Consider the following inequalities.
(i) 3p − q < 4
(ii) 3q − p < 12
Which one of the following expressions below satisfies the above two inequalities?
Options:
(A) p + q < 8
(B) p + q = 8
(C) 8 ≤ p + q < 16
(D) p + q ≥ 16
Official Answer Key:
A
Step-by-Step Solution & Explanation
• Add (i) and (ii): (3p−q)+(3q−p) < 4+12 ⟹ 2p+2q < 16
• Dividing by 2: p+q < 8
• Distractor logic: (B),(C),(D) all propose p+q ≥ 8 in some form, contradicting the strict inequality derived.
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