x1, x2, …, x10 are real numbers. a1 = x1, a2 is defined as the average of {x1, x2}, a3 as the average of {x1, x2, x3

[Max@Math Revolution]

[GMAT math practice question]

x1, x2, …, x10 are real numbers. a1 = x1, a2 is defined as the average of {x1, x2}, a3 as the average of {x1, x2, x3}, ….., a10 as the average of {x1, x2,…,x10}. What is the value of x10?

1) a1 = 5
2) an+1 = an+2

[Max@Math Revolution]

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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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since we have 10 variables (x1, x2,…,x10) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

a10 = (x1 + x2 + … + x10) / 10 and a9 = (x1 + x2 + … + x9) / 9
x10 = 10a10 – 9a9

a10 = a1 + 9*2 = 5 + 18 = 23.
a9 = a1 + 8*2 = 5 + 16 = 21.
x10 = 10a10 – 9a9 = 10*23 – 9*21 = 230 – 189 = 41.

Since both conditions together yield a unique solution, they are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

However, each condition alone does not provide enough information on its own, and therefore neither condition alone is sufficient.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.