GMAT Data Insights · Question of the Day

GMAT Data Insights Question of the Day

A fresh daily question to build accuracy, reinforce recall, and turn practice into a steady habit.

Friday, September 18, 2026

Is the system of equations $2x + 3y = 7$ and $ax + by = c$ inconsistent?

(1) $\frac{a}{2} = \frac{b}{3} ≠ \frac{c}{7}$ (2) $a = 4$ , $b = 6$ , and $c = 15$

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Question of the Day

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Is the system of equations $2x + 3y = 7$ and $ax + by = c$ inconsistent?

(1) $\frac{a}{2} = \frac{b}{3} ≠ \frac{c}{7}$ (2) $a = 4$ , $b = 6$ , and $c = 15$

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient to answer the question asked. (correct answer)

Explanation: A system is inconsistent when the coefficient ratios are equal but the constant ratio is different. For 2x + 3y = 7 and ax + by = c, inconsistency occurs when a/2 = b/3 but c/7 ≠ a/2 (equivalently c/7 ≠ b/3). Statement (1): This directly states the condition for inconsistency, so the system is inconsistent. Sufficient. Statement (2): a = 4, b = 6, c = 15. Check ratios: a/2 = 2, b/3 = 2, c/7 = 15/7 ≈ 2.14. Since a/2 = b/3 = 2 but c/7 ≠ 2, the system is inconsistent. Sufficient.