# Data Sufficiency: Yes/No Basic Technique

If $$t$$ is a positive integer, is $$t$$ a multiple of $$3$$? >(1) $$3$$ is a factor of $$\frac{t}{4}$$. >(2) $$4t+3$$ is a multiple of $$3$$.
Incorrect. [[snippet]] In this question, either one of the statements is __Sufficient__.
Correct. [[snippet]] Stat. (1): If 3 is a factor of $$\frac{t}{4}$$, then $$\frac{t}{4}$$ is a multiple of 3, so >$$\frac{t}{4} = 3 \times \text{Some integer}$$. Multiply this equation by 4 to get >$$t = 12 \times \text{Some integer}$$. Thus, It follows that $$t$$ is a multiple of 12 and is therefore also a multiple of 3. This is a definite "Yes," so **Stat.(1) → S → AD**. Stat. (2): First isolate the equation: >$$4t+3 = \text{Multiple of 3}$$ >$$4t = (\text{Multiple of 3}) - 3$$. Now recall the rules of adding and subtracting multiples: >$$\text{Multiple of } n \pm \text{Multiple of } n = \text{Multiple of } n$$. Since $$4t$$ is the difference between multiples of 3, it _must_ be a multiple of 3. Since 4 is not a multiple of 3, $$t$$ itself must be a multiple of 3 for the product to be divisible by 3. This is a definite "Yes," so **Stat.(2) → S → D**.
Incorrect. [[snippet]] In this question, either one of the statements is __Sufficient__.
Incorrect. [[snippet]] Yes, Stat. (2) is __Sufficient__, but what about Stat. (1)?
Incorrect. [[snippet]] Yes, Stat. (1) is __Sufficient__, but what about Stat. (2)?
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.