ASVAB Study GuideMathematics Knowledge Practice Test 6
Tap an answer to check it instantly and read the explanation. 10 questions: 3 easy, 4 medium and 3 hard.
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Question 1 easy
Solve for x: $$5x - 3 > 3x + 9$$
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Correct answer: B — x > 6
First, subtract $$3x$$ from both sides of the inequality: $$2x - 3 > 9$$. Next, add 3 to both sides: $$2x > 12$$. Finally, divide by 2: $$x > 6$$.
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Question 2 easy
Which inequality represents the statement: "Negative four times a number increased by seven is less than fifteen"?
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Correct answer: B — $$-4x + 7 < 15$$
Negative four times a number translates to $$-4x$$. "Increased by 7" means adding $$7 (-4x + 7)$$. "Is less than fifteen" means the inequality symbol is '<' followed by 15. Putting it together yields $$-4x + 7 < 15$$.
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Question 3 easy
Solve the compound inequality: $$-3 \le 2x + 5 < 11$$
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Correct answer: A — $$-4 \le x < 3$$
Subtract 5 from all three parts of the inequality: $$-3 - 5 \le 2x < 11 - 5$$, which simplifies to $$-8 \le 2x < 6$$. Next, divide every part by 2: -4 ≤ x < 3.
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Question 4 medium
Solve for x: $$|3x - 4| = 11$$
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Correct answer: A — $$x = 5 \text{ or } x = \frac{-7}{3}$$
An absolute value equation splits into two separate cases: $$3x - 4 = 11$$ or $$3x - 4 = -11$$.
Case 1: $$3x = 15$$ → $$x = 5$$.
Case 2: $$3x = -7$$ → $$x = \frac{-7}{3}$$.
Therefore, the solutions are $$x = 5$$ or $$x = \frac{-7}{3}$$
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Question 5 medium
Which of the following points lies on the line given by the equation $$4x - 3y = 12$$?
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Correct answer: B — $$(3, 0)$$
To test which point lies on the line, substitute the x and y coordinates into the equation $$4x - 3y = 12$$.
Testing $$(3, 0)$$: $$4(3) - 3(0) = 12 - 0 = 12$$, which matches the right side of the equation. Thus, (3, 0) is a valid point.
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Question 6 medium
Your platoon has 35 male members. This number is three more than twice the number of female members. How many female members are in the platoon?
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Correct answer: C — 16
Let f represent the number of female members. According to the problem, $$2f + 3 = 35$$. Subtract 3 from both sides: $$2f = 32$$. Divide by 2: $$f = 16$$
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Question 7 medium
Jessica has taken four tests in her math class and scored 85, 80, 75, and 90 percent. Her final exam is worth two test grades. What score does she need on the final exam to get an 88 percent overall in the class?
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Correct answer: D — 99
The final exam counts as 2 test grades, making a total of 6 test grades (4 regular tests + 2 for the final). To achieve an 88% average across 6 grades, she needs a total of $$88 \times 6 = 528$$ points. Her current sum of 4 tests is $$85 + 80 + 75 + 90 = 330$$ points. The remaining points needed for the final are $$528 - 330 = 198$$ points. Since the final exam is worth 2 test grades, divide by 2: $$198 \div 2 = 99$$
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Question 8 hard
Ms. Davis has 25 fifth-grade students. Each student has either a sibling, a pet, or both. If 15 students have a sibling and 19 have a pet, how many students have both a sibling and a pet?
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Correct answer: B — 9
Use the Principle of Inclusion-Exclusion: Total = Only Sibling + Only Pet + Both. Alternatively, add the individual groups $$(15 + 19 = 34)$$. Since there are only 25 students, the excess represents those counted twice who have both: $$34 - 25 = 9$$ students.
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Question 9 hard
Rachel's cellular carrier charges a monthly rate of $14.50 and $0.30 per minute for international calls. If her total monthly bill is $26.50, how many minutes did Rachel spend on international calls?
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Correct answer: C — 40
Set up a linear equation where m is the number of international minutes: $$14.50 + 0.30m = 26.50$$. Subtract the base monthly rate from the total bill: $$0.30m = 26.50 - 14.50$$, which simplifies to $$0.30m = 12.00$$. Divide by 0.30: $$m = 12.00 \div 0.30 = 40$$ minutes.
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Question 10 hard
Charles has $50 and is saving $8 per week. David has $110 and is saving $6 per week. How long will it be before David and Charles have the same amount of money?
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Correct answer: D — 30 weeks
Let w represent the number of weeks. Charles's total money will be $$50 + 8w$$, and David's total money will be $$110 + 6w$$. Set them equal to each other to find when they match: $$50 + 8w = 110 + 6w$$. Subtract $$6w$$ from both sides: $$50 + 2w = 110$$. Subtract 50 from both sides: $$2w = 60$$. Divide by 2: $$w = 30$$ weeks.