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)
Z W Y X
Two adjacent may be interchanged
The entire sequence can be reversed
The least number of changes needed to put the letters into alphabetical order from left to right
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)
A cube with edges of length 4 cm
A rectangular box 20 cm by 24 cm by 32 cm
The number of cubes needed to fill the rectangular box
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.