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Percents: Percent Translation

If $$b$$ is more than $$90\%$$ of $$a$$, is $$b \lt 65$$? >(1) $$a \gt 75$$ >(2) $$a - b\gt 5$$
According to Stat. (2), >$$a - b \gt 5$$. In words, that means that the difference between $$a$$ and $$b$$ is greater than 5. Remember the issue of the question: is $$b\lt 65$$? Try to __Plug In__ values for $$a$$ and $$b$$ that will be both greater and smaller than 65, and see whether they satisfy the requirement for a difference of 5. For simplicity's sake, take $$b$$ as exactly 90% of $$a$$. You can always assume that $$b$$ is slightly greater than 90% (say, 90.1%), but the difference is negligible. * If $$a = 60$$, then $$b = 54$$. In this case, $$b$$ could be a little more than 54, which satisfies the difference of 5 from $$a=60$$ but is smaller than 65, giving an answer of "Yes." * If $$a = 70$$, then $$b = 63$$. In this case, $$b$$ could be 64, which is less than 65, so it's still "Yes." * _However_, if $$a = 80$$, then $$b = 72$$. In this case, $$b$$ could be 73, which satisfies the difference of 5 from $$a=80$$ but is greater than 65, giving an answer of "No." Thus, there is no definite answer, so **Stat.(2) → IS → A**.
Incorrect. [[snippet]] According to Stat. (1), $$a$$ can be 76, 77, 78, or even 10,000, so obviously it is possible to find an $$a$$ large enough for $$b$$ to be greater than 65 ("No"). But is it always "No"? If $$a \gt 75$$, then $$b$$ must be greater than 90% of 75. Use 10% blocks: You can calculate that 10% of 75 is 7.5. Thus, 90% of 75 will equal >$$9 \times 7.5 = (10-1) \times 7.5 = 75-7.5 = 67.5$$. Thus, $$b$$ must in any case be greater than 67.5, which will make it greater than 65. That's a definite "No," but that is still a single definite answer to the question stem, which means that it is sufficient. **Stat.(1) → S → AD**.
Incorrect. [[snippet]] According to Stat. (2), >$$a - b \gt 5$$. In words, that means that the difference between $$a$$ and $$b$$ is greater than 5. Remember the issue of the question: is $$b\lt 65$$? Try to __Plug In__ values for $$a$$ and $$b$$ that will be both greater and smaller than 65, and see whether they satisfy the requirement for a difference of 5. For simplicity's sake, take $$b$$ as exactly 90% of $$a$$. You can always assume that $$b$$ is slightly greater than 90% (say, 90.1%), but the difference is negligible. * If $$a = 60$$, then $$b = 54$$. In this case, $$b$$ could be a little more than 54, which satisfies the difference of 5 from $$a=60$$ but is smaller than 65, giving an answer of "Yes." * If $$a = 70$$, then $$b = 63$$. In this case, $$b$$ could be 64, which is less than 65, so it's still "Yes." * _However_, if $$a = 80$$, then $$b = 72$$. In this case, $$b$$ could be 73, which satisfies the difference of 5 from $$a=80$$ but is greater than 65, giving an answer of "No." Thus, there is no definite answer, so **Stat.(2) → IS → ACE**.
Correct. [[snippet]] According to Stat. (1), $$a$$ can be 76, 77, 78, or even 10,000, so obviously it is possible to find an $$a$$ large enough for $$b$$ to be greater than 65 ("No"). But is it always "No"? If $$a \gt 75$$, then $$b$$ must be greater than 90% of 75. Use 10% blocks: You can calculate that 10% of 75 is 7.5. Thus, 90% of 75 will equal >$$9 \times 7.5 = (10-1) \times 7.5 = 75-7.5 = 67.5$$. Thus, $$b$$ must in any case be greater than 67.5, which will make it greater than 65. That's a definite "No," but that is still a single definite answer to the question stem, which means that it is sufficient. **Stat.(1) → 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.
EACH 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.
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