SCAT Quantitative Comparisons: Algebra 3 — Questions and Answers
Question 1: Given x = 1. Compare: Column A: |x − 3| | Column B: |3 − x|
- Column A is greater
- Column B is greater
- The two quantities are equal (Correct answer)
- The relationship cannot be determined
Correct answer: The two quantities are equal
|x − 3| and |3 − x| are always equal because |a| = |−a| for any real number.
Question 2: Given x = 4. Compare: Column A: √x + √x | Column B: √(4x)
- Column A is greater
- Column B is greater
- The two quantities are equal (Correct answer)
- The relationship cannot be determined
Correct answer: The two quantities are equal
Column A = 2 + 2 = 4 and Column B = √16 = 4, so both quantities equal 4.
Question 3: Given x² = 16. Compare: Column A: x | Column B: 4
- Column A is greater
- Column B is greater
- The two quantities are equal
- The relationship cannot be determined (Correct answer)
Correct answer: The relationship cannot be determined
x² = 16 means x = 4 or x = −4; since both are possible, the relationship cannot be determined.
Question 4: Given 0 < x < 1. Compare: Column A: x² | Column B: x
- Column A is greater
- Column B is greater (Correct answer)
- The two quantities are equal
- The relationship cannot be determined
Correct answer: Column B is greater
When 0 < x < 1, squaring makes the value smaller, so x² < x and Column B is greater.
Question 5: Compare: Column A: 2x + 3 when x = 7 | Column B: 3x − 4 when x = 5
- Column A is greater (Correct answer)
- Column B is greater
- The two quantities are equal
- The relationship cannot be determined
Correct answer: Column A is greater
Column A = 14 + 3 = 17 and Column B = 15 − 4 = 11, so Column A is greater.
Question 6: Compare: Column A: the product of any two negative numbers | Column B: 0
- Column A is greater (Correct answer)
- Column B is greater
- The two quantities are equal
- The relationship cannot be determined
Correct answer: Column A is greater
The product of two negative numbers is always positive, which is always greater than 0.
Question 7: Given x − y = 5 and y > 0. Compare: Column A: x | Column B: 5
- Column A is greater (Correct answer)
- Column B is greater
- The two quantities are equal
- The relationship cannot be determined
Correct answer: Column A is greater
Since x = 5 + y and y > 0, x must be greater than 5, so Column A is always greater.
SCAT Quantitative Comparisons: Algebra 3
Given x = 1.
Compare: Column A: |x − 3| | Column B: |3 − x|