Data set A consists of 10 positive integers less than 60 . The list shown gives 9 of the integers

Question

Data set A consists of 10 positive integers less than 60 . The list shown gives 9 of the integers from data set A. 43 , 45 , 44 , 43 , 38 , 39 , 40 , 46 , 40 The mean of these 9 integers is 42 . If the mean of data set A is an integer that is greater than 42 , what is the value of the largest integer from data set A?

Accepted Answer

The correct answer is 52 . The mean of a data set is calculated by dividing the sum of the data values by the number of values. It&rsquo;s given that data set A consists of 10 values, 9 of which are shown. Let x represent the 10 th data value in data set A, which isn&rsquo;t shown. The mean of data set A can be found using the expression 43 + 45 + 44 + 43 + 38 + 39 + 40 + 46 + 40 + x 10 , or 378 + x 10 . It&rsquo;s given that the mean of the 9 values shown is 42 and that the mean of all 10 numbers is greater than 42 . Consequently, the 10 th data value, x , is larger than 42 . It&rsquo;s also given that the data values in data set A are positive integers less than 60 . Thus, 42 < x < 60 . Finally, it&rsquo;s given that the mean of data set A is an integer. This means that the sum of the 10 data values, 378 + x , is divisible by 10 . Thus, 378 + x must have a ones digit of 0 . It follows that x must have a ones digit of 2 . Since 42 < x < 60 and x has a ones digit of 2 , the only possible value of x is 52 . Since 52 is larger than any of the integers shown, the largest integer from data set A is 52 .

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