SCAT Quantitative Comparisons: Algebra 5

Question 1

Compare: Column A: the number of real solutions to x² + 1 = 0 | Column B: 0

Accepted Answer

The two quantities are equal

Answer

x² + 1 = 0 has no real solutions since x² ≥ 0, so Column A = 0, which equals Column B.

Question 2

Given 2x + 3y = 12 and x = 3. Compare: Column A: y | Column B: 2

Accepted Answer

The two quantities are equal

Answer

Substituting x = 3 gives 6 + 3y = 12, so y = 2, making both columns equal.

Question 3

Given x > 2. Compare: Column A: x² − 4 | Column B: x − 2

Accepted Answer

Column A is greater

Answer

Column A = (x−2)(x+2) and Column B = (x−2); since x > 2, dividing both by (x−2) > 0 gives x+2 > 1, so Column A is greater.

Question 4

Given x = 5. Compare: Column A: x² − 2x + 1 | Column B: (x − 1)²

Accepted Answer

The two quantities are equal

Answer

x² − 2x + 1 is the expanded form of (x − 1)², so both expressions are always identical.

Question 5

Given x + y = 8 and xy = 12. Compare: Column A: x² + y² | Column B: 40

Accepted Answer

The two quantities are equal

Answer

Using x² + y² = (x+y)² − 2xy = 64 − 24 = 40, so both columns are equal.

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