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(1)  One-third the product of two numbers is 24.  One-half the product of these same two numbers is

(A)  72  (B)  54  (C)  48  (D)  36  (E) 12

Solution

(2)  

The area of rectangle ABCD  is 72.  Point F is on AB such that BF = 4. What is the sum of the areas of triangles CBF and DAF?

(A)  18  (B)  24  (C)  36  (D)  42 

(E)  Cannot be determined from the given information

Solution

(3)  Ms. Brady has 28 students in her class.  The ratio of boys to girls in the class is 2 t 5.  How many new boys must be added to the class to make the ratio of boys to girls 1:2?

(A)  1  (B)  2  (C)  4  (D)  12  (E)  32

Solution

(4)

The vertices of rectangle ABCD all lie on the same circle as shown.  The circumference of the circle is 64π.  What is the length of AC?

(A)  8  (B)  16  (C)  32  (D)  64  (E)  128

Solution

(5) Ten cards are numbered 10, 11, 12,. . . . , 19, one number per card.  Brain removes three cards whose numbers are primes, and puts the remaining cards in  a hat.  If one card is then drawn at random from the hat, what is the probability that its number is a prime?

(A)  1/10  (B)  1/9  (C)  1/5  (D)  2/5  (E) None of these

Solution

(6)  In the figure, all line segments meet at right angles.  What is the area enclosed by the figure?

(A)  84  (B)  72  (C)  70  (D)  68  (E)  64

Solution

(7) The perimeter of a square is four times the circumference of a circle with radius of 1 m. What is the area of the square ?

(A)   4π²  (B)  2π²  (C)   π²  (D)  π 

(E)  cannot be determined.

Solution

(8)  Assume that the notation ┴ (q, r, s, t) means  “Multiply q and r, then add the product to s and divide by t”.  What is the value of   ┴(2, 6, 4, 8) +  ┴ (4, 7, 2, 6)?

(A)  7.0  (B)  7.5  (C)  8.0  (D)  8.5  (E)  9.0

Solution

(9)   When the sum of a list of integers is divided by the mean of the integers, the result is x.  What does x represent?

(A)  the sum of the integers 

(B)  half the sum of the integers 

(C)  the mean of the integers 

(D)  the number of integers in the list 

(E)  half the number of integers in the list

Solution

(10) A piece of paper is used to make a cylinder (without a top and bottom) that is 8 inches long and has a radius of 1.5 inches.  Assuming no part of the paper overlaps, what is the area of the piece of paper?

(A)  12 sq. in.  (B)  24 sq. in.  (C)  6  sq. in.

(D)  6 sq. in.   (E)  24 sq. in.

Solution

(11)   Express 6.925 x 10⁵ in standard form.

(A)  0.00006925  (B)  0.0006925  (C)  6.92 

(D)  692,500  (E)  6,925,000

Solution

(12) 

 On the number line above, X is located at -10, Y is at -2, and Z is at 8.  M (not shown) is the midpoint of XY, and N (not shown) is the  midpoint of YZ.  What is the midpoint of MN?

(A)  -4.5  (B)  -1.5  (C)  1.5  (D)  4.5  (E)  5.5

Solution

(13) If 0 < y < 1, which of the following statements must be true?

(A)  y² > y³  (B)  y > 0.5y  (C)  y > y³ 

(D)  All of the above  (E)  None of the above

Solution

(14) The area of the square ABCD is 4 times larger than the area of square WXYZ.  If the area of square WXYZ is 9, what is the difference between the length of a side of square ABCD and the length of a side of square WXYZ?

(A)  3  (B)  4  (C)  6  (D)  9  (E)  12

Solution

 (15)  Triangle GHI is similar to Triangle JKL.

What is the length of side JK?

(A)  8  (B)  9  (C)  15  (D)  16  (E)  21

Solution

(16) Wesley and two of his friends are driving cross country nonstop and have agreed to take turns driving in 7-hours shifts.  Each person will drive for one shift, and take two shifts off to rest.  If Wesley’s first shift starts at 6:00 a.m., at what time will Wesley complete his third shift?

(A)  1:00 a.m.  (B)  5:00 a.m.  (C)  6:00 a.m.

(D)  7:00 a.m.  (E)  8:00 a.m.

Solution

(17) What is the difference between the largest and lowest integer in the sequence of consecutive odd integers whose sum is 15 ?

(A)  2  (B)  4  (C)  5  (D)  9  (E)  12

Solution

(18)  The half life of a substance is the time it takes for a substance to decrease to half its initial amount. John has a pile of goo that decreases in amount at a constant rate. If John initially had 100 pounds of goo, and ten days later, he only had 25 pounds of goo, what is the half of the goo ?

(A)  10 days  (B)  5 days   (C)  7.5 days 

(D)  20 days   (E)  25 days

Solution

(19)  What is the value of (9⁴ - 8⁴)/(9² + 8²) ?

(A)  1  (B)  16  (C)  17  (D)  18  (E)  155

Solution

(20)  Jackie fills a jug with water continuously. It takes her 2 minutes to fill up 50% of the empty space in the jug with water. After every 2 minutes, she puts a penny into a jar to celebrate. How many pennies will she have in the jar at the instant the jug has less tan 30% empty space left ?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  4

Solution

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