(1)  In the sequence of numbers 1, 2, 2, 3, 3, 3,. . . [assume the pattern of one 1, two 2s, three 3s, four 4s, and so on continues], the number in the 40th position will be

(A)  8  (B)  9  (C)  10  (D)  11  (E)  40


(2)  Each side of a square is an integral number of inches, and its area is 576 square inches.  If each side of the square is increased by 1 foot, forming a new square, the area of the new square, in square inches, is

(A)  577  (B)  588  (C)  720  (D)  1,296 

(E)  not determined


(3)  Let P = 18/25, Q = 5/7, and R = 3/4.  Then

(A)  P < Q < R  (B)  P < R < Q  (C)  Q < P < R

(D)  Q < R < P  (E)  R < P < Q


(4)  A water container is 3/4 full.  After 20 ounces of water is removed, the container is 1/4 full.  How many ounces of water does a full container hold?

(A)  20  (B)  40  (C)  60  (D)  80  (E)  100


(5) For how many integer values of n will the expression (n-10) / (14-n) have a positive value?

(A)  0  (B)  1  (C)  3  (D)  4  (E)  5



A square of side 4 is topped by a semicircle, as shown.  Point P is the center of the arc at the top.  Then the shaded area is equal to

(A)  π + 2  (B)  (π/2) + 2  (C)  2π + 2

(D)  2π – 4  (E)  2π + 4


(7)  (46 x 34 x 22) / (42 x 34 x 26) =

 (A)  1  (B)  2  (C)  8  (D)  16  (E)  24


(8) Which one of the following numbers is less than 1/3?

(A)  1111/3333  (B)  299/895  (C)  .1 x 4 

(D)  .4 x 1  (E)  5! / 6!


(9)  The ratio of a to b is 3 to 4.  The ratio of b to c is 5 to 6.  The ratio of a to c is

(A)  9:10  (B)  5:8  (C)  1:2  (D)  2:5  (E)  none of these



(All lines shown are either vertical or horizontal)  If x and y are integers, and the shaded area is 52, then the perimeter of the figure is

         (A)  20  (B)  24  (C)  52  (D)  56  (E)  196


(11)  One-half of one-sixth is equal to

(A)  one-third of one-fourth  (B)  one-third 

(C)  one  (D)  two  (E)  three


(12)  The areas of triangles ABC and XYZ are each 10.  The area of the shaded region is 14.  Then the area of triangle XWC is

(A)  12  (B)  8  (C)  6  (D)  3  (E)  2


(13) 1  1/10  + 2  11/100 + 3  111/1000 (mixed fractions)  =

(A)  6.111  (B)  6.123  (C)  6.111111  (D)  6.321  (E)  6.6


(14)  If x is positive and x2 + x = 50, then x is a number between

(A)  6 and 7  (B)  7 and 8  (C)  8 and 9 

(D)  9 and 10  (E)  10 and 11


(15)  In the figure, C is a point on line segment AE.  If AB = BC, what is the measure of angle DCE?

(A)  80°  (B)  75°  (C)  60°  (D)  25°  (E)  20°


(16)  Barbara is 7 years older than Carole is now.  Katie is half as old as Carole is now.  If Katie is now 16 years old, how many years old is Barbara now?

(A)  15  (B)  23  (C)  32  (D)  39  (E)  46


(17)  3.4 x 102 + 3.4 x 102 is equal to

(A)  6.8 x 102  (B)  6.8 x 104  (C)  3.4 x 104 

(D)  3,400  (E)  3,434


(18)  The points S, P, Q, and R are on the sides of rectangle ABCD such that SQ is perpendicular to PR.  APXS is a square whose side is 3.  The area of SXRD is 12 and the area of PBQX is 27.  What is the perimeter of rectangle ABCD?

(A)  84  (B)  72  (C)  38  (D)  36  (E)  18


(19)  Kobi has $9.83, made up of nickels and pennies only.  Which of the following could not be a possible value for the number of pennies?

(A)  208  (B)  113  (C)  93  (D)  88  (E)  85


(10)  If (2x – 3) / 4 = 8, then 2x + 3 =

(A)  41  (B)  38  (C)  35  (D)  29  (E)  28


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L.C.M method to solve time and work problems

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Remainder when 2 power 256 is divided by 17

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