**11. Correct answer: 8, 10 or 12**

Given:

When the positive even integer *n* is increased by 50% of itself, the result is between 10 and 20:

To find:

One possible value of *n *

Solution:

Topic(s): Percent

10 < *n* + 50%*n * < 20

10 < *n* + 0.5*n* < 20

10 < 1.5*n* < 20

6.67 < *n* < 13.33

Remember, *n* is an even integer.

The possible even integers in the required range, 6.67 < *n* < 13.33, would be 8, 10 and 12

**Answer: Any one of following: 8, 10 or 12**

**12. Correct answer: 3400**

Given:

The perimeter of the rectangle is 250.

The length of one side is 40.

To find:

Area of the rectangle

Solution:

Topic(s): Area and perimeter of rectangle

First, we need to find the length of the other side of the rectangle.

Formula of perimeter of rectangle: 2(*l* + *w*)

Substitute in the given values:

2(40 + *w*) = 250

80 + 2*w* = 250

2*w* = 170

*w* = 85

Next, we calculate the area

Formula for area of rectangle: *lw
*

**Answer: 3400**

**13. Correct answer: 450**

Given:

A school ordered $600 worth of light bulbs

Some bulbs cost $1 each

Some bulbs cost $2 each

There are twice as many $1 bulbs as $2 bulbs

To find:

The number of light bulbs ordered altogether

Solution:

Topic(s): Integer word problem

Let *b* be the number of $2 light bulbs ordered

2*b* be the number of $1 light bulbs ordered

Altogether, the school ordered $600 worth of light bulbs.

*b *× 2 + 2*b* × 1 = 600

2*b* + 2*b* = 600

4*b* = 600

*b* = 150

Total number of bulbs = *b* + 2*b* = 3*b* = 3 × 150 = 450

**Answer: 450**

**14. Correct answer: 1/2**

Given:

4(*x* + *y*)(*x* – *y*) = 40 (equation 1)

*x* – *y *= 20 (equation 2)

To find:

*x* + *y*.

Solution:

Topic(s): Substitution

Substitute equation 2 into equation 1

4(*x* + *y*) × 20 = 40

4(*x* + *y*) = 2

(*x* + *y*) =

**Answer: **

**15. Correct answer: 12**

Given:

The center of the circle has coordinates (5, 12)

The circle touches the *x*-axis at one point only.

To find:

The radius of the circle.

Solution:

Topic(s): Tangent of circle

First, we can sketch the diagram.

For the circle to touch the *x*-axis at only one point, the *x*-axis must be a tangent to the circle. A tangent is perpendicular to the radius at the point of contact. So the radius must be 12

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