Multiple choice

Directions: In the following question, you have to compare Quantity I and Quantity II and then determine which of the following options describes the comparison. a + b + c = 5 ab + bc + ca = 8 Quantity I: Value of a2 + b2 + c2 Quantity II: 6

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I Quantity II

  4. Quantity I ≥ Quantity II

  5. No relation
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A Correct answer
Explanation

Using a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + bc + ca), the value is 25 - 16 = 9. Since 9 > 6, Quantity I is greater than Quantity II.

AI explanation

Use the algebraic identity (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) to find the required value. Substituting the given values results in 52 = a2 + b2 + c2 + 2(8), which simplifies to 25 = a2 + b2 + c2 + 16. Solving this gives a2 + b2 + c2 = 9, making Quantity I greater than Quantity II.

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