Strategies for Multiple-Choice

• read the question thoroughly and select the best answer that fits
• learn in advance all the critical definitions, formulas, and concepts that appear in common questions,
• use the test booklet, not your answer sheet, for any scratch work
• spend less time on the easy questions, this allows more time for the harder questions
• detailed calculations should not be necessary. Look for a trick or a shortcut if the question seems time consuming
• if you want to guess an answer, choose one and try to work out ‘in reverse’ if the answer is correct.

Question: The weight of a bag of mangoes plus four more than twice that weight equals 40 pounds. How much, in pounds, does the bag of mangoes weigh?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 20

Answer: B

Explanation: Start with C: assume the bag weighs 14 pounds. (Why start with C? If you start with the middle number and your answer is too high, you can choose a lower number; if your answer is too low, you can choose a higher number.) four more than twice 14 is 32; 14 plus 32 is 46 which is too high. Try B, a lower number , assume the bag weighs 12 pounds. Four more than twice 12 is 28; 12 plus 28 is 40.

Question: If Mark can shape three surfboards in 50 minutes, how many surfboards can he shape in five hours?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20

Answer: C

Explanation: As the time increases so does the number of shaped surfboards. Hence, we set up a direct proportion. First, convert 5 hours into minutes: 5 hours = 5 x 60 minutes = 300 minutes. Next, let x be the number of surfboards shaped in 5 hours. Finally, forming the proportion yields

3/50 = x/300
3(300)/50 = x
18 = x

Question: If n is an odd integer, which one of the following is an even integer?

Answer:D

Explanation: Chose an odd integer for n, lets say, 1 and substitute it into each answer choice. In choice A, 3(1) + 2 = 5, which is not an even integer. Choice B, is not an even integer, nor is C and Choice E, the nn = 1(1) = 1, is not an even integer.

Question: If a, b, and c are consecutive integers and a I. b - c = 1
II. abc/3 is an integer
III. a + b + c is even

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

Answer: B

Explanation: Let, x, x+1, x + 2 stand for the consecutive integers a, b, and c, in that order. Plugging this into statement I yields b - c = (x + 1) - (x + 2) = -1. Hence, statement I is false. For statement II, since a, b, and c are three consecutive integers, one of them must be divisible by 3. Hence, abc/3 is an integer, and statement II is true. As to statement III, suppose a is even, b is odd, and c is even. Then a + b is odd since even + odd = odd. Hence, a + b + c = (a + b) + c = (odd) + even = odd. Thus statement III is not necessarily true.

Question: If (x + 3)/(x - 3) = y, what is the value of x in terms of y?
(A) 3 - y
(B) 3/y
(C) (2 + y)/(y - 2)
(D) (-3y - 3)/(1 - y)
(E) 3y/2

Answer: D

Explanation:First, multiply both sides of the equation by x - 3: (x - 3)(x = 3)/(x - 3) = (x 3)y. Cancel the (x - 3’s) on the left side of the equation: x + 3 = (x - 3)y. Cancel the y:x + 3 = xy - 3y. Subtract xy and 3 from both sides: x - xy = -3y -3. Factor out the x on the left side of the equation: x(1 - y) = -3y -3. Finally, divide both sides of the equation by 1 - y:x = (-3y -3)/(1 - y).

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