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Venn Diagram with 3 sets, need help with the solution

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by Alex Lbn » Thu Jun 03, 2010 11:51 am
The Economic News Weekly 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 3 continents (Asia, Europe and North America)?

(1) The Economic News Weekly has 38 reporters in total covering at least 1 of the following countries: Asia, Europe and North
America.

(2) There are more Economic News Weekly reporters covering only Asia than there are Economic News Weekly reporters
covering only North America.
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by 4GMAT_Mumbai » Thu Jun 03, 2010 12:51 pm
Hi,

With the information given in the statement alone, if 'x' is the number of ppl who do all three geographies, we can conclude that

n(Asia alone) = 15 - x
n(Europe alone) = 9 - x
n(NA alone) = 7 - x

n(Asia Union Europe Union NA) = (15 - x) + (9-x) + (7-x) + x + 4 + 6 + 7. Thus, this is an expression involving the term -2x

1. Stmt 1: n(Asia Union Europe Union NA) is given as 38. So, x can be calculated.

2. Stmt 2: This statement does not add any new information. If n(Asia alone) is 15 - x and if n(NA alone) is 7 - x; for all values of x; the former will be greater than the later. Hence, x could be any of the values 0 throgh 7. Not sufficient.

My answer would hence be A.

Hope this helps. Thanks.
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by indiantiger » Thu Jun 03, 2010 6:08 pm
Image

Please see the image attached, so we need find the common portion shown in all sets shown as colorless.

Now statement gives us :
(1) The Economic News Weekly has 38 reporters in total covering at least 1 of the following countries: Asia, Europe and North
America

This provides us the total count of reporters

we can have this equation = Total reporters in asia + total reporters in EU + total reporters in N.America - (common reporters in Asia and EU) - (common reporters in Asia and N.America) - (common reporters in EU and N.America) - (total common reporters in all three)

=> 38 = 25+20+20 -6-4-7 -(total common reporters in all three)
=> (total common reporters in all three) = 65 - 17 - 38
=> 10 (statement is suff)

(2) There are more Economic News Weekly reporters covering only Asia than there are Economic News Weekly reporters
covering only North America.

Does not give any specific numbers or numeric relationship so not sufficient.

ANS (A)

Let me know if I have done any step wrong.
"Single Malt is better than Blended"
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