Multiple choice

Directions: The question given below consists of a statement followed by Quantity I and Quantity II. Find the relationship between the quantities and choose the answer accordingly. The average marks obtained by Khalil in four tests were 73.5. When the marks of the fifth tests were added, the average increased by 2.9. Quantity I: If the marks obtained by Khalil in the first test were marked 76 but the original marks were 67, what would be the new average for five tests? Quantity II: If the marks obtained by Khalil in the each of the first three tests were increased by 2 and in each of the last two tests were decreased by 8, then what would be the new average for the five tests?

  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 relationship cannot be established
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A Correct answer
Explanation

Original sum of 4 tests = 73.5 * 4 = 294. Adding a 5th test increases the average by 2.9, so the new average is 76.4 and the sum is 382. The 5th test mark is 382 - 294 = 88. Quantity I: New sum = 382 - 67 + 76 = 391, new average = 391 / 5 = 78.2. Quantity II: Total change = (3 * 2) + (2 * -8) = 6 - 16 = -10. New average = 76.4 - (10 / 5) = 74.4. Since 78.2 > 74.4, Quantity I > Quantity II.

AI explanation

Khalil's total marks for the first four tests were 73.5 times 4, equaling 294. When the fifth test is added, his new total for five tests becomes (73.5 plus 2.9) multiplied by 5, which is 382. For Quantity I, changing the first test score from 67 to 76 increases the total by 9, so the new average is (382 plus 9) divided by 5, resulting in 78.2. For Quantity II, increasing three tests by 2 and decreasing two tests by 8 gives a total change of 6 minus 16, a decrease of 10, so the new average is (382 minus 10) divided by 5, resulting in 74.4. Therefore, Quantity I is greater than Quantity II.

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