Multiple choice

Does the average age of the class decrease if ten new students join the class? (1) Nine out of ten new students have age greater than the average of the class. (2) The eldest among the ten has age less than the new average (i.e. the average ages including these students).

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original sum be S and count be n. Average = S/n. New average = (S + sum of 10)/(n+10). Statement 2 says the eldest of the 10 is less than the new average. If the largest of the new items is less than the new average, then all new items are less than the new average, which forces the average to decrease.

AI explanation

Statement 2 alone is sufficient because if the eldest of the ten new students is younger than the new average, the new average must be lower than the old average, proving the decrease. Statement 1 alone is not sufficient because it only compares the new students to the old average and lacks the necessary information to establish the new average. Therefore, statement 2 alone is sufficient to answer the question, but statement 1 alone is not.

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