**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: **

5*t = *45

*tk* = 1

To find:

The value of *k *

**Solution: **

*Topic(s): Substitution *

Substitute for *t*.

Or you may recognize that *k* is a reciprocal of *t. *

**Answer: (B)**

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

**Given: **

4 turns of the crank raise a window 2 inches

**To find: **

Number of turns to raise the window inches

Solution:

*Topic(s): Proportional word problem *

Think of the problem as:

If 2 inches then 4 turns. If inches then how turns?

**Answer: (B) 7**

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

** Given: **

** To find: **

**Solution: **

*Topic(s): Substitution*

**Answer: (C) 1**

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

** Given: **

intersect at *O *

**To find:**

*y* – *x*

**Solution:**

*Topic(s): Supplementary, alternate, complementary angles*

Angles *POT* and *SOT* are supplementary angles.

20 + *y* = 180 ⇒ *y* = 160

Angles *POT* and *ROS* are alternate angles.

Angle *ROS* = angle *POT* = 20

Angle NOR and ROS are complementary angles.

*x* + 20 = 90 ⇒ *x* = 70

*y* − *x* = 160 − 70 = 90

**Answer: (C) 90**

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

** Given: **

Each session is hours long

Each break is hour long

Each lunch is 1 hour long

Session IV ends at 4:30 P.M.

**To find: **

The time that session I should begin

**Solution:**

Write down the time taken

Event |
Time taken |
Beginning Time |
Ending Time |

Session I |
1.5 |
||

Break |
0.25 |
||

Session II |
1.5 |
||

Lunch |
1 |
||

Session III |
1.5 |
||

Break |
0.25 |
||

Session IV |
1.5 |
4:30 P.M. |

Add the time taken from beginning of Session 1 to the end of Session IV:

1.5 + 0.25 + 1.5 + 1 + 1.5 + 0.25 +1.5 = 7.5

Count back 7.5 hours from 4:30 and you will get 9:00

**Answer: (D) 9:00 A.M.**

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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