ASVAB Arithmetic Reasoning and Mathematics Knowledge Practice Questions

B: To find the least common multiple, you should identify the prime factors of each number. The prime factor of 7 is 7, since it is a prime number. The prime factors of 9 are 3 and 3. The prime factors of 21 are 7 and 3. Therefore the LCM must have two factors of 3 and one factor of 7; 3 × 3 × 7 = 63. To check your work, you can confirm that 7, 9 and 21 all divide evenly into 63.

B: Since the price of the watch has gone down, the percent change must represent a decrease. Using the formula for percent change, divide the actual change by the original amount. Since the watch was originally $200 and during the sale it is $160, the watch decreased in price by $40. Divide $40 by the original amount of $200 to get 0.2, or 20%.

D: Any number divisible by both 3 and 5 must be divisible by 3 × 5, since 3 and 5 are both prime numbers. That’s 15, which is the smallest number. Add another 15 to 15 to find the next number, 30. Then add another 15, which equals 45. The next number would be 60, but that’s above the range of values indicated in the question. So there are 3 possible values: 15, 30, and 45.

D: The graph shows a portion of a straight line and asks what would be the value of the x-coordinate if the line were extended so that y = 100. In order to answer this question, you will first need to determine the equation for the line shown on the graph in the standard y = mx + b form. Two good reference points that the line passes through are (2, 0) and (0, −1). The slope, m, is (0 – (-1)) / (2-0) = 1/2. Since b is the y-intercept, the second point (or the graph itself) shows that b = −1. So the line is defined by the equation y = (1/2)x − 1. Substitute 100 for y: 100 = (1/2)x − 1. Multiply both sides by 2: 200 = x − 2, so x = 202

A: The question asks you to determine which of the answer choices can be plotted as a straight line on the coordinate plane. Since x = 3 does not include y in the equation, you might be tempted to eliminate this answer. However, because y does not appear in the equation, x = 3 for all values of y. Thus, this equation represents a straight, vertical line crossing the x-axis at 3. You can verify that y = 1/x is not a straight line by picking 3 numbers for x such as 1, 2, and 3. The corresponding y values are 1, 1/2 , and 1/3 . Since y decreases by different amounts for the same increase in x, this is not a straight line. Eliminate choice (B). Choice (C) can be eliminated because it contains three variables; the coordinate plane has only two. (This equation might describe a straight line in three dimensions.) Choice (D) has the term x^2, so it is not a linear equation and therefore would not be graphed with a straight line.