- Question #1: If a, b and c are consecutive integers, a < b < c, and a + b + c = 96, what is the value of b?
(a) 30
(b) 31
(c) 32
(d) 33
(e) 34- Solution: If a, b and c are consecutive numbers, b = a + 1 and c = a + 2.
Then, a + (a + 1) + (a + 2) = 96, so 3·a + 3 = 96.
a = (96 – 3)/3 = 31.
b = a + 1 = 32.
- Solution: If a, b and c are consecutive numbers, b = a + 1 and c = a + 2.
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Question #2: If a is an integer chosen randomly from the set {3, 5, 6, 9} and b is an integer chosen randomly from the set {2, 3, 4}, what is the probability that a/b is an integer?
(a) .125
(b) .250
(c) .333
(d) .5
(e) .55
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Answer: We have 4 possible integers for a and 3 for b, so the number of possible combinations for a/b is 4 · 3 = 12.
a/b is an integer only for 4 combinations:
1. a = 3 and b = 3
2. a = 6 and b = 2
3. a = 6 and b = 3
4. a = 9 and b = 3
The probability that a/b is an integer is 4/12 = 1/3 = .333.
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Answer: We have 4 possible integers for a and 3 for b, so the number of possible combinations for a/b is 4 · 3 = 12.
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Question #2: What is the sum of 10% of x and 20% of 2x?
(a) 10% of x
(b) 20% of x
(c) 30% of x
(d) 50% of x
(e) 100% of x-
Answer: 10% of x is .1x.
20% of 2x = .2·2x = .4x.
The sum of 10% of x and 20% of 2x is .1·x + .4·x = .5·x. In conclusion the sum is 50% of x.
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Answer: 10% of x is .1x.