question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 28?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 8
answer: Stream of consciousness: (1056 / 28) gives remainder 20
20 + 8 = 28, So we need to add 8 The answer is (E).


q: The compound ratio of 2/3, 6/7, 4/3 and 1/8 is given by?
Options:
(A) 2/21
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68
a: Stream of consciousness: 2/3 * 6/7 * 4/3 * 1/8 = 48/504 = 2/21 The answer is (A).


question: In a race with 30 runners where 5 trophies will be given to the top 9 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 9^5 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
answer: Stream of consciousness: 9 people can be prized with 5 distinct prizes in 9^5 ways The answer is (A).


q: What is the are of an equilateral triangle of side 24 cm?
Options:
(A) 66âˆš3 cm2
(B) 74âˆš3 cm2
(C) 64âˆš3 cm2
(D) 64âˆš5 cm2
(E) 144âˆš3 cm2
a: Stream of consciousness: Area of an equilateral triangle = âˆš3/4 S2
If S = 24, Area of triangle = âˆš3/4 * 24 * 24 = 144âˆš3 cm2; The answer is (E).


question: If n is an integer, then the least possible value of |15 - 8n| is?
Options:
(A) 0
(B) 2
(C) 1
(D) 3
(E) 5
answer: Stream of consciousness: |15 - 8n| represents the distance between 15 and 8n on the number line. Now, the distance will be minimized when 8n, which is multiple of 8, is closest to 15. Multiple of 8 which is closest to 15 is 16 (for n = 2), so the least distance is 1: |15 - 16| = 1. The answer is (C).


question: A marble shop contains 5 blue marbles, 5 red marbles, and 5 green marbles. If 2 marbles are purchased at random from the shop, what is the probability that the 2 marbles will be of the red?
Options:
(A) 5/15
(B) 2/21
(C) 20/15
(D) 5/210
(E) 4/14
answer:
Stream of consciousness: Of the 15 marbles we are wanting red:
Probability of choosing 1st red marble: 5/15
Probability of Choosing 2nd red marble: 4/14
Multiply and you get 20/210 simplified to 2/21 The answer is (B).
question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 28?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 8
answer: Stream of consciousness: (1056 / 28) gives remainder 20
20 + 8 = 28, So we need to add 8 The answer is (E).


q: The compound ratio of 2/3, 6/7, 4/3 and 1/8 is given by?
Options:
(A) 2/21
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68
a: Stream of consciousness: 2/3 * 6/7 * 4/3 * 1/8 = 48/504 = 2/21 The answer is (A).


question: In a race with 30 runners where 5 trophies will be given to the top 9 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 9^5 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
answer: Stream of consciousness: 9 people can be prized with 5 distinct prizes in 9^5 ways The answer is (A).


q: What is the are of an equilateral triangle of side 24 cm?
Options:
(A) 66âˆš3 cm2
(B) 74âˆš3 cm2
(C) 64âˆš3 cm2
(D) 64âˆš5 cm2
(E) 144âˆš3 cm2
a: Stream of consciousness: Area of an equilateral triangle = âˆš3/4 S2
If S = 24, Area of triangle = âˆš3/4 * 24 * 24 = 144âˆš3 cm2; The answer is (E).


question: If n is an integer, then the least possible value of |15 - 8n| is?
Options:
(A) 0
(B) 2
(C) 1
(D) 3
(E) 5
answer: Stream of consciousness: |15 - 8n| represents the distance between 15 and 8n on the number line. Now, the distance will be minimized when 8n, which is multiple of 8, is closest to 15. Multiple of 8 which is closest to 15 is 16 (for n = 2), so the least distance is 1: |15 - 16| = 1. The answer is (C).


question: A marble shop contains 5 blue marbles, 5 red marbles, and 5 green marbles. If 2 marbles are purchased at random from the shop, what is the probability that the 2 marbles will be of the red?
Options:
(A) 5/15
(B) 2/21
(C) 20/15
(D) 5/210
(E) 4/14
answer:
user
Stream of consciousness: Of the 15 marbles we are wanting red:
Probability of choosing 1st red marble: 5/15
Probability of Choosing 2nd red marble: 4/14
Multiply and you get 20/210 simplified to 2/21 The answer is (B).
assistant
question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 28?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 8
answer: Stream of consciousness: (1056 / 28) gives remainder 20
20 + 8 = 28, So we need to add 8 The answer is (E).


q: The compound ratio of 2/3, 6/7, 4/3 and 1/8 is given by?
Options:
(A) 2/21
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68
a: Stream of consciousness: 2/3 * 6/7 * 4/3 * 1/8 = 48/504 = 2/21 The answer is (A).


question: In a race with 30 runners where 5 trophies will be given to the top 9 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
(A) 9^5 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
answer: Stream of consciousness: 9 people can be prized with 5 distinct prizes in 9^5 ways The answer is (A).


q: What is the are of an equilateral triangle of side 24 cm?
Options:
(A) 66âˆš3 cm2
(B) 74âˆš3 cm2
(C) 64âˆš3 cm2
(D) 64âˆš5 cm2
(E) 144âˆš3 cm2
a: Stream of consciousness: Area of an equilateral triangle = âˆš3/4 S2
If S = 24, Area of triangle = âˆš3/4 * 24 * 24 = 144âˆš3 cm2; The answer is (E).


question: If n is an integer, then the least possible value of |15 - 8n| is?
Options:
(A) 0
(B) 2
(C) 1
(D) 3
(E) 5
answer: Stream of consciousness: |15 - 8n| represents the distance between 15 and 8n on the number line. Now, the distance will be minimized when 8n, which is multiple of 8, is closest to 15. Multiple of 8 which is closest to 15 is 16 (for n = 2), so the least distance is 1: |15 - 16| = 1. The answer is (C).


question: A marble shop contains 5 blue marbles, 5 red marbles, and 5 green marbles. If 2 marbles are purchased at random from the shop, what is the probability that the 2 marbles will be of the red?
Options:
(A) 5/15
(B) 2/21
(C) 20/15
(D) 5/210
(E) 4/14
answer:
Stream of consciousness: Of the 15 marbles we are wanting red:
Probability of choosing 1st red marble: 5/15
Probability of Choosing 2nd red marble: 4/14
Multiply and you get 20/210 simplified to 2/21 The answer is (B).