Overlapping sets

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 am; Thanked: 14 times; Followed by:5 members

Overlapping sets

by Mo2men » Mon Jun 11, 2018 5:19 pm

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The Financial News Daily has 25 reporters covering Asia, 20 covering Europe, and 20 covering North America. Four reporters cover Asia and Europe but not North America, 6 reporters cover Asia and North America but not Europe, and 7 reporters cover Europe and North America but not Asia. How many reporters cover all of the 3 continents (Asia, Europe, and North America)?

(1) The Financial News Daily has 38 reporters in total covering at least 1 of the following continents: Asia, Europe, and North America.
(2) There are more Financial News Daily reporters covering only Asia than there are Financial News Daily reporters covering only North America.

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Source: Beat The GMAT — Data Sufficiency | Mon Jun 11, 2018 5:19 pm

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by GMATGuruNY » Mon Jun 11, 2018 6:14 pm

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Mo2men wrote:The Financial News Daily has 25 reporters covering Asia, 20 covering Europe, and 20 covering North America. Four reporters cover Asia and Europe but not North America, 6 reporters cover Asia and North America but not Europe, and 7 reporters cover Europe and North America but not Asia. How many reporters cover all of the 3 continents (Asia, Europe, and North America)?

(1) The Financial News Daily has 38 reporters in total covering at least 1 of the following continents: Asia, Europe, and North America.
(2) There are more Financial News Daily reporters covering only Asia than there are Financial News Daily reporters covering only North America.

An explanation for the formula below can be found in my post here:
https://www.beatthegmat.com/og-13-178-v ... 11188.html

Here is the formula with regard to the prompt above:
Total = A + E + N - (AE + AN + EN) - 2(AEN) + None.

The prompt gives values for A, E, N, AE, AN, and EN.
Plugging these values into the formula above, we get:
Total = 25 + 20 + 20 - (4 + 6 + 7) - 2(AEN) + None
Total = 48 - 2(AEN) + None

To determine the value of AEN, we need to know the values in blue.

Statement 1:
Total = 38.
Since every reporter covers at least 1 continent, none = 0.
SUFFICIENT.

Statement 2:
Since the values in blue are unknown, the value of AEN cannot be determined.
SUFFICIENT.

The correct answer is A.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jun 14, 2018 9:52 am

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Mo2men wrote:The Financial News Daily has 25 reporters covering Asia, 20 covering Europe, and 20 covering North America. Four reporters cover Asia and Europe but not North America, 6 reporters cover Asia and North America but not Europe, and 7 reporters cover Europe and North America but not Asia. How many reporters cover all of the 3 continents (Asia, Europe, and North America)?

(1) The Financial News Daily has 38 reporters in total covering at least 1 of the following continents: Asia, Europe, and North America.
(2) There are more Financial News Daily reporters covering only Asia than there are Financial News Daily reporters covering only North America.

We can use the formula:

total = A + E + NA - (A and E only) - (A and NA only) - (E and NA only) - 2(all three) + none

total = 25 + 20 + 20 - 4 - 6 - 7 - 2(all three) + none

total = 48 - 2(all three) + none

We need to determine "all three." If we know the "total" and "none," then we can determine "all three."

Statement One Alone:

The Financial News Daily has 38 reporters in total covering at least 1 of the following continents: Asia, Europe, and North America.

Thus, total = 38 and none = 0. So we have:

38 = 48 - 2(all three) + 0

2(all three) = 10

all three = 5

Statement one alone is sufficient.

Statement Two Alone:

There are more Financial News Daily reporters covering only Asia than there are Financial News Daily reporters covering only North America.

This doesn't tell us the total number of reporters or the number of reporters covering none of the regions. Statement two alone is not sufficient.

Answer: A

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