**This is for SAT in Jan 2016 or before.**

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.

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

Given:

To find:

The possible values of *n*

Solution:

Topic(s): Symbol problems

We then test the given statements for the values of *n*:

** Answer: (A) I only**

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

Given:

20% of *x* = 80% of *y*

To find:

*y* in terms of *x*

Solution:

Topic(s): Percent

Translate ‘of” as ‘×’

Convert between percent and decimal.

**Answer: (B) y = 25%x**

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

Given:

*x* + *y* is even

(*x* + *y*) 2 + *x* + *z* is odd

*x*, *y* and *z* are positive integers

To find:

The statement that is true

Solution:

Topic(s): Odd and even numbers

You were given that *x* + *y* is even.

Applying the rule: Even × Even = Even

(*x* + *y*)^{2} = (*x* + *y*) × (*x* + *y*) = Even

You were also given that (*x* + *y*)^{2} + *x* + *z* is odd.

Applying the rule: Even + Odd = Odd

Since (*x* + *y*)^{2} is even, so, *x* + *z* is odd

Applying the same rule again: Even + Odd = Odd

If *z* is even, then *x* must be odd.

** Answer: (C) If z is even, then x must be odd.**

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

Given:

0 < *x* < 1

To find:

The statements that must be true

Solution:

Topic(s): Fractions

Given 0 < *x* < 1, we can say the *x* is a positive fraction with a value less than 1.

If a positive fraction with a value less than 1 is raised to a positive integer exponent then the larger the exponent the smaller the result.

This means that conditions I. *x* 2 > *x* 3 and III. *x* > *x* 3 are true.

Half of a positive integer is less than the original integer.

This means that condition II. is true.

**Answer: (E) I, II and III **

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

Given:

A scatter plot

To find:

The function that models the relationship between *t*, the number of seconds to complete the maze and *p,* the number of practices.

Solution:

If we were to draw a line to reflect the approximate values of the data on the graph, we would get a horizontal line that intersects the *y*-axis between 40 and 50.

A horizontal line would have an equation of the form *t*(*p*) = *c*, where *c* is a constant.

Out of all the answers given only (A) *t*(*p*) = 40, satisfies that condition.

**Answer: (A) t(p) = 40**

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

Given:

The pattern consisting of 5 *L* by *W *rectangles

To find:

The number of *L* by *W *rectangles needed to cover a region 12*L* by 10*L*

Solution:

Since the region to be covered is given is in terms of *L*, we would want to get the width and length of the above pattern to be in terms of *L* as well.

The above pattern forms a rectangle.

From the two vertical sides, we know that:

The width of the rectangle is then

The above pattern is a rectangle with dimensions:

In order to cover the region without any leftovers, we need to place the width of the rectangle along the side that is 10*L*. The number of rectangles that we can place along the side 10*L* is:

The length of the rectangle is 2*L*. The number of rectangles that can be placed along the side 12*L* is 12*L* ÷ 2*L* = 6.

So, we would need 6 × 6 = 36 of rectangles with the above pattern.

Be careful! The question wants the number of rectangles of dimensions *L* by *W*.

The above pattern has 5 rectangles of dimensions *L* by *W*.

So, the answer is 36 × 5 = 180

**Answer: (E) 180**

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