Multiple choice

Passage

Directions: The question statement is followed by two quantities i.e. Quantity I and Quantity II. Select the option from given answer choices which reflects correct relationship between Quantity I and Quantity II as per the calculations based on question statement/s.

It is given that 4m + 12 x 162m – 12 = 643m – 20 and n2 – 30n + 216 = 0 Quantity I: Value of 'n'. Quantity II: Value of 'm'.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or cannot be calculated
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C Correct answer
Explanation

For the first equation, 4^(m+12) * 16^(2m-12) = 64^(3m-20) becomes 2^(2m+24) * 2^(8m-48) = 2^(18m-120). Equating exponents: 10m - 24 = 18m - 120, so 8m = 96, m = 12. For the second equation, n^2 - 30n + 216 = 0 factors to (n-12)(n-18) = 0, so n = 12 or 18. Comparing n and m: if n=12, n=m; if n=18, n>m. Thus n >= m.

AI explanation

By equating the bases in the first equation, 22m+24 times 232m-24 equals 263m-20, which simplifies to 234m = 263m-20 and m = 4. Factoring the second equation n2 - 30n + 216 = 0 gives (n - 18)(n - 12) = 0, yielding n = 18 or n = 12. Since both possible values for n are greater than or equal to m, Quantity I is greater than or equal to Quantity II.

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