Multiple choice

Directions: The following problem consists of a question and two statements labelled as (1) and (2). You have to decide whether the data given in the statements is sufficient to answer the question. Mark the appropriate choice from (1) to (4). Can we find the value of the eleventh number in a set of eleven numbers, if (1) the average of the first ten numbers in the set is given (2) the average of all the eleven numbers is given

  1. statements (1) and (2) together are not sufficient

  2. statements (1) and (2) taken together are sufficient but neither statement (1) alone nor statement (2) alone is sufficient

  3. statement (1) alone is sufficient, but statement (2) alone is not sufficient

  4. statement (2) alone is sufficient, but statement (1) alone is not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the set be x1, ..., x11. (1) gives the sum of the first 10. (2) gives the sum of all 11. Subtracting the sum of the first 10 from the sum of all 11 gives the 11th number. Both are required.

AI explanation

The average formula dictates that the sum of the first ten numbers equals ten times their average. Using both statements, the value of the eleventh number is found by taking the sum of all eleven numbers, which is eleven times the second average, and subtracting the sum of the first ten numbers. Neither statement provides the sums independently, so both statements taken together are sufficient.

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