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# Data Sufficiency: Plugging into Yes/No Data Sufficiency

If $$z$$ is a positive three-digit integer, is $$z$$ a multiple of 7? >(1) All of the factors of 133 are factors of $$z$$. >(2) If the number of hundreds in $$z$$ is multiplied by 2 and then added to the remaining two-digit number, the result is divisible by 7.
Correct. [[snippet]] According to Stat. (1), all of the factors of 133 are also factors of $$z$$. That means that if 7 is a factor of 133, then the answer to the question stem is "__Yes__." If you divide 133 by 7, you get 19. (You could also notice that 133 is 7 less than 140, so it is a multiple of 7.) So 7 is a factor of 133. Hence, **Stat.(1) → Yes → S → AD**. For Stat. (2), __Plug In__ values for $$z$$. Try $$z = 133$$. The number of hundreds in 133 is 1 (hundred). And so, >$$(\text{Number of hundreds} \times 2) + \text{Remaining two-digit number}$$ >$$= (1 \times 2) + 33 = 35$$, which is divisible by 7 as the statement says. Now answer the question. The answer is "__Yes__." In fact, after __Plugging In__ $$z = 133$$, it may become clearer to you that Stat. (2) is just the divisibility test for 7. Therefore, the answer for Stat. (2) is a definite "__Yes__." Hence, **Stat.(2) → Yes → S → D**.
Incorrect. [[snippet]] For Stat. (2), __Plug In__ values for $$z$$. Try $$z = 133$$. The number of hundreds in 133 is 1 (hundred). And so, >$$(\text{Number of hundreds} \times 2) + \text{Remaining two-digit number}$$ >$$= (1 \times 2) + 33 = 35$$, which is divisible by 7 as the statement says. Now answer the question. The answer is "__Yes__." In fact, after __Plugging In__ $$z = 133$$, it may become clearer to you that Stat. (2) is just the divisibility test for 7. Therefore, the answer for Stat. (2) is a definite "__Yes__." Hence, **Stat.(2) → Yes → S → BD**.
Incorrect. [[snippet]] According to Stat. (1), all of the factors of 133 are also factors of $$z$$. That means that if 7 is a factor of 133, then the answer to the question stem is "__Yes__." If you divide 133 by 7, you get 19. (You could also notice that 133 is 7 less than 140, so it is a multiple of 7.) So 7 is a factor of 133. Hence, **Stat.(1) → Yes → S → AD**.
Incorrect. [[snippet]] According to Stat. (1), all of the factors of 133 are also factors of $$z$$. That means that if 7 is a factor of 133, then the answer to the question stem is "__Yes__." If you divide 133 by 7, you get 19. (You could also notice that 133 is 7 less than 140, so it is a multiple of 7.) So 7 is a factor of 133. Hence, **Stat.(1) → Yes → S → AD**.
Incorrect. [[snippet]] According to Stat. (1), all of the factors of 133 are also factors of $$z$$. That means that if 7 is a factor of 133, then the answer to the question stem is "__Yes__." If you divide 133 by 7, you get 19. (You could also notice that 133 is 7 less than 140, so it is a multiple of 7.) So 7 is a factor of 133. Hence, **Stat.(1) → Yes → S → AD**.
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.