SAT Practice Test 1, Section 3: 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.

1. Correct answer: (B)

Given:
2x + 3 = 9

To find:
4x – 3

Solution:
Topic(s): Isolate variable, substitution

Substitute x = 3 into 4x – 3
4(3) – 3 = 12 – 3 = 9

Answer: (B) 9

2. Correct answer: (D)

Given:
There are 8 sections of seats
Each section has at least 150 seats but not more than 200 seats

To find:
The total number of seats

Solution:
Topic(s): Translating words to equations

Smallest number of seats is 150 × 8 = 1200
Largest number of seats is 200 × 8 = 1600
The only given answer between 1200 and 1600 is 1,300

Answer: (D) 1,300

3. Correct answer: (A)

Given:
is perpendicular to l

To find:
Line segment that has the greatest length

Solution:
Topic(s): Right triangles, Pythagoras theorem

The line segments given in the answers form the hypotenuse of right triangles.
From the Pythagoras theorem: The longer the two sides of a triangle, the longer will be the hypotenuse.
So, we choose the longest side, which is and the hypotenuse is

Answer: (A)

4. Correct answer: (D)

Given:
The graph showing the total number of children in the family at the end of the year
A set of twins were born

To find:
The year the twins were born

Solution:
Look at the graph and find the year where there was a change (jump) of two children. There was an increase of two children from 1996 and 1997. This indicates that the twins were born in 1997.

Answer: (D) 1997

Given:
The average of x and y is 5. Number of terms = 2
The average of x, y and z is 8. Number of terms = 3

To find:
The value of z

Solution:
The formula for average (arithmetic mean) is:

The formula can also be written as
SumofTerms = Average × Numberof Terms .....(formula 2)

Substitute the given values into formula 2:
x + y = 5 × 2 = 10 (equation 1)
x + y + z = 8 × 3 = 24 (equation 2)

Subtract equation 1 from equation 2
z = 14

Answer: (B) 14

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