Five positive integers, not necessarily distinct, have a mean of and a median of . What is the greatest possible value of the largest of the five integers?
Answer and explanation
Correct answer: C.
- Step 1: Let the ordered integers be . The total sum is , and the median is .
- Step 2: To maximize , minimize , , and . Since all values are positive integers, the smallest choices are and . Since , the smallest allowable value for is .
- Step 3: Substitute into the sum equation: .
Answer
.
Why not the others: uses instead of positive integers ( with no median constraint); allows , violating the median definition; subtracts from ; uses instead of minimizing .
Practise more Data analysis.
Free questions with an explanation for every one, and full timed GRE mock tests.
More Data analysis questions
- The average of numbers is . When a new number, , is added, what is the new average?
- A data set has a standard deviation of . Every value is multiplied by , and then is added to each result. What is the standard dev…
- Two fair six-sided dice are rolled. Given that the dice do not show the same number, what is the probability that the sum is a prime number?
- How many integers from to , inclusive, have digits that add up to ?
- An urn contains red, blue, and green marbles. Three marbles are drawn at random without replacement. What is the probability tha…
- The average of numbers is . When the largest number is removed, the average of the remaining numbers is . When the smallest…