Question 1 :

If the sum of a number and 4 is 2003, then the number is ?

(A)   1998       (B)  1990        (C)  1999

Solution :

Let x be the required number

x + 4  =  2003

Subtract 4 on both sides

x  =  2003 - 4

x  =  1999

So, the required number is 1999.

Question 2 :

The question paper in an exam consists 80 problems. James has solved 68 of them. The percentage of the problems he has solved?

(A)  50            (B)  80             (C)  85

Solution :

Total number of questions in the question paper  =  80

Number of solved question  =  68

Percentage of problems he has solved  =  (68/80) 100

=  (17/20) 100

=  17(5)  =  85

So, 85% of questions solved.

Question 3 :

An author of a math competition was looking through a tentative exam, when he realized that he could not use one of his proposed problems. Frustrated, he had decided to take a nap instead, and slept from 10.47 am to 7.32 pm. For how many minutes did he has sleep ?

(A)  585     (B)  620     (C)  225

Solution :

To find the number of minutes he has sleep, let us find the number of hours he has slept.

12.00  -  10.47  =  2.13

7.32

------

9.45

Number of minutes for 9 hours  =  9 (60)  =  540

=  540 + 45

=  585

So, the number of minutes he has sleep 585.

Question 4 :

If a rectangle ABCD has the lengths, AB = 7m and AC = 25, then its area is ?

(A)   130        (B) 150         (C)  168

Solution : In a right triangle ABC,

AC2  =  AB2 + BC2

252  =  72 + BC2

625 - 49  =  BC2

BC2  =  576

BC  =  √576  =  24

Area of rectangle  =  Length  Width

=  7 ⋅ 24

=  168 m2

So, the area of rectangle 168 m2.

Question 5 :

If the diagonal of a square is 4 feet long, then the area of the square is

(A) 5              (B) 9            (C)  8

Solution :

Diagonal of a square  =  4 ft

a2 + a2  =  42

2a2  =  16

a2  =  8

Area of square 8 square feet.

Question 6 :

If two angles are supplementary and one of the angles is 9 times as large as the other, what is the measure of the larger angle?

(A)   162    (B)   150   (C)   165

Solution :

Let "x" be the unknown angle

"9x" be the other angle

x + 9x  =  180

10x  =  180

Divide both sides by 10

x  =  18

9x  =  9(18)  =  162

So, the measure of larger angle is 162.

Question 7 :

ABCD is a square with the length of 8 units each side. A second square A1B1C1D1 is formed by joining the midpoints of AB, BC, CD,and DA. Find the sum of the areas of these two squares

(A)   96 cm2        (B)  104 cm2        (C)  48 cm2

Solution : Area of the square ABCD =  a2

=  8 =  64 cm2

To find the area of square A1B1C1D1, we have to find the side length of A1B1

(A1B1)=  42 + 42

(A1B1) =  16 + 16  =  32  =  4√2

Area of square A1B1C1D1  =  (4√2)2   =  32 cm2

Question 8 :

If p + q = 13, q + r = 14, r + p = 15, then the value of r is

(A)   6              (B)   8                 (C)  5

Solution :

p + q = 13  ----(1)

q + r = 14  ------(2)

r + p = 15  ----(3)

(2) - (3)

q + r - r - p  =  14 - 15

q - p = -1  ---(4)

p + q + p - q  =  13 + (-1)  =  12

2p  =  12

p  =  6

p + r  =  15

r  =  15 - 6 = 9

So, the value of r is 9.

Question 9 :

The number of three-digit perfect squares are,

(A)  12          (B)   19             (C)   22

Solution :

The value of 102 is 100,

The value of 182 is 324

The value of 312 is 961.

From 10 to 31, we have 22 numbers.

So, the number of three digit perfect squares are 22.

Question 10 :

A train is running at a speed of 20 m/sec.. If it crosses a pole in 30 seconds, find the length of the train in meters.

(A)  200 meter       (B)  800 meter       (C)   600 meter

Solution :

The distance covered by the train to cross the pole is

=  Length of the train

Given : Speed is 20 m/sec and time taken to cross the pole is 30 seconds

We know,

Distance  =  Speed  Time

So,

length of the train  =  Speed  Time

Length of the train  =  20  30

Length of the train  =  600 meters

So, length of the train is 600 meters. If you need any other stuff in math, please use our google custom search here.

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