# CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

###### CAT Questions | Averages | Averages

The question is from CAT Ratio, Mixtures and Averages. Details about average of 5 numbers are given and our task is to arrange them in ascending order. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019.

Question 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.

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### Explanatory Answer

##### Method of solving this CAT Question from Ratio, Mixtures and Averages: Given a set of numbers, mean of the overall set, how does one arrange them in ascending order.

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

The question is "Write down a, d, c, d and e in ascending order."

##### Hence, the answer is "Ascending order should be e, c, a, d, b".

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