**11. Correct answer: (B) **

**Given: **

The rectangle *ABCD* is made up of 7 non-overlapping rectangles

The 2 smallest rectangles have the same area

Each of the other rectangles has twice the area of the next smaller rectangle

**To find: **

The area of the shaded rectangle is what fraction of the area of the rectangle *ABCD *

**Solution: **

*Topic(s): Area of rectangle*

Fill up the rectangle, each time reducing the area by half.

**Answer: (B)**

**12. Correct answer: (B) **

**Given:**

2*x* < *y* < 0

**To find: **

The answer that is the greatest value

**Solution: **

*Topic(s): Signed operations*

We can choose any values for *x* and *y* that is true for the inequality.

2*x* < *y* < 0

Choose *y* = – 1 and *x* = – 2.

Test each of the answers. Be careful about the signed operations.

(A) –2*x* = –2 (–2) = 4

(B) – (2*x* + *y*) = – (2(–2) + (–1)) = – (–4 + (–1)) = – (–4 – 1)

= – (–5) = 5

(C) 2*x* = 2(–2) = – 4

(D) 0

(E) –*y* = –(–1) = 1

The greatest value is (B) 5

**Answer: (B) 5**

**13. Correct answer: (C)**

**Given:**

He delivers

*n* packages on Monday

4 times as many on Tuesday as on Monday

3 more packages on Wednesday than on Monday

**To find: **

The average number of packages delivered per day over the 3 days

**Solution: **

*Topic(s): Statistics *

Given *n *= Mon

Then, 4*n* = Tues

*n* + 3 = Wed

**Answer: (C) 2 n + 1**

**14. Correct answer: (E) **

** Given: **

**To find: **

The answers that must be true

**Solution:**

*Topic(s): Exponents, difference of two squares, distributive rule*

Square both sides of the equation.

Recognize that it is a difference of two squares or use the distributive rule.

**Answer: (E)**

**15. Correct answer: (E) **

**Given:**

The graphs:

*y* = *x*^{2}

*y* = *a* – *x*^{2}

*PQ* = 6

**To find:**

The value of *a*

**Solution:**

*Topic(s): Coordinate geometry*

The two graphs are symmetrical about the *y*-axis.

If *PQ* = 6,then the point *Q* is units from the *y*-axis.

This means that the *x*-coordinate of point *Q* is 3.

The *y*-coordinate of *Q* can be obtained by substituting *x* = 3 into the equation *y* = *x* 2.

*y = x*^{2} = 3^{2} = 9

Point *Q* is (3, 9).

Point *Q* also belongs to the graph *y* = *a* – *x* 2.

Substituting *x* = 3 and *y* = 9 into *y* = *a* – *x* 2.

9 = *a* – 3^{2
}*a* = 9 + 9 = 18

**Answer: (E) 18**

**16. Correct answer: (D) **

**Given: **

Set *X *has *x* members

Set *Y *has *y* members

Set *Z* has all members that are either in set *X* or set *Y* with the exception of *k* common members

To find:

The expression that represents the number of members in set *Z *

**Solution: **

*Topic(s): Sets *

Number of members in set *X* excluding *k* is *x *– *k*.

Number of members in set *Y* excluding *k* is *y *– *k*.

Number of members in set *Z* =* x *– *k* + *y *– *k* = *x* + *y* – 2*k*

**Answer: (D) x + y – 2k**

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