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The Financial News Daily has 25 reporters covering Asia, 20 covering

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Bunuel
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The Financial News Daily has 25 reporters covering Asia, 20 covering [#permalink] New post   03 Jan 2016, 11:36
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80% (02:05) correct 20% (02:44) wrong based on 180 sessions
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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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Re: The Financial News Daily has 25 reporters covering Asia, 20 covering [#permalink] New post   05 Jan 2016, 18:51
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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.
38=15-x+7-x+9-x+17+x
x=5
sufficient

(2) There are more Financial News Daily reporters covering only Asia than there are Financial News Daily reporters covering only North America.
not sufficient


Answer:A
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Re: The Financial News Daily has 25 reporters covering Asia, 20 covering [#permalink] New post   14 Jun 2018, 10:47
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Bunuel 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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Re: The Financial News Daily has 25 reporters covering Asia, 20 covering [#permalink] New post   14 Jun 2018, 11:21
I memorized the 3-overlapping sets formula:
Asia = 25; Europe = 20; North America = 20
Asia and Europe = 4; Asia and North America = 6; Europe and North America = 7

Total = 25 + 20 + 20 - (4 + 6 + 7) - 2 (reporters covering all 3 continents designate "X")

(1) This is Total, Sufficient
(2) There are more Financial News Daily reporters covering only Asia than there are Financial News Daily reporters covering only North America.
Only Asia > Only North America
25 - 4 - 6 - X > 20 - 6 - 7 - X
15 - X > 7 - X
Thus the number of reporters covering all of the 3 continent can be 1, 2, 3, 4, 5, 6, 7 Insufficient

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Re: The Financial News Daily has 25 reporters covering Asia, 20 covering [#permalink] New post   15 Feb 2020, 14:41
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JeffTargetTestPrep wrote:

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


Where did the 2 come from for the reporters covering all three areas?
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Re: The Financial News Daily has 25 reporters covering Asia, 20 covering [#permalink]
15 Feb 2020, 14:41
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Bunuel
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