SAT Practice Test 1, Section 6: Questions 11 - 15

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: 104

Given:
Each angle of triangle ABC has the same measure as each angle in triangle XYZ
Length of one side of triangle XYZ is 24

To find:
One possible perimeter of triangle XYZ

Solution:
Topic(s): AA rule, similar triangles, perimeter of triangle

You were told that the each corresponding angles of the two triangles are equal. This fulfils the AA Rule, so we know the two triangles are similar. Being similar triangles, the ratio of the corresponding sides of the two triangles would also be the same.

Lets take the ratio of the sides to be

Perimeter = sum of all three sides = 24 + 48 + 32 = 104

There are other possible measurements for triangle XYZ, but you only need to find one of them.

Answer: 104

12. Correct answer: 202

Given:
Sum of 5 consecutive integers is 5

To find:
The value of the greatest of these integers

Solution:
Topic(s): Consecutive number problem

Let x = first consecutive number

The greatest number is x + 4 = 198 + 4 = 202

Answer: 202

13. Correct answer: 3

Given:
y = g(x)
h(x) = g(2x) + 2

To find:
The value for h(1)

Solution:
h(x) = g(2x) + 2
h(1) = g(2 × 1) + 2
= g(2) + 2

The value of g(2) from the graph is 1.
h(1) = 1 + 2 = 3

Answer: 3

14. Correct answer: 24

Given:
Exactly 4 actors try out for 4 parts in a play
Each actor can perform any one part
No one can perform more than one part

To find:
The number of different assignments of actors possible

Solution:
Topic(s): Permutations

When you select number after number from the same group, the number of possible outcomes will decrease by 1 for each choice.

The number of possible assignments is 4 × 3 × 2 × 1 = 24

Answer: 24

15. Correct answer: 40

Given:
Triangle PQR is equilateral
intersect at point P

To find:
The value for y

Solution:
Topic(s): Equilateral triangles, vertical angles

Since triangle PQR is equilateral, each of its angles is 60º.

This means that angle QPR is 60º.

Angle SPT and angle VPR are vertical angles and so are equal.

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