Solved Examples (Quantitative Multiple Choice Questions (One Answer))

Directions: Select a single answer choice.

1. If 3x = −9, then 3x³ − 2x + 4 =

   1. −83
   2. −71
   3. −47
   4. −17
   5. 61

   (B. -71) First solving 3x = −9, x = −3. Now plug into 3x³ − 2x + 4:
   3x³ − 2x + 4 =
   3(−3)³ − 2(−3) + 4 =
   3(−27) + 6 + 4 =
   −81 + 6 + 4 = −71

2. In the series 8, 9, 12, 17, 24 . . . the next number would be

   1. 29
   2. 30
   3. 33
   4. 35
   5. 41

   (C. 33) In the series, 8, 9, 12, 17, 24 . . .

   9 − 8 = 1	17 − 12 = 5
   12 − 9 = 3	24 − 17 = 7

   Hence, the difference between the next term and 24 must be 9 or
   x − 24 = 9
   and x = 33

   Hence, the next term in the series must be 33

3. A third-grade class is composed of 16 girls and 12 boys. There are 2 teacheraides in the class. The ratio of girls to boys to teacher-aides is

   1. 16:12:1
   2. 8:6:2
   3. 8:6:1
   4. 8:3:1
   5. 4:3:1

   (C. 8:6:1) Girls to boys to teacher-aides are in proportion 16 to 12 to 2. Reduced to lowest terms, 16:12:2 equals 8:6:1.

4. If 4a + 2 = 10, then 8a + 4 =

   1. 5
   2. 16
   3. 20
   4. 24
   5. 28

   (C. 20) One may answer this question by solving
   4a + 2 = 10
   4a = 8
   a= 2
   Now, plugging in 2 for a:
   8a + 4 = 8(2) + 4 = 20
   A faster way of solving this is to see the relationship between the quantity 4a + 2 (which equals 10) and 8a + 4. Since 8a + 4 is twice 4a + 2, the answer must be twice 10, or 20.

5. The closest approximation of (69.28 x .004)/.03 is

   1. .092
   2. .92
   3. 9.2
   4. 92
   5. 920

   (C. 9.2) This problem is most easily completed by rearranging and approximating as follows:
   (69.28 x .004)/.03 ≅ 69 x .1 = 6.9
   which is the only reasonably close answer to 9.2.

6. (7/10 x 14 5 x 1/28)/(10/17 x 3/5 x 1/6 x 17) =

   1. 4⁄7
   2. 1
   3. 7⁄4
   4. 2
   5. 17⁄4

   (C. 7⁄4)

   

7. 
   In the figure above, AB is one edge of a cube. If AB equals 5, what is the surface area of the cube?

   1. 25
   2. 100
   3. 125
   4. 150
   5. 300

   (D. 150) Since one edge of the cube is 5, all edges equal 5. Therefore, the area of one face of the cube is:
   (5)(5) = 25
   Since a cube has 6 equal faces, its surface area will be:
   (6)(25) = 150