SCAT Quantitative Comparisons: Algebra 3

Question 1

Given x = 1. Compare: Column A: |x − 3| | Column B: |3 − x|

Accepted Answer

The two quantities are equal

Answer

|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)

Accepted Answer

The two quantities are equal

Answer

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

Accepted Answer

The relationship cannot be determined

Answer

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

Accepted Answer

Column B is greater

Answer

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

Accepted Answer

Column A is greater

Answer

Column A = 14 + 3 = 17 and Column B = 15 − 4 = 11, so Column A is greater.

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