CAT 2022 Averages Question (Medium)

Question

The average of a non-decreasing sequence of numbers is 300. If is replaced by , the new average becomes 400. Then, the number of possible values of is

Accepted Answer

Step 1 Define Variables and Initial Equations Let be the number of elements in the sequence. Let the original sequence be . The sequence is non-decreasing, so . The average of the original sequence is 300. This means the sum of the original sequence is Equation 1 Step 2 Formulate the Equation for th

CAT 2022

Quantitative

Averages

Medium

The average of a non-decreasing sequence of $N$ numbers $a_1, a_2, \ldots, a_N$ is 300. If $a_1$ is replaced by $6a_1$ , the new average becomes 400. Then, the number of possible values of $a_1$ is

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