Data Sufficiency

[Math Revolution GMAT math practice question]

What is the value of f(10)?

1) f(x) = 2 for 0 ≤ x < 3
2) f(x+3) = 2f(x)

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the value of f(10)?

1) f(x) = 2 for 0 ≤ x < 3
2) f(x+3) = 2f(x)

The proposer´s idea (when both statements are considered together) is probably based on the following:

$$f\left( {10} \right) = 2 \cdot f\left( 7 \right) = {2^2} \cdot f\left( 4 \right) = {2^3} \cdot f\left( 1 \right) = {2^4}$$

If so, there is a continuity problem related to the (not defined) interval (if it is an interval!) in which the rule given by statement (2) applies.

In other words, the problem is not well-stated.

Regards,
Fabio.

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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.

When asked about a function, we assume there are many variables so that E is most likely to be the answer.

Conditions 1) & 2):
Repeatedly applying condition 2) gives f(10) = 2f(7), f(7) = 2f(4) and f(4) = 2f(1), so that f(10) = 2f(7) = 4f(4) = 8f(1).
Since f(1) = 2 by condition 1), f(10) = 8*2 = 16.
Both conditions together are sufficient.

It is easy to see that neither condition is sufficient on its own.

Therefore, C is the answer.
Answer: C