**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,

AC^{2} = AB^{2} + BC^{2}

25^{2} = 7^{2} + BC^{2}

625 - 49 = BC^{2}

BC^{2} = 576

BC = √576 = 24

Area of rectangle = Length **⋅** Width

= 7 **⋅ **24

= 168 m^{2}

So, the area of rectangle 168 m^{2}.

**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

a^{2} + a^{2} = 4^{2}

2a^{2} = 16

a^{2} = 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 A_{1}B_{1}C_{1}D_{1} is formed by joining the midpoints of AB, BC, CD,and DA. Find the sum of the areas of these two squares

(A) 96 cm^{2} (B) 104 cm^{2} (C) 48 cm^{2}

**Solution :**

Area of the square ABCD = a^{2}

= 8^{2 } = 64 cm^{2}

To find the area of square A_{1}B_{1}C_{1}D_{1}, we have to find the side length of A_{1}B_{1}

(A_{1}B_{1)}^{2 }= 4^{2} + 4^{2}

(A_{1}B_{1)}^{2 } = 16 + 16 = 32 = 4√2

Area of square A_{1}B_{1}C_{1}D_{1 = }(4√2)^{2 }= 32 cm^{2}

**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)

Add 1^{st} and 4^{th} equation

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 10^{2} is 100,

The value of 18^{2} is 324

The value of 31^{2} 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.

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