**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.

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

Given:

Total cost of 3 pencils is $4.50

The cost per pencil is increased by 50 cents

To find:

The cost of 5 pencils at the new rate

Solution:

Topic(s): Integer word problem

First, we find original price of one pencil.

$4.50 ÷ 3 = $1.50

New price of each pencil = $1.50 + $0.50 = $2.00

5 pencils will cost $2 × 5 = $10

**Answer: (E) $10.00**

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

Given:

A table representing the relationship between *x* and *y *

To find:

The linear equation that describes the relationship

Solution:

Topic(s): Coordinate geometry

First, we have to determine the slope.

slope =

Next, we need to determine the *y*-intercept i.e. when *x* = 0

The equation is then *y = *4*x* − 1

**Answer: (E) y = 4x − 1**

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

**Given: **

The figure

The two circles are tangent at point *B
*

The circumference of the circle with center

**To find: **

The length of

Solution:

Topic(s): Circumference of circle

The formula for circumference of a circle is *C* = 2π*r*

So, the radius is directly proportional to the circumference.

If the circumference of the circle with center *A* is twice that of the circumference of the circle with center *C* then the radius *AB *will be twice that of radius *BC
*

Given *AC* = 6

*AC = AB + BC = *6

2*BC* + *BC = *6*
*3

**Answer: (B) 2**

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

Given:

To find:

The lettered points in the figure that has coordinates (*x, y*)

Solution:

Topic(s): Absolute value

**Answer: (B) B**

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

Given:

A chart that shows the ages of 1000 people

To find:

The number of people with ages < 40

Solution:

Those people with ages < 40 are in the groups *x* < 20 (30%) and 20 ≤ *x* < 40 (20%)

30% + 20% = 50%

50% of 1000 = 0.5 × 1000 = 500

**Answer: (D) 500**

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