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07 Aug 2026, 10:16
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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.
(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.
07 Aug 2026, 10:16
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Official Solution:
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?
Across all “would not use” responses, the two reasons were selected a total of:
\(96 + 48 = 144\) times
So there were 144 total “would not use” responses.
Now divide the users into three non-overlapping groups:
• \(B\) = users who would use both interfaces
• \(O\) = users who would use exactly one interface
• \(N\) = users who would use neither interface
Each user who would use both interfaces gives 0 “would not use” responses, because that user would use each of the two interfaces.
Each user who would use exactly one interface gives 1 “would not use” response, because that user would use one interface and would not use the other.
Each user who would use neither interface gives 2 “would not use” responses, because that user would not use either of the two interfaces.
Therefore:
\(O + 2N = 144\)
The question asks for:
\(B + O + N\)
(1) 60 users said that they would use both interfaces.
So \(B = 60\).
But \(O\) and \(N\) are still not fixed.
For example, if \(N = 0\), then \(O = 144\), so the total number of users is:
\(60 + 144 + 0 = 204\)
But if \(N = 40\), then \(O = 64\), so the total number of users is:
\(60 + 64 + 40 = 164\)
Not sufficient.
(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.
So \(N = B\).
The total number of users is:
\(B + O + N\)
Since \(B = N\), this becomes:
\(N + O + N = O + 2N\)
But from the given information:
\(O + 2N = 144\)
So the total number of users is 144.
Sufficient.
Answer: B
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?
Across all “would not use” responses, the two reasons were selected a total of:
\(96 + 48 = 144\) times
So there were 144 total “would not use” responses.
Now divide the users into three non-overlapping groups:
• \(B\) = users who would use both interfaces
• \(O\) = users who would use exactly one interface
• \(N\) = users who would use neither interface
Each user who would use both interfaces gives 0 “would not use” responses, because that user would use each of the two interfaces.
Each user who would use exactly one interface gives 1 “would not use” response, because that user would use one interface and would not use the other.
Each user who would use neither interface gives 2 “would not use” responses, because that user would not use either of the two interfaces.
Therefore:
\(O + 2N = 144\)
The question asks for:
\(B + O + N\)
(1) 60 users said that they would use both interfaces.
So \(B = 60\).
But \(O\) and \(N\) are still not fixed.
For example, if \(N = 0\), then \(O = 144\), so the total number of users is:
\(60 + 144 + 0 = 204\)
But if \(N = 40\), then \(O = 64\), so the total number of users is:
\(60 + 64 + 40 = 164\)
Not sufficient.
(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.
So \(N = B\).
The total number of users is:
\(B + O + N\)
Since \(B = N\), this becomes:
\(N + O + N = O + 2N\)
But from the given information:
\(O + 2N = 144\)
So the total number of users is 144.
Sufficient.
Answer: B
