Sets: Table A/not A - How to Set a Table
All of the students who took a certain test answered the two first questions on the test. If 60% of the students answered the first question on the test correctly, and 40% of the students answered the second question on the test correctly, then what percent of the students answered neither of the two questions correctly?
>(1) 20% of the students answered both the first and the second questions on the test correctly.
>(2) Two-thirds of the students who did not answer the second question on the test correctly answered the first question on the test correctly.
For Stat. (2), add "{color:dark-blue}two-thirds of the students who did not answer the second question on
the test correctly answered the first question on the test
correctly{/color}" to the table. Since Total / Not 2 equals 60, write $$\frac{2}{3}$$ of $$60=\color{blue}{40}$$ in 1 / Not 2.
| | 2 | Not 2 | Total |
|-------|----|---------------------------------------------------------|------------------------------------|
| 1 | | $$\color{blue}{40}$$ | $$60$$ |
| Not 1 | | $$?=\color{green}{20}$$ | $$40$$ |
| Total | $$40$$ | $$60$$ | $$100$$ |
By completing the Not 1 / 2 column, you can determine the required quantity.
Note that although the question asks for percents, taking the
value Not 1 / Not 2 out of 100 students in the class still yields a
percentage—another reason why __Plugging In__ 100 is a good
idea whenever percents are involved. Thus, **Stat.(2) → S → D**.
Incorrect.
[[snippet]]
Make sure that you work according to the DS work order. You ought
to give each statement a fair chance to prove itself sufficient. It is
true that Stat. (1) is sufficient, but what about Stat. (2)?
Incorrect.
[[snippet]]
Make sure that you work according to the DS work order. You ought
to
give each statement a fair chance to prove itself sufficient. It is
true that Stat. (2) is sufficient, but what about Stat. (1)?
Incorrect.
[[snippet]]
Make sure that you work according to the DS work order. You ought to
give each statement a fair chance to prove itself sufficient. In this
question, *either one* of the statements is sufficient.
Incorrect.
[[snippet]]
Make sure that you work according to the DS work order. You ought to
give each statement a fair chance to prove itself sufficient. In this
question, *either one* of the statements is sufficient.
Correct.
[[snippet]]
Before you continue, you can calculate two other values:
| | 2 | Not 2 | Total |
|-------|----------------------------------|------------------------------------|------------------------------------|
| 1 | | | $$60$$ |
| Not 1 | | $$?$$ | $$\color{green}{40}$$ |
| Total | $$40$$ | $$\color{green}{60}$$ | $$100$$ |
For Stat. (1), add "{color:dark-blue}20% of the students answered both the first and the second questions on the test correctly{/color}" to the table. Write "{color:dark-blue}20{/color}" in the 1 / 2 box. Complete the table to find out the required quantity:
| | 2 | Not 2 | Total |
|-------|----------------------------------|------------------------------------|------------------------------------|
| 1 | $$\color{blue}{20}$$ | $$\color{green}{40}$$ | $$60$$ |
| Not 1 | | $$?=\color{green}{20}$$ | $$40$$ |
| Total | $$40$$ | $$60$$ | $$100$$ |
Note that although the question asks for percents, taking the
value Not 1 / Not 2 out of 100 students in the class still yields a
percentage—another reason why __Plugging In__ 100 is a good
idea whenever percents are involved. The information in Stat. (1) enables you to uniquely determine the value of the required quantity, so **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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