Strategies for Problem Solving (or Discrete Quantitative) Questions

• time is in short supply so avoid lengthy computations and look for the short-cut to the correct answer
• sketch diagrams on your scratch pad in order to visualize a problem and add any extra lengths, angles or areas
• if you cannot answer a question, start at an answer choice and work your way back to the question
• look at the answer choices after reading the question – the correct answer might become apparent

Each of the following questions have five answer choices. For each of the questions, select the best answer choice given.

Question:
If the length and width of a rectangle are both tripled, the ratio of the area of the original rectangle to the area of the enlarged rectangle is:
(A) 1:3
(B) 1:6
(C) 1:9
(D) 1:8
(E) 2:9

Answer: C

Explanation: Ratio = original rectangle/enlarged rectangle = 1LW/9LW = 1/9 = 1:9

Question:
At a luncheon table where 12 men are seated, one-half of the men belong to Club A, one-third belong to Club B, and one-fourth belong to both clubs. How many men belong to neither?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Answer: C

Explanation: Half the 12 (6) belong to Club A, 3 of these also belong to A and B. One third (4) belong to Club B, of these, 3 also belong to Club A. Thus, 7 men are accounted for as club members and 5 men belong to neither club.

Question:
A rectangular field 100 feet long is twice as long as it is wide. The number of feet of fencing needed to enclose the field is
(A) 150
(B) 300
(C) 400
(D) 500
(E) 600

Answer:B

Explanation: Since the length is twice the width, then the width is 50. Perimeter = 50 + 50 + 100 + 100 = 300 feet.

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