rencsee wrote:

A group of students is preparing for Reading Comprehension, 70% of the students read frequently The

Economist and 60% of the students read frequently the Wall Street Journal to get better at Reading Comprehension. What percentage of all the students in the group don't read frequently either of the two journals?

1. There are 80 students in the group.

2. 40% of the students read frequently both journals.

Information given:

70% of the students read The

Economist.

60% of the students read the Wall Street Journal.

These percentages will be the same no matter how many students there are.

If there are 100 students:

70 students read the

Economist.

60 students read the Wall Street Journal.

If there are 50 students:

35 students read the

Economist.

30 students read the Wall Street Journal.

The number of students does not affect the percentages, it only affects the absolute number that each percentage represents.

Question:

What percentage of all the students in the group don't read frequently either of the two journals?

Statement 1: There are 80 students in the group.

Since we have only percentage information, this answer has no effect on our ability to determine what percentage of students do not read either.

For example we could have:

70% of 80 = 56 read the

Economist.

60% of 80 = 48 read the Wall Street Journal.

4 read both.

0 read neither.

or we could have:

70% of 80 = 56 read the

Economist.

60% of 80 = 48 read the Wall Street Journal.

All of the people who read the

Economist read the Wall Street Journal as well. So, 48 read both.

24 read neither.

Insufficient.

Statement 2: 40% of the students read frequently both journals.

With this information we can tell how much overlap there is between the percentage of students who read the

Economist and the percentage who read the Wall Street Journal.

This overlap in percentage terms will be the same regardless of the number of students.

If there are 100 students:

70 students read the

Economist.

60 students read the Wall Street Journal.

40% of 100 = 40 read both.

So the overlap is 40 students.

A + B - Both + Neither = Total

70 + 60 - 40 + Neither = 100

Neither = 10

10/100 = 10%

If there are 50 students:

35 students read the

Economist.

30 students read the Wall Street Journal.

40% of 50 = 20 read both.

So the overlap is 20 students.

A + B - Both + Neither = Total

35 + 30 - 20 + Neither = 50

Neither = 5

5/50 = 10%

For any number of students, the Neither percentage will be 10%.

Sufficient.

The correct answer is (B).

_________________

Marty Murray

Chief Curriculum and Content Architect

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