GMAT Maths | GMAT Statistics Questionbank

GMAT Sample Questions | Average | Arithmetic Mean

This GMAT practice question is a problem solving question testing basics of computing arithmetic mean (average) of a set of numbers. An easy GMAT 600 level Math sample question.

Question 1: 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

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Explanatory Answer

Hints to solve this GMAT Statistics question
  1. Find out the sum of the 4 numbers other than x in both scenarios.
  2. Apportion the difference between the two sums equally to all the 5 numbers.
Step 1 of solving this GMAT Statistics Question: 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 of solving this GMAT Statistics Question: Difference in the sum of the two series

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

Step 3 of solving this GMAT Statistics Question: Calculating the average of the second series

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 than that of the first series, 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

Choice A is the correct answer.

 

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