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The arithmetic mean of 22.5, 56, 42.5, 2x+1, xтИТ2, 3x, 36 is 30. Find x, where x>0.
9
7
6
4
9
Sum all known constants first (22.5 + 56 + 42.5 + 1 - 2 + 36 = 156) and the variables (2x + x + 3x = 6x). Since the sum is 30 * 7 = 210, we have 156 + 6x = 210, leading directly to 6x = 54.
A set of seven numbers: 22.5, 56, 42.5, 2x + 1, x - 2, 3x, 36. The arithmetic mean is 30. x > 0.
Mean=nтИСxiтАЛтАЛ
Sum all known constants first (22.5 + 56 + 42.5 + 1 - 2 + 36 = 156) and the variables (2x + x + 3x = 6x). Since the sum is 30 * 7 = 210, we have 156 + 6x = 210, leading directly to 6x = 54.
Carelessly summing the numbers or miscounting the total number of terms (n=7), which often leads to errors in the division step.
Define the sum of the terms
To find the mean, we sum the seven provided terms: 22.5+56+42.5+(2x+1)+(xтИТ2)+3x+36.
Sum=156+6x
Set up the mean equation
Since the mean of 7 terms is 30, the total sum must be 30├Ч7=210.
7156+6xтАЛ=30
Solve for x
Multiply by 7 to get 156+6x=210, then subtract 156 to get 6x=54. Dividing by 6 yields x=9.
x=654тАЛ=9
A is correct because the calculation 6x=54 results in x=9, which matches option A.
This concept of 'Mean' is foundational for Data Interpretation (DI) problems often found in competitive exams, where finding missing values in a set is a common pattern.
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