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.

6. Correct answer: (A)

Given:
A figure of 3 lines intersecting at a point

To find:
The pair of angles that is NOT sufficient for determining all six angle measures.

In order to determine all the six angles, given the value of two angles, the two given angles must be part of a line.

This will then allow us to calculate the third angle (supplementary angles). Then, we can determine the other three angles (vertical angles)

Check the answers to find out which pair does NOT form a line

(A) t and z does not form part of a line
(B) t and y forms part of a line
(C) s and x forms part of a line
(D) r and t forms part of a line
(E) r and s forms part of a line

Correct answer: (A)

7. Correct answer: (C)

Given:
The sum of 2 numbers that differ by 1 is t

To find:
The value of the greater of the 2 numbers in terms of t

Solution: Topic(s): Integer problems

Let x be the greater number x – 1 be the smaller number

Given the sum of the numbers is t i.e.

x + x – 1 = t ⇒ 2x = t + 1 ⇒

Answer: (C)

8. Correct answer: (A)

Given:
A table that shows how many students in a class of 12 had 0, 1, 2 or 3 siblings
A new student joined the class and the average number of siblings per student becomes equal to the median number of siblings per student

To find:
The number of siblings the new student had

Solution: Topic(s): Statistics

The median of 12 items is the average of the 6^{th} and 7^{th} item.Looking at the table, the numbers of siblings of the 6^{th} and 7^{th} students are both 1. So, the median is 1.

If we add another student then we would have 13 students.The median would be the number of siblings of the 7^{th} student.

We then check whether adding this new student would change the median. If the new student has 0 or 1 sibling, the 7^{th} student still has 1 sibling.If the new student has 2 or 3 siblings, the 7^{th} student still has 1 sibling.The median would still be 1 even after we add the new student.

Let n be the number of siblings of the new student.
Given average = median

Answer: (A) 0

9. Correct answer: 2/5, .4

Given:
2(x – 3) = 8

To find:

Solution: Topic(s): Cross-multiply

Answer:

10. Correct answer: 128

Given:
Twice a number decreased by 3 is 253

To find:
The number

Solution: Topic(s): Translating words to equations

Let n be the number

Answer: 128

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