CAT Practice : Averages, Ratios, Mixtures

Change in average

    Q.18: Consider 5 distinct positive numbers a, b, c, d, and e. The average of these numbers is k. If we remove b from this set, the average drops to m (m is less than k). Average of c, b, d and e is K. We also know that c is less than d and e is less than k. The difference between c and b is equal to the difference between e and d. Average of a, b, c and e is greater than m. Write down a, d, c, d and e in ascending order.


  • Correct Answer
    Ascending order should be e, c, a, d, b.

Detailed Solution

Average of a, b, c, d and e is k, Average of b, c, d and e is also k, this implies that a = k.

If we remove b, the average drops, this implies that b is higher than the average.
e is less than k, or e is less than a. c is less than d.

e < a < b, c < d
Average of a, b, c and e is greater than average a, c, d and e. This tells us that d < b

From this, we get that b is the largest number

b - c = d - e
b + e = c + d
a + b + c + d + e = 5a
Or, b + c + d + e = 4a

b + e = 2a, c + d = 2a. Or, e, a, b is an AP, c, a, d is an AP.

e is the smallest number (as b is the largest number).

Or, the ascending order should be e c a d b

Correct Answer: Ascending order should be e, c, a, d, b

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