Question #1: If a • b = 18 and a / b = 2, a > 0, b > 0
then:
(a) a = 18 and b = 1
(b) a = 9 and b = 2
(c) a = 18 and b = 9
(d) a = 6 and b = 3
(e) a = 6 and b = 6
Answer: a / b = 2
a = 2•b.
a•b = (2• b)• b
a•b = 2• b 2.
2• b 2 = 18
b 2 = 9,
b = 3 because b > 0,
a = 2• b
a = 6.
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Question #2: The ratio of the radii of two circles is r1/r2 = 6. What is the ratio of the perimeters P1/P2 and the ratio of the areas of the two circles A1/A2?
(a) perimeter ratio = 1/6, area ratio = 36
(b) perimeter ratio = 36, area ratio = 6
(c) perimeter ratio = 6, area ratio = 36
(d) perimeter ratio = 1/8, area ratio = 8
(e) perimeter ratio = 1/6, area ratio = 6
Answer: r1 / r2 = 6;
Perimeter1 / Perimeter2 = (2• ¶• r1)/(2• ¶• r2) = r1/ r2 = 6
Area1 / Area2 = (¶• r12)/ (¶• r22) = r12 / r22 = 36
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Question #3: What value x satisfies both 1/x < 1/7 and x 2 > 16?
(a) x = 1
(b) x = -5
(c) x = -1
(d) x = 7
(e) x = 6
Answer: x 2> 16 means (x - 4)• (x + 4) > 0.
x can be lower than -4 or higher than 4.
1/x < 1/7; (7-x) / 7x < 0.
x can be lower than 0 or higher than 7.
In conclusion, x can be lower than -4 or higher than 7.
The only correct answer is x = -5.
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Question #4: A lottery sells 1000 tickets and there is only one winning number. 200 New Jersey residents buy 2 tickets each, 300 New Yorresidents buy 1 ticket each and the rest are sold in
Connecticut. What is the probability that the wining ticket was bought in New Jersey?
(a) 3/5
(b) 1/2
(c) 2/5
(d) 1/5
(e) 4/5
Answer: There are 400 tickets sold in New Jersey out of a total of 1000, so the probability will be 400/1000 = 2/5.
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Question #5: Celsius degrees can be transformed in Fahrenheit degrees by using the formula : °C=(5/9)• (°F-32). What is x, if x degrees Celsius is equal to x
degrees Fahrenheit?
(a) 40
(b) -40
(c) -20
(d) 20
(e) -30
Answer: x = (5/9)• (x - 32).
9•x = 5•(x - 32).
In conclusion, x = -40C = -40F
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