Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. If P is the smallest five-digit number in the range 10000 to 99999 that leaves a remainder of 4 when divided by 6, 8, 10, and 15 Quantity I: The remainder when P is divided by 11 Quantity II: 5

  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 No relation
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A Correct answer
AI explanation

First, find the least common multiple (LCM) of the divisors 6, 8, 10, and 15, which equals 120. The smallest five-digit number is 10000, and dividing this by 120 gives a quotient of 83 with a remainder of 40, meaning the next multiple of 120 is found by calculating 84 * 120 = 10080. Adding the specific remainder of 4 gives P = 10084. Dividing 10084 by 11 gives a quotient of 916 with a remainder of 8. Since 8 is greater than 5, Quantity I > Quantity II.

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