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SAT Practice Test 4, Section 4: Questions 6 - 10

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This is for SAT in Jan 2016 or before.



6. Correct answer: (A)

A “simple square” is any integer > 1 that has only three positive integer factors – itself, its square root, and 1.

To find:
The answer that is a simple square

Topic(s): Square root of integers

Answer: (A) 121

7. Correct answer: (B)

In the triangle XYZ, XZ is , which is the length of the altitude

To find:
Area of triangle XYZ in terms of h

Topic(s): Area of triangle

From the diagram, we can see that XZ is the base (b) and h is the height of the triangle.

Area of triangle XYZ =

Answer: (B)

8. Correct answer: (B)


= 432 (where a and b are positive integers)

To find:
The value of ab.

Topic(s): Exponents, factors

First, multiply the exponents

Next, find the prime factors of 432.

432 = 3 × 3 × 3 × 2 × 2 × 2 × 2 = 3 3 × 2 4

Then, we change the base to get the exponents of 3 and 2 in order to match with the exponents of a and b.

33 × 24 = 33 × 42 = a3b2a = 3, b = 4
ab = a × b = 3 × 4 = 12

Answer: (B) 12

9. Correct answer: 990

To find:
The greatest three-digit integer that has a factor of 10

Topic(s): Factors

Having a factor of 10, means the integer must end with a 0.
In order for it to be the greatest, the other two digits must be 9s.

So, the 3-digit integer must be 990.

Answer: 990

10. Correct answer: 30

A recipe for chili for 20 people requires 4 pounds of beans

To find:
Pounds of beans required to make chili for 150 people

Topic(s): Proportional word problem

Rewrite the problem as:

If 20 people then 4 pounds, if 150 people then how many pounds?

20 → 4

150 →

Answer: 30



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