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4. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

　　A. 2.5π

　　B. 3π

　　C. 5π

　　D. 4π

　　E. 10π

Correct Answer: C

Explanation:

Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5. Circumference = π.diameter = 5π

5. Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?

　　A. 4

　　B. 7

　　C. 8

　　D. 12

　　E. it cannot be determined from the information given.

Correct Answer: D

Explanation:

If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as n + (n + 1) + (n + 2) + (n + 3 ) and (n + 3) + (n + 4) + (n + 5) + (n + 6) Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12

6. The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance from A to C?

　　I 11

　　II 1

　　III 7

　　A. I only

　　B. II only

　　C. I and II only

　　D. II and III only

　　E. I, II, or III.

Correct Answer: E

Explanation:

Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.

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