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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.

**6. Correct answer: (A) **

**Given: **

are all integers

*x* + 1 is the median of these integers

**To find:**

The value of *x*

**Solution: **

*Topic(s): Statistics*

The median is the middle value of a list when the numbers are in order.

We know that *x* + 1 is in the middle but we do not know whether the list is in ascending or descending order.

Lets assume that the list is given in ascending order then

Since all the answers given are greater than 3, we can continue with the assumption that the list is in ascending order.

Then, we can have the two inequalities,

This tells us that 4.5 < *x* < 6.

The only answer that fits that range is 5.

**Answer: (A) 5**

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

**Given: **

The net profit is *P*(*n*) = 0.75*n* – 50, where *n* is the number sold

**To find:**

The number sold in order to get a net profit of $100

**Solution: **

*Topic(s): Isolate variable*

Answer: (E) 200

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

**Given:**

*x*^{2} + *y*^{2} = 73

*xy* = 24

**To find: **

(*x* + *y*)^{2}

**Solution: **

*Topic(s): Square of sum, distributive rule*

Recognize that (*x* + *y*)^{2} is the square of sum or you may use the distributive rule

(*x* + *y*)^{2} = *x*^{2} + 2*xy* + *y*^{2} = *x*^{2} + *y*^{2} + 2*xy* = 73 + 2(24) = 73 + 48 = 121

**Answer: (D) 121**

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

**Given:**

*AD* = 1

*DC* =

**To find:**

The value of *z *

**Solution: **

*Topic(s): 30° - 60° - 90° triangle*

Triangle *ABC* has two equal angles *x**°*.

This means that length of *AD* = *BD* = 1. (If two angles of a triangle are equal, then the sides opposite those angles are equal)

Given the sides of ratio 1: √3 means that triangle *BCD* is a 30°- 60°- 90° triangle. (If you forget, you may check the diagrams given at the reference section). This means that *z* = 30

**Answer: (D) 30**

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

**Given: **

30% of 40% of a positive number = 20% of *w*% of the same number

**To find:**

The value of *w *

**Solution: **

*Topic(s): Percent*

Let *n *be the positive number*.*

Translate “of” as "×".

30% × 40% × *n* = 20% × *w*% × *n
*120% = 20% ×

120 = 20 ×

**Answer: (B) 60**

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