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More Lessons for SAT Preparation

Math Worksheets

The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the The Official SAT Study Guide Second Edition.

It would be best that you go through the SAT practice test questions in the Study Guide first and then look at the worked solutions for the questions that you might need assistance in. Due to copyright issues, we are not able to reproduce the questions, but we hope that the worked solutions will be helpful.

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

Given:

To find:

What happens to the value of *y* when both *x* and *z* are doubled

Solution:

Topic(s): Exponents

Double *x* and *z*

**Answer: (E) y is multiplied by 4**

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

Given:

The value of the automobile *n* years from the date of purchase is

To find:

The number of years from the date of purchase when the value of the automobile will be $3,200

Solution:

Topic(s): Exponents

**Answer: (B) Two**

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

Given:

The figure showing how three wires are braided

To find:

The numbered step when the braid repeat the original order *A, B, *

Solution:

The orders of the braids are as follows:

Start: ABC

1 BAC

2 BCA

3 CBA

4 CAB

5 ACB

6 ABC

The braid repeats the original order at step 6.

**Answer: (D) 6**

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

Given:

A set of eleven different numbers

To find:

Which of the following will not affect the value of the median

Solution:

Topic(s): Statistics

If the eleven different numbers were to be arranged in order, the median would be the 6^{th} number.

We would have to determine which of the answers would not change the median.

(A) Doubling each number. *(The median is also doubled)
*(B) Increasing each number by 10.

(C) Increasing the smallest number only.

(D) Decreasing the largest number only.

(E) Increasing the largest number only. ü *(Increasing the largest number would not affect the median)*

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

Given:

The figure

*SBT* is one quarter of a circle with center *R* and radius 6

Length plus width of rectangle *ABCR *= 8

To find:

Perimeter of the shaded region

Solution:

Topic(s): Circumference of circle

Length of arc

Given *AR* + *RC* = length + width = 8

*SR* + *RT* = 6 + 6 = 12

*SA *+ *CT* = *SR* + *RT* – (*AR* + *RC*) = 12 – 8 = 4

*AC* = *BR* = radius of circle = 6

Perimeter of shaded region = 6 + 4 + 3π = 10 + 3π

Answer: (B) 10 + 3π

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