CA Foundation · Quantitative Aptitude · Linear Inequalities
If p > q and m is a negative real number, which of the following statements must be true?
The correct statement is pm < qm. When both sides of an inequality are multiplied by a negative number, the inequality sign reverses. So p > q becomes pm < qm when m is negative, whereas adding m alone would leave the direction unchanged.
- Apm > qm
- Bpm < qmCorrect
- Cp + m < q + m
- Dp/m > q/m
Explanation
Multiplying both sides of an inequality by a negative number reverses its direction. Since p > q and m < 0, pm < qm. Option 1 keeps the original direction and is wrong. Adding m to both sides keeps the direction, so p + m > q + m, which makes option 3 wrong. Dividing by m also reverses it, so p/m < q/m, and option 4 is wrong.
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