Averages: The Average Pie
The difference between John's and Paul's heights is twice the difference between John's and Thom's heights. If John is the tallest, what is the average (arithmetic mean) height of the three?
>(1) Paul is 163 centimeters tall.
>(2) Thom is 173 centimeters tall.
According to Stat. (2), $$T=173$$. Plug this into the equation:
>$$J+P = 2T$$
>$$J + P = 2(173) = 346$$
It may seem as if Stat. (2) is also insufficient, but now you know the value of $$T$$ and the sum of $$J$$ and $$P$$. That means that the sum of the three heights is
>$$(J+P)+T = 346 + 173 = 519$$.
So the average is $$\frac{519}{3} = 173$$, a specific value. **Stat.(2) → S → B**.
A more visual and intuitive way to think about this is that the conditions in the question stem tell you that Thom is exactly halfway between John and Paul in terms of height. If three values are equally spaced, their average is equal to the middle value. So the average of their heights *will be* Thom's height.
Incorrect.
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According to Stat. (1), $$P=163$$. Plug this into the equation:
>$$J = 2T-P$$
>$$J = 2T-163$$
This is insufficient to find $$J$$ and $$T$$ (or even their sum), in order to calculate the average. Stat.(1) → IS → BCE
Incorrect.
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According to Stat. (2), $$T=173$$. Plug this into the equation:
>$$J+P = 2T$$
>$$J + P = 2(173) = 346$$
It may seem as if Stat. (2) is also insufficient, but now you know the value of $$T$$ and the sum of $$J$$ and $$P$$. That means that the sum of the three heights is
>$$(J+P)+T = 346 + 173 = 519$$.
So the average is $$\frac{519}{3} = 173$$, a specific value. **Stat.(2) → S → BD**.
Correct.
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According to Stat. (1), $$P=163$$. Plug this into the equation:
>$$J = 2T-P$$
>$$J = 2T-163$$
This is insufficient to find $$J$$ and $$T$$ (or even their sum), in order to calculate the average. Stat.(1) → 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.
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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