Set Venn diagram the only the intersection of both(u1 and u2) is given that is 60, and no information on only u1 and only u2 is given then we cannot infer the exact value. Those who have chosen interface 1 may choose or not choose the interface 2 - chances of overlap are there.

Statement 2: We have been given that, Number of users said they would use both interfaces = number of users said that they would use neither interface

The value for the number of users with use for neither interfaces would be: s1 + cn1 + s2 + cn2
where value of (s1 + s2) = 96 and value of (cn1 + cn2) = 48
This would give use the total number of users with neither would be used = 96 + 48 = 144

And the other remaining part which is the number of people who would use both is equal given to the above number = 144
Hence sufficient

So answer would be B
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Let Both=B, neither= N, only one =X

X+2N=144
total users =T=B+X+N

(1)B=60

T=60+(144-2N)+N=204-N not suff

(2) N=B

T=B+(144-2B)+B=144

unique value, sufficient

ans is b
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Let,
B = user who use both interface
N = user who use neither interface (2 "would not use " response)
O = user who use exactly one interface (One "would not use" response).
T = total no of users = B + O + N

Given,
Total would not use" response ,
96 + 48 = 144

We get,
O + 2 N = 144


Statement 1: B = 60

144 = 60 + O + N (No unique pair, two variable)


Not sufficient

Statement 2,

N = B

So, T = B + O + B = O + 2B

(using O+2N = 144 & N=B)

O+2B = 144
T = 144

Suficient.

Answer: B (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.

 


This question was provided by GMAT Club
for the GMAT World Cup Competition

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