If p q r 15 Quantity I Maximum value of pqr if p q r are positive integers Quantity II Maximum value...........

Quantitative Aptitude (SBI-PO) Data Sufficiency

If p + q + r = 15.

Quantity I: Maximum value of pqr, if p, q, r are positive integers.

Quantity II: Maximum value of pqr, if p, q, r ≥ -10.

This questions was previously asked in

SBI PO Prelims (02 Jan, 2022)

QI > QII

QI < QII

QI ≤ QII

QI ≥ QII

Cannot be determined

- Quantity I considers maximizing \(pqr\) with the condition that \(p, q, r\) are positive integers.

- The best strategy is to distribute the sum \(p + q + r = 15\) as evenly as possible.

- A common choice is \(p = 5\), \(q = 5\), \(r = 5\). Thus, \(pqr = 5 \times 5 \times 5 = 125\).

- Quantity II allows \(p, q, r\) to include negative values, making them capable of much larger absolute values when negative.

- To maximize, using extreme values like \(p = 40\), \(q = -10\), \(r = -15\) gives \(pqr = 40 \times (-10) \times (-15) = 6000\).

- Answer: By comparing, \(125 < 6000\).

- Correct Answer: Option 2: QI < QII.

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