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

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

Given:

*x* and *y* are consecutive odd integers

*y* > *x*

To find:

*y*^{2} – *x*^{2}

Solution:

Topic(s): Consecutive numbers, distributive property

Since *x* and *y* are consecutive odd integers, we know that *y* = *x* + 2.

Substitute *y* = *x* + 2 in *y* 2 – *x* 2

(*x* + 2)^{2} – *x*^{2} = *x*^{2} + 4*x* + 4 – *x*^{2} (use distributive rule)

= 4*x* + 4

** Answer: (E) 4 x + 4 **

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

Given:

Line *l *passes through the origin and is perpendicular to the line 4*x* + *y = *k , where *k* is a constant

The two lines intersect at the point (*t, t* + 1)

To find:

The value of *t *

Solution:

Topic(s): Equation of a line

Rewrite the equation as *y* = *mx* + *c*, in order to get the slope *m*.

4*x* + *y* = *k* ⇒ *y* = 4*x* + k

The slope is – 4.

In the coordinate plane, two lines are perpendicular if the product of their slopes ( m) is –1.

Let the slope of line *l* be *n*. Since line *l* is perpendicular to the above line:

Line *l *passes through the origin; this means that its intercept at the y-axis is 0.

The equation for line *l* is then

(equation 1)

The line *l* passes through the point (*t, t *+ 1).

Substitute *x* = *t* and *y* = *t* + 1 into equation 1

** Answer: (A) **

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

Given:

Average of *x* and *y* is *k *

To find:

Average of *x, y* and *z *

Solution:

Topic(s): Statistics

Given that the average of *x* and *y* is *k*.

Find the average of *x*, *y* and *z *

** Answer: (A) **

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

Given:

Given figure

Triangle *ABC* is equilateral with sides = 2

*WY* is diameter of circle with center *O *

To find:

Area of circle

Solution:

Topic(s): Triangles, Pythagoras theorem, area of circle

Triangle

Let *d* = length of *YW*

Using Pythagorean theorem:

*d *is also the diameter of the circle.

The radius of the circle is

Area of circle:

** Answer: (C) **

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

Given:

When 15 is divided by the positive integer *k, *the remainder is 3

To find:

The number of different values of *k *

*
*Solution:

When 15 is divided by the positive integer

15 = *nk* + 3, where *n* is a positive integer less than 3

*⇒ nk* = 12

We now put in the values for *n* to test how many of them are divisible by 12. (Remember *n* is positive and less than 3).

*n* = 1, *k* = 12

*n* = 2, *k* = 6

*n* = 3, *k* = 4

There are three possible values for *k*.

** Answer: (C) Three **

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