21. If .2t = 2.2 - .6s and .5s = .2t + 1.1, then s =
(a) 1
(b) 3
(c) 10
(d) 11
(e) 30
Ans : (b)
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22. Five years ago, Beth's age was three times that of Amy. Ten years ago, Beth's age was one half that of Chelsea. If C repre- sents Chelsea's current age, which of the following represents Amy's current age?
(a) c/6 + 5
(b) 2c
(c) (c-10)/3
(d) 3c-5
(e) 5c/3 - 10
Ans : (a)
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23. A portion of $7200 is invested at a 4% annual return, while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?
(a) $160
(b) $320
(c) $400
(d) $720
(e) $1,600
Ans : (b)
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24. An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drainpipe in 6 hours. If both pipes are fully open at the same time, in how many hours will the empty pool be filled to capacity?
(a) 4
(b) 4.5
(c) 5
(d) 5.5
(e) 6
Ans : (e)
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25. If r = (3p + q)/2 and s = p - q, for which of the following values of p would r2 = s2?
(a) 1q/5
(b) 10 - 3q/2
(c) q - 1
(d) 3q
(e) 9q/2 - 9
Ans : (a)
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26. At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?
(a) 38
(b) 40
(c) 44
(d) 48
(e) 50
Ans : (c)
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27. On the xy-coordinate plane, points A and B both lie on the circumference of a circle whose center is O, and the length of AB equals the circle's diameter. If the (x,y) coordinates of O are (2,1) and the (x,y) coordinates of B are (4,6), what are the (x,y) coordinates of A?
(a) (3, 3/2)
(b) (1, 2/2)
(c) (0, -4)
(d) (2/2, 1)
(e) (-1, -2/2)
Ans : (c)
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28. If a rectangle's length and width are both doubled, by what percent is the rectangle's area increased?
(a) 50
(b) 100
(c) 200
(d) 300
(e) 400
Ans : (d)
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29. If a rectangle's length and width are both doubled, by what percent is the rectangle's area increased?
(a) 9
(b) 12
(c) 16
(d) 21
(e) 39
Ans : (b)
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30. Point Q lies at the center of the square base (ABCD) of the pyramid pictured above. The pyramid's height (PQ) measures exactly one half the length of each edge of its base, and point E lies exactly halfway between C and D along one edge of the base. What is the ratio of the surface area of any of the pyramid's four triangular faces to the surface area of the shaded triangle?
(a) 3 :√2
(b) √5:1
(c) 4√3:3
(d) 2√2:1
(e) 8:√5
Ans : (d)
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