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The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, then the mean of the largest three numbers is divisible by which of the following?
- 2
- 3
- 13
- 14
Correct answer: 3
Solution
Sum of all 4 numbers = 4*37 = 148. Sum of smallest 3 = 3*34 = 102. Largest number = 148 - 102 = 46. Range = largest - smallest = 15, so smallest = 46 - 15 = 31. Mean of largest three = (148 - 31)/3 = 117/3 = 39. The number 39 = 3*13, so it is divisible by both 3 and 13.
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