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# Data Sufficiency: Yes/No Basic Technique

Is \$\$y-x < 60\$\$? >(1) When \$\$x\$\$ and \$\$y\$\$ are rounded to the nearest unit, the results are 15 and 75, respectively. >(2) When \$\$x\$\$ and \$\$y\$\$ are rounded to the nearest ten, the results are 20 and 70, respectively.
Incorrect. [[snippet]] Stat.(2): A rounded value of 20 when \$\$x\$\$ is rounded to the nearest ten allows values of >\$\$15 \le x \lt 25\$\$. Likewise, a rounded value of 70 when \$\$y\$\$ is rounded to the nearest ten allows values of >\$\$65 \le y \lt 75\$\$. Plug in the extremes: when \$\$y\$\$ and \$\$x\$\$ are the furthest they can be from each other (i.e., \$\$x=15\$\$ and \$\$y=74.99\$\$), the difference is \$\$74.99 - 15 = 59.99\$\$. So the difference between \$\$y\$\$ and \$\$x\$\$ must be smaller than 60. That's a definite "Yes," so Stat.(2) → Yes → S.
Incorrect. [[snippet]] Stat.(1): A rounded value of 15 when \$\$x\$\$ is rounded to the nearest unit allows values of >\$\$14.5 \le x \lt 15.5\$\$. Likewise, a rounded value of 75 when \$\$y\$\$ is rounded to the nearest unit allows values of >\$\$74.5 \le y \lt 75.5\$\$. Plug in the extremes. If \$\$x\$\$ and \$\$y\$\$ are the closest they can be to each other (i.e., \$\$x=15.49\$\$ and \$\$y=74.5\$\$), then \$\$y - x = 59.01\$\$, which is less than 60, and the answer is "Yes." Note that \$\$x\$\$ must be smaller than 15.5, so you can plug in a value that is very close to 15.5 (e.g., 15.49). But if \$\$x\$\$ and \$\$y\$\$ are the furthest they can be from each other (i.e., you have \$\$x=14.5\$\$ and \$\$y=75.49\$\$), then \$\$y - x = 60.99\$\$, which is greater than 60, and the answer is "No." So the answer is "Maybe," and Stat.(1) → Maybe → IS → BCE.
Incorrect. [[snippet]] Stat.(2): A rounded value of 20 when \$\$x\$\$ is rounded to the nearest ten allows values of >\$\$15 \le x \lt 25\$\$. Likewise, a rounded value of 70 when \$\$y\$\$ is rounded to the nearest ten allows values of >\$\$65 \le y \lt 75\$\$. Plug in the extremes: when \$\$y\$\$ and \$\$x\$\$ are the furthest they can be from each other (i.e., \$\$x=15\$\$ and \$\$y=74.99\$\$), the difference is \$\$74.99 - 15 = 59.99\$\$. So the difference between \$\$y\$\$ and \$\$x\$\$ must be smaller than 60. That's a definite "Yes," so Stat.(2) → Yes → S.
Stat.(2): A rounded value of 20 when \$\$x\$\$ is rounded to the nearest ten allows values of >\$\$15 \le x \lt 25\$\$. Likewise, a rounded value of 70 when \$\$y\$\$ is rounded to the nearest ten allows values of >\$\$65 \le y \lt 75\$\$. Plug in the extremes: when \$\$y\$\$ and \$\$x\$\$ are the furthest they can be from each other (i.e., \$\$x=15\$\$ and \$\$y=74.99\$\$), the difference is \$\$74.99 - 15 = 59.99\$\$. So the difference between \$\$y\$\$ and \$\$x\$\$ must be smaller than 60. That's a definite "Yes," so Stat.(2) → Yes → S → B.
Incorrect. [[snippet]] Stat.(1): A rounded value of 15 when \$\$x\$\$ is rounded to the nearest unit allows values of >\$\$14.5 \le x \lt 15.5\$\$. Likewise, a rounded value of 75 when \$\$y\$\$ is rounded to the nearest unit allows values of >\$\$74.5 \le y \lt 75.5\$\$. Plug in the extremes. If \$\$x\$\$ and \$\$y\$\$ are the closest they can be to each other (i.e., \$\$x=15.49\$\$ and \$\$y=74.5\$\$), then \$\$y - x = 59.01\$\$, which is less than 60, and the answer is "Yes." Note that \$\$x\$\$ must be smaller than 15.5, so you can plug in a value that is very close to 15.5 (e.g., 15.49). But if \$\$x\$\$ and \$\$y\$\$ are the furthest they can be from each other (i.e., you have \$\$x=14.5\$\$ and \$\$y=75.49\$\$), then \$\$y - x = 60.99\$\$, which is greater than 60, and the answer is "No." So the answer is "Maybe," and Stat.(1) → Maybe → IS → BCE.
Correct. [[snippet]] Stat.(1): A rounded value of 15 when \$\$x\$\$ is rounded to the nearest unit allows values of >\$\$14.5 \le x \lt 15.5\$\$. Likewise, a rounded value of 75 when \$\$y\$\$ is rounded to the nearest unit allows values of >\$\$74.5 \le y \lt 75.5\$\$. Plug in the extremes. If \$\$x\$\$ and \$\$y\$\$ are the closest they can be to each other (i.e., \$\$x=15.49\$\$ and \$\$y=74.5\$\$), then \$\$y - x = 59.01\$\$, which is less than 60, and the answer is "Yes." Note that \$\$x\$\$ must be smaller than 15.5, so you can plug in a value that is very close to 15.5 (e.g., 15.49). But if \$\$x\$\$ and \$\$y\$\$ are the furthest they can be from each other (i.e., you have \$\$x=14.5\$\$ and \$\$y=75.49\$\$), then \$\$y - x = 60.99\$\$, which is greater than 60, and the answer is "No." So the answer is "Maybe," and Stat.(1) → Maybe → IS → BCE.
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.