Four values from a data set of 5 elements are 10, 10, 11, and 11. What

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable, x which is the fifth data value and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1):
The fifth data value could be \(x = 9\) or \(x = 12\).
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2):
\(\frac{( x + 10 + 10 + 11 + 11 )}{5} > 10\)
\(=> x + 10 + 10 + 11 + 11 > 50\)
\(=> x + 42 > 50\)
\(=> x > 8\)
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2) :
Condition 1) tells us that \(x = 9\) or \(x = 12\), and condition 2) tells us that \(x > 8\).
So, \(x = 9\) or \(x = 12\).
Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

Answer: E

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

Statement 1:
If the fifth number is 9, range = 11-9=2.
If the fifth number is 12 range = 12-10=2.
So, fifth number can be 9 or 12.
INSUFFICIENT.

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Statement 2:
Average of five numbers is GREATER than 10. That means, TOTAL of the five numbers is greater than 50.
Sum of know four numbers is 42.
So, the fifth number will be GREATER than 8. That is, the fifth number can be anything such as 9,10,11,12, etc.
INSUFFICIENT.

Combining both statements,
9 &12 Are common in both statements (9&12 suffice both statements).
So, the fifth number can be 9 or 12.
INSUFFICIENT.

E answer

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