SCAT Quantitative Comparisons: Algebra 2 — Questions and Answers
Question 1: Given x > 0. Compare: Column A: 3x + 5 | Column B: 2x + 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
Subtracting 2x + 5 from both sides gives x > 0, so Column A is always greater.
Question 2: Given x = 3. Compare: Column A: x² + 2x | Column B: 3x + 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 = 9 + 6 = 15 and Column B = 9 + 5 = 14, so Column A is greater.
Question 3: Given x + y = 10 and x > y > 0. Compare: Column A: x | Column B: y
- 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 condition x > y is stated directly, so Column A is greater without further calculation.
Question 4: Compare: Column A: 2(x + 3) | Column B: 2x + 7
- 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
Column A expands to 2x + 6, which is always 1 less than 2x + 7, so Column B is always greater.
Question 5: Given x > 1. Compare: Column A: x/2 | Column B: 1/x
- 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
At x = 1.2, Column B > Column A, but at x = 3, Column A > Column B, so the relationship cannot be determined.
Question 6: Given x = 5. Compare: Column A: (x − 3)² | Column B: x² − 6x + 9
- 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
x² − 6x + 9 is the expanded form of (x − 3)², so both expressions are always identical.
Question 7: Given x < 0. Compare: Column A: x² | Column B: x³
- 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
For any negative x, x² is positive and x³ is negative, so Column A is always greater.
SCAT Quantitative Comparisons: Algebra 2
Given x > 0.
Compare: Column A: 3x + 5 | Column B: 2x + 5