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04 Apr 2025, 00:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:14) correct
32%
(01:51)
wrong
based on 216
sessions
History
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Time
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Not Attempted Yet
A team is composed of exactly 4 executives and 3 associates. How many such teams can be formed?
(1) If two fewer executives were available for selection there would be an equal number of executives and associates available for selection.
(2) If two more associates were available for selection exactly 10 different teams of 3 associates could be selected.
(1) If two fewer executives were available for selection there would be an equal number of executives and associates available for selection.
(2) If two more associates were available for selection exactly 10 different teams of 3 associates could be selected.
04 Apr 2025, 03:54
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Bunuel
Question: How many teams of 4 executives and 3 associates can be formed?
We need total executives and associates to answer this question
Statement 1: Executives = Associates + 2
NOT SUFFICIENT
Statement 2: (a+2)C3 = 10
But 5C3 = 10
i.e. a+2 = 5
i.e. a = 3
But we don't know about the number of executives hence
NOT SUFFICIENT
Combining the statements
a = 3 and E = 5
total Teams = 5C4*3C3 = 5
SUFFICIENT
Answer: Option C
Related (Official Question) Video:
04 Apr 2025, 04:39
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Team needs exactly 4 executives and 3 associates
To find the number of teams that can be formed, we need the number of executives and associates
Statement 2
nC3 = 10
n!/(n-3)!*3! = 10
n(n-1)(n-2) = 60 = 5*4*3
n = 5
This means number of associates, A is 5-2 = 3
But we don't the number of executives
Insufficient
Eliminates B,D
Statement 1
E-2 = A
But we don't know the value of E or A
Insufficient
Eliminates A
Combined
A = 3
E-2 = 3 => 5
We can now calculate the number of teams using 5C4 *3C3
Suffcient
Answer C
To find the number of teams that can be formed, we need the number of executives and associates
Statement 2
nC3 = 10
n!/(n-3)!*3! = 10
n(n-1)(n-2) = 60 = 5*4*3
n = 5
This means number of associates, A is 5-2 = 3
But we don't the number of executives
Insufficient
Eliminates B,D
Statement 1
E-2 = A
But we don't know the value of E or A
Insufficient
Eliminates A
Combined
A = 3
E-2 = 3 => 5
We can now calculate the number of teams using 5C4 *3C3
Suffcient
Answer C
Bunuel
