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

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.

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

Given:

The length of a drawing of a tool is of the length of the actual tool

The length of the drawing of the toll is 6 inches

To find:

The length of the actual tool

Solution:

Topic(s): Translating words to equations

Let *x* be the length of the actual tool.

**Answer: (C) 16**

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

Given:

is an integer

To find:

Which of the following must *x* be

Solution:

Topic(s): Odd and even numbers

In order for to be an integer *x* + 3 must be divisible by 2 i.e. *x* + 3 must be even

In order for *x* + 3 to be even, we can check the rules for Addition of Integers

odd + odd = even

*x* + 3 = odd

Therefore, *x* must be odd

** Answer: (E) an odd integer**

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

Given:

The figure

Points *Q* and *S *are the center of the circles, which are tangent to the *x*-axis

To find:

The slope of the line *QS *

Solution:

Topic(s): Coordinate geometry

**Answer: (B) **

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

Given:

*n* and *p* are integers greater than 1

*p* is a factor of both *n* + 3 and *n* + 10

To find:

The value of *p *

Solution:

Topic(s): Factors

If *p* is a factor of *n* + 3 then there exists an integer *a *where *ap = n *+ 3 (equation 1)

If *p *is factor of *n* + 10 then there exists an integer *b *where *bp = n + *10 (equation 2)

Equation 2 – equation 1:

*bp = n + *10 - (*n *+ 3)

*p*(*b* - *a*) = 7

*p = *1 or *p* = 7 (because 7 has only two factors 1 and 7)

We are given *p* > 1, so the answer is *p* = 7

**Answer: (B) 7**

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

Given:

The figure of a cube

*B, C, * and *E* are midpoints of 3 of the edges

To find:

The angles with the least measure

Solution:

Topic(s): Inversely proportional

If we put all the triangles onto the same plane we would get the following figure:

We can see that if the heights of the triangles remain the same, the size of the angles adjacent to the base would be inversely proportional to the lengths of the base.The longest base is *YD*.

So, the angle with the least measure would then be

**Answer: (D) **

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

Given:

*xy* = 7

*x* – *y* = 5

To find:

*x*^{2}*y* – *xy*^{2}

Solution:

*x*^{2}*y* – *xy*^{2 }

*= xy*(*x* – *y*)

= 7(5)

= 35

**Answer: (D) 35**

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