Directions: Select one or more answer choices according to the specific question directions. If the question does not specify how many answer choices to select, select all that apply.
- The correct answer may be just one of the choices or as many as all of the choices, depending on the question.
- No credit is given unless you select all of the correct choices and no others.
If the question specifies how many answer choices to select, select exactly that number of choices.
Question 1:
Which of the following integers are multiples of both 2 and 3?
Indicate all such integers.
A. 8
B. 9
C. 12
D. 18
E. 21
F. 36
Explanation:
one can first identify the multiples of 2, which are 8, 12, 18 and 36, and then among the multiples of 2 identify the multiples of 3, which are 12, 18 and 36. Alternatively, if one realize that every number that is a multiple of 2 and 3 is also a multiple of 6, one can identify the choices that are multiples of 6.
The correct answer consists of Choices C (12), D (18) and F (36).
Question 2:
Which two of the following numbers have a product that is between –1 and 0?
Indicate both of the numbers.
A. -20
B. –10
C. [latex]2^{-4}[/latex]
D. [latex]3^{-2}[/latex]
Explanation:
For this question, one must select a pair of answer choices.
The product of the pair must be negative, so the possible products are
(–20) ([latex]2^{-4}[/latex]), (–20) ([latex]3^{-2}[/latex]), (–10) ([latex]2^{-4}[/latex]), and (–10) ([latex]3^{-2}[/latex]).
The product must also be greater than –1.
The first product is [latex]\frac{-20}{2^4}[/latex] = -[latex]\frac{20}{16}[/latex] < -1,
The second product is [latex]\frac{-20}{3^2}[/latex] = -[latex]\frac{20}{9}[/latex] < -1 and
The third product is [latex]\frac{-10}{2^4}[/latex] = -[latex]\frac{10}{16}[/latex] > -1
So one can stop there.
The correct answer consists of Choices B (–10) and C ([latex]2^{-4}[/latex]).