q: There are 3 teams each with 4 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?
Options:
(A) 50
(B) 23
(C) 48
(D) 28
(E) 45
a: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 16 possibilities (4*4) since each team has 4 players. So there are a total of 48 possibilities (16*3). I hope this method is easier for you to understand. The answer is (C).
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q: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 5 businessmen, how many possible team submissions are possible?
Options:
(A) 74
(B) 100
(C) 162
(D) 198
(E) 202
a: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 5C2 = 40
2) 2 tech1 businessman: 4C2 x 5C1 = 30
3) 3 tech0 businessmen: 4C3 = 4
Total: 144+54+4 = 74 The answer is (A).
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q: SHOW TIMER STATISTICS
To apply for the position of photographer at a local magazine, Veronica needs to include three or four of her pictures in an envelope accompanying her application. If she has pre-selected five photos representative of her work, how many choices does she have to provide the photos for the magazine?
Options:
(A) 5
(B) 10
(C) 12
(D) 15
(E) 50
a: Veronica can choose 3 photos in 5C3 = 10 ways
She can choose 4 photos in 5C4 = 5 ways
Total number of ways = 10 + 5 = 15 The answer is (D).
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q: You have found a mutant algae that doubles in size every hour. It takes 18 hours for one algae plant to take up half of a certain lake.
How long would it take for two of these plants to take up half of the same lake?
Options:
(A) 7
(B) 17
(C) 27
(D) 37
(E) 47
a:
At 17 hours the one plant will take up 1/4 of the lake (1/2 of 1/2). At 17 hours the two plants would be double the size of the one plant and double 1/4 is one half. The answer is (B).
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