**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.

**Given: **

3*b* + 1 < 10

**To find: **

The value that CANNOT be *b*

**Solution: **

*Topic(s): Isolate variable*

3*b* + 1 < 10 ⇒ 3*b* < 9 ⇒ *b* < 3

All the answers are less than 3 except for (E) 3

**Answer: (E) 3**

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

**Given:**

2^{4x} = 16

**To find:**

The value of *x*

**Solution:**

*Topic(s): Exponents*

2^{4x} = 16

16 = 2 × 2 × 2 × 2 = 2 4

2^{4x} = 2^{4}

Since the bases are the same, we equate the exponents.

4*x* = 4 ⇒*x* =1

**To find: **

How much greater is *r* + 5 than *r* – 2

**Solution:**

To find out how much greater, we can subtract (*r* – 2) from (*r* + 5).

(*r* + 5) – (*r* – 2) = *r* + 5 – *r* +2 = 7

**Answer: (E) 7**

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

**Given: **

A rectangular box with no lid is cut along the vertical edges and flattened

**To find: **

The figure that represents the flattened shape

**Solution: **

*Topic(s): Nets of solids *

Only the figure (E) can form a box with the right dimensions.

**Answer: (E)**

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

**Given: **

A path from point *A *to point *D* is determined by moving upward or to the right along the grid lines

**To find: **

The different paths that can be drawn from *A* to *D* that do not include either *B* or *C*

** Solution: **

There are four possible paths that do not include

** Answer: (B) Four**

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