q: Right triangle ABC is the base of the prism in the figure above. If AB=AC=√2 and the height of the prism is 3, what is the volume of the prism?
Options:
(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 6
a: Stream of consciousness: Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3 The answer is (D).


question: In how many different ways could couples be picked from 8 men and 5 women?
Options:
(A) 8
(B) 5
(C) 13
(D) 40
(E) 20
answer: Stream of consciousness: Number of mens = 8
Number of womens = 5
Different ways could couples be picked = 8c1 * 5c1 = 8 * 5 = 40 ways The answer is (D).


q: An design manager has 10patterns of chairs & 7patterns of tables. In how many ways can he make a pair of table & chair?
Options:
(A) 70
(B) 40
(C) 80
(D) 90
(E) 100
a: Stream of consciousness: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 7 ways
Hence one chair and one table can be arranged in 10 x 7 ways = 70 ways The answer is (A).


question: In a bucket there are 3 blue balls and 2 red balls. What is the probability of drawing at least one blue ball when drawing two consecutive balls randomly?
Options:
(A) 9/10
(B) 16/20
(C) 2/5
(D) 3/5
(E) ½
answer: Stream of consciousness: P(at least one blue) = 1 - P(no blue, so 2 red) = 1- 2/5*1/4 = 9/10. The answer is (A).


q: Find the probability that the number drawn is a factor of 50.
Options:
(A) 1/25
(B) 1/50
(C) 3/25
(D) 3/50
(E) 7/50
a: Stream of consciousness: The factors of 50 are 1, 2, 5, 10, 25, 50
Therefore, required probability = 6/100 = 3/50. The answer is (D).


q: On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every nine minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
Options:
(A) 150%
(B) 200%
(C) 250%
(D) 300%
(E) 350%
a:
Stream of consciousness: Dolphin once in 3 min;
Beluga once in 9 min;
So, dolphin comes up 3 times frequently than beluga, which is 300% (9-3)/2*100. The answer is (D).
q: Right triangle ABC is the base of the prism in the figure above. If AB=AC=√2 and the height of the prism is 3, what is the volume of the prism?
Options:
(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 6
a: Stream of consciousness: Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3 The answer is (D).


question: In how many different ways could couples be picked from 8 men and 5 women?
Options:
(A) 8
(B) 5
(C) 13
(D) 40
(E) 20
answer: Stream of consciousness: Number of mens = 8
Number of womens = 5
Different ways could couples be picked = 8c1 * 5c1 = 8 * 5 = 40 ways The answer is (D).


q: An design manager has 10patterns of chairs & 7patterns of tables. In how many ways can he make a pair of table & chair?
Options:
(A) 70
(B) 40
(C) 80
(D) 90
(E) 100
a: Stream of consciousness: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 7 ways
Hence one chair and one table can be arranged in 10 x 7 ways = 70 ways The answer is (A).


question: In a bucket there are 3 blue balls and 2 red balls. What is the probability of drawing at least one blue ball when drawing two consecutive balls randomly?
Options:
(A) 9/10
(B) 16/20
(C) 2/5
(D) 3/5
(E) ½
answer: Stream of consciousness: P(at least one blue) = 1 - P(no blue, so 2 red) = 1- 2/5*1/4 = 9/10. The answer is (A).


q: Find the probability that the number drawn is a factor of 50.
Options:
(A) 1/25
(B) 1/50
(C) 3/25
(D) 3/50
(E) 7/50
a: Stream of consciousness: The factors of 50 are 1, 2, 5, 10, 25, 50
Therefore, required probability = 6/100 = 3/50. The answer is (D).


q: On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every nine minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
Options:
(A) 150%
(B) 200%
(C) 250%
(D) 300%
(E) 350%
a:
user
Stream of consciousness: Dolphin once in 3 min;
Beluga once in 9 min;
So, dolphin comes up 3 times frequently than beluga, which is 300% (9-3)/2*100. The answer is (D).
assistant
q: Right triangle ABC is the base of the prism in the figure above. If AB=AC=√2 and the height of the prism is 3, what is the volume of the prism?
Options:
(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 6
a: Stream of consciousness: Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3 The answer is (D).


question: In how many different ways could couples be picked from 8 men and 5 women?
Options:
(A) 8
(B) 5
(C) 13
(D) 40
(E) 20
answer: Stream of consciousness: Number of mens = 8
Number of womens = 5
Different ways could couples be picked = 8c1 * 5c1 = 8 * 5 = 40 ways The answer is (D).


q: An design manager has 10patterns of chairs & 7patterns of tables. In how many ways can he make a pair of table & chair?
Options:
(A) 70
(B) 40
(C) 80
(D) 90
(E) 100
a: Stream of consciousness: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 7 ways
Hence one chair and one table can be arranged in 10 x 7 ways = 70 ways The answer is (A).


question: In a bucket there are 3 blue balls and 2 red balls. What is the probability of drawing at least one blue ball when drawing two consecutive balls randomly?
Options:
(A) 9/10
(B) 16/20
(C) 2/5
(D) 3/5
(E) ½
answer: Stream of consciousness: P(at least one blue) = 1 - P(no blue, so 2 red) = 1- 2/5*1/4 = 9/10. The answer is (A).


q: Find the probability that the number drawn is a factor of 50.
Options:
(A) 1/25
(B) 1/50
(C) 3/25
(D) 3/50
(E) 7/50
a: Stream of consciousness: The factors of 50 are 1, 2, 5, 10, 25, 50
Therefore, required probability = 6/100 = 3/50. The answer is (D).


q: On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every nine minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
Options:
(A) 150%
(B) 200%
(C) 250%
(D) 300%
(E) 350%
a:
Stream of consciousness: Dolphin once in 3 min;
Beluga once in 9 min;
So, dolphin comes up 3 times frequently than beluga, which is 300% (9-3)/2*100. The answer is (D).