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

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: (B)

Given:
Z W Y X
Two adjacent may be interchanged
The entire sequence can be reversed

To find:
The least number of changes needed to put the letters into alphabetical order from left to right

Solution:
We need to change the sequence from Z W Y X to W X Y Z.

The least steps needed would involve changing from

Z W Y X to Z Y X W and then reverse the entire sequence.

Swap W and Y; Z W Y X → Z Y W X

Swap W and X; Z Y W X → Z Y X W

Reverse entire sequence: Z Y X W → W X Y Z

The least number of changes needed is 3.

Answer: (B) 3

12. Correct answer: (D)

Given:
A cube with edges of length 4 cm
A rectangular box 20 cm by 24 cm by 32 cm

To find:
The number of cubes needed to fill the rectangular box

Solution:
Volume of cube = 4 × 4 × 4 = 64

Volume of rectangular box = 20 × 24 × 32 = 15360

Divide volume of rectangular box by volume of cube
= 15360 ÷ 64 = 240

Note that you should only divide the volumes when you are sure that the smaller shape can fit into the larger shape without any leftover space.

Given:
When it is noon (EST) in New York City, it is 9.00 a.m. (PST) in San Francisco

A plane took off from New York City at noon EST and arrived in San Francisco at 4.00 p.m. on the same day

A second plane left San Francisco at noon PST and took exactly the same amount of time for the trip

To find:
The second plane’s arrival time (EST) in New York City

Solution:
When it is 9:00 a.m. PST, it is 12:00 noon EST.

The time difference from PST to EST is +3 hours.

A plane took off at 12:00 noon EST and arrived at 4:00 p.m. PST.

4:00 p.m. PST would be 4 + 3 = 7:00 p.m. EST.

The time taken would be from 12:00 noon to 7:00 p.m., which is 7 hours.

A second plane took off at 12:00 noon PST and took the same amount of time as the first plane, which is 7 hours. It would then be arriving at 7:00 p.m. PST.

7:00 p.m. PST would be 7 + 3 = 10.00 p.m. EST

Answer: (A) 10.00 p.m. EST

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