SAT Practice Test 1, Section 9: Questions 11 - 16

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:
2x < 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.
2x < y < 0

Choose y = – 1 and x = – 2.

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

(A) –2x = –2 (–2) = 4

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

= – (–5) = 5

(C) 2x = 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, 4n = Tues

n + 3 = Wed

Answer: (C) 2n + 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 = x²
y = a – x²
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 = x² = 3² = 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 – 3²
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 – 2k

Answer: (D) x + y – 2k

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