GMAT® Problem Solving : Arithmetic Mean

Concept: Finding average of a set of numbers based on data from another set of numbers.

This GMAT practice question is a problem solving question testing basics of computing arithmetic mean (average) of a set of numbers.

Question: If the mean of numbers 28, x, 42, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x?

  1. 78
  2. 58
  3. 390
  4. 310
  5. 66

Video Explanation

Scroll for explanatory answer text

Explanatory Answer

Use these hints and try

  1. Find out the sum of the 4 numbers other than x in each case.
  2. Apportion the difference between the two sums equally to all the 5 numbers.

Step 1: Find the sum of both the series

x is common to both the series. So, x is not going to make a difference to the average.

Only the remaining 4 numbers will contribute to the difference in average between the two series.

Sum of the 4 numbers, excluding x, of the first series is 28 + 42 + 78 + 104 = 252

Sum of the 4 numbers, excluding x, of the second series is 48 + 62 + 98 + 124 = 332

Step 2: Difference in the sum of the two series

The difference between the sum of the two sets of numbers = 332 - 252 = 80

Step 3: The average of the second series is

The sum of the second series is 80 more than the sum of the first series.

If the sum of the second series is 80 more, the average of the second series will be \\frac{80}{5}) = 16 more than the first series.

Therefore, the average of the second series = 62 + 16 = 78.

Alternative Approach

Observe that each number in the new series, with the exception of "x", has increased by 20

This will increase the overall sum of the second series by 4 * 20 = 80

The overall sum increasing by 80 is the equivalent of each number in the series increasing by \\frac{80}{5}) = 16

If each number in the series increases by 16 the average will increase by 16 to 78

Complete Explanation

x is common to both the series. So, x is not going to make a difference to the average.

Only the remaining 4 numbers will contribute to the difference in average between the two series.

Sum of the 4 numbers, excluding x, of the first series is 28 + 42 + 78 + 104 = 252

Sum of the 4 numbers, excluding x, of the second series is 48 + 62 + 98 + 124 = 332

The difference between the sum of the two sets of numbers = 332 - 252 = 80

The sum of the second series is 80 more than the sum of the first series.

If the sum of the second series is 80 more, the average of the second series will be \\frac{80}{5}) = 16 more than the first series.

Therefore, the average of the second series = 62 + 16 = 78.

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