# SAT Practice Test 4, Section 4: Questions 1 - 5

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.

Given:

To find:
The value of x

Solution:
Topic(s): Substitution

Substitute equation 3 into equation 2
y 3z = 3 × 2 = 6

Substitute y = 6 into equation 1
x – 6 = 8 ⇒ x = 14

Given:
Since Todd (t) is older than Marta (m), t > m
Since Todd (t) is younger than Susan (s), t < s

To find:
The relationship between t, m and s

Solution:
So, m < t < s

Answer: (A) m < t < s

Given:
Areas of two regions are equal
Sum of the area of the regions is 5

To find:
The average of the areas of the two regions

Solution:

Average =

Given:
S is the set of all integers that can be written as n 2 + 1, where n is a nonzero integer.

To find:
The integer that is in the set S

Solution:
Topic(s): Squares of integers

(SAT recommends that you know the square of integers from 1 to 12)

Given:
Point O is the center of the circle.
x = 40

To find:
The angle y

Solution:
Topic(s): Isosceles triangle, sum of angles in a triangle

We can deduce that the triangle is an isosceles triangle because the two sides of the triangle are the radii of the circle, which are equal.

The base angles of an isosceles triangle are equal.

So, the other angle of the triangle is also y.

The sum of angles in a triangle is 180º.

So, 40 + y + y = 180
2y = 140
y = 70

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