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# Data Sufficiency: Yes/No Basic Technique

If $$a$$, $$b$$, and $$i$$ are integers, is $$4(3b + 2) = 5a$$? >(1) If $$i$$ is divided by 5, then the quotient is $$a$$ and the remainder is 3. >(2) If $$i$$ is divided by 12, then the quotient is $$b$$ and the remainder is 11.
According to Stat. (1+2), >$$i = 5a + 3$$ >$$i = 12b + 11$$ Since they both equal $$i$$, you can set them equal to each other: >$$5a + 3 = 12b + 11$$. At this point, the fact that you see $$5a$$ should lead you to try to manipulate the equation to see if you can get $$5a = 4(3b+2)$$: >$$5a = 12b + 11 - 3$$ >$$5a = 12b + 8$$ >$$5a = 4(3b + 2)$$. Thus, the combination of the statements tells you that the equation in the question stem is always correct. That's a definite "Yes," so **Stat.(1+2) → Yes → S → C**.
Incorrect. [[snippet]] According to Stat. (1+2), >$$i = 5a + 3$$ >$$i = 12b + 11$$ Since they both equal $$i$$, you can set them equal to each other: >$$5a + 3 = 12b + 11$$. At this point, the fact that you see $$5a$$ should lead you to try to manipulate the equation to see if you can get $$5a = 4(3b+2)$$: >$$5a = 12b + 11 - 3$$ >$$5a = 12b + 8$$ >$$5a = 4(3b + 2)$$. Thus, the combination of the statements tells you that the equation in the question stem is always correct. That's a definite "Yes," so **Stat.(1+2) → Yes → S → C**.
Incorrect. [[snippet]] According to Stat. (1), >$$i = 5a + 3$$. Even if you find a definite value for $$a$$ from this equation, $$b$$ can have any value. There is no definite answer, so **Stat.(1) → No → IS → BCE**. According to Stat. (2), >$$i = 12b + 11$$. Even if you find a definite value for $$b$$ from this equation, $$a$$ can have any value. There is no definite answer, so **Stat.(2) → No → IS → CE**.
Incorrect. [[snippet]] According to Stat. (2), >$$i = 12b + 11$$. Even if you find a definite value for $$b$$ from this equation, $$a$$ can have any value. There is no definite answer, so **Stat.(2) → No → IS → ACE**.
Incorrect. [[snippet]] According to Stat. (1), >$$i = 5a + 3$$. Even if you find a definite value for $$a$$ from this equation, $$b$$ can have any value. There is no definite answer, so **Stat.(1) → No → IS → BCE**.
Correct. [[snippet]] According to Stat. (1), >$$i = 5a + 3$$. Even if you find a definite value for $$a$$ from this equation, $$b$$ can have any value. There is no definite answer, so **Stat.(1) → No → IS → BCE**. According to Stat. (2), >$$i = 12b + 11$$. Even if you find a definite value for $$b$$ from this equation, $$a$$ can have any value. There is no definite answer, so **Stat.(2) → No → IS → CE**.
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.