Some questions on the Praxis Core exam may appear as verbal problems, where an algebraic problem is written using words instead of mathematical operators and symbols.
The following practice questions require you to convert a verbal into an equation before you can solve the problem. The first question asks you to find the product of two consecutive even numbers. The second question asks you to find the value of y based on two opposite numbers.
Practice questions
- Two consecutive even integers have a sum of 18. What is the product of the two integers?
A. 10 B. 100 C. 80 D. 8 E. 18
- Two numbers are opposites. Their product is –81. The higher number is 3 more than twice y. What is the value of y?
A. –3 B. 9 C. –6 D. –243 E. 3
Answers and explanations
- The correct answer is Choice (C).
If you represent the lower of the two even integers as x, you can represent the greater one as x + 2. Now you can set their sum equal to 18 and solve for x to find the lower even integer:
Because the lower even integer is 8, the higher one is 10. The product of 8 and 10 is 80, Choice (C).
- The correct answer is Choice (E).
Any two numbers that are opposites have the same absolute value. Because the square root of 81 is 9, the two numbers that are opposites and have a product of –81 are 9 and –9. The higher of the two is the positive one, 9. That is the number that's 3 more than twice y; you can represent this situation with the equation 9 = 2y + 3 and solve for y:
The value of y is 3, Choice (E).
