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What is x, if the average of five numbers, x, 6, 3, 15 and 12 is equal to the median?
(1)  6 < x < 12
(2)  x is median of the five numbers
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 
  • c)
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 
  • d)
    EACH statement ALONE is sufficient. 
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is x, if the average of five numbers, x, 6, 3, 15 and 12 is equal...
Steps 1 & 2: Understand Question and Draw Inferences
Arithmetic mean is same as median
  • As there are five elements, median must be one of them
 
Step 3: Analyze Statement 1
6<x<12
  • As x is less than two numbers (12, 15) and greater than the other two (3, 6), it must be the median
  • x is the average of all the numbers
It is given that the mean is same as the median
  • (3+6+12+15+x)/5 = x
  • 3+6+12+15+x = 5x
  • 4x = 36
  • x = 9
Therefore statement 1 is sufficient.
 Step 4: Analyze Statement 2
x is median of the five numbers
It is given that the mean is same as the median
  • (3+6+12+15+x)/5 = x
  • 3+6+12+15+x = 5x
  • 4x = 36
  • x = 9
Therefore statement 2 is sufficient.
Step 5: Analyze Both Statements Together (if needed)
We get a unique answer in step 3 and step 4, so this step is not required
Answer: Option (D)
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Most Upvoted Answer
What is x, if the average of five numbers, x, 6, 3, 15 and 12 is equal...
How can 1 be sufficient?

x lies between 6&12 hence it could be 7,8,9,10,11.

How did we presume that the mean of the five nos is x in the first case?! It doesn't say that x is the median in the statement 1!!

Hence only statement 2 should be sufficient because it says clearly that x is the median. And hence as inferred from original question - The avg of the nos is equal to median.
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