Hi, I'm sure I'm doing this wrong but I've run into a case where I used the Venn Diagram method to solve this overlapping sets question to arrive at one answer (C, both statements together are sufficient), however when I use the Double Set Matrix method (like the book), I arrive at A. What am i doing wrong? Or can the Double Set Matrix method produce solutions that the Venn Diagram method can't?

Q: There are 19 batters on a baseball team. Every batter bats either Right handed only, Left handed only, or both Right handed and Left handed. How many of the 19 batters bat left handed?

1) 7 of the batters bat right handed but do not bat left handed.
2) 4 of the batters bat both right handed and left handed.

Venn Diagram Method

I set up the equation below:

R = Right handed batters
L = Left handed batters
B = Both Right handed and Left handed

L - B + B + R - B = 19
L + R - B = 19

I have one linear equation with 3 variables. Statements 1) and 2) together will give me R and B. I can then solve for our target, L. Answer is C

Double Set Matrix method

Statement 1) is sufficient

Statement 2) is insufficient

Answer is A

Would appreciate any help!!!

Rob

Statement 1 tells you more than you've shown for your Venn. :)

1) 7 of the batters bat right handed but do not bat left handed.

So 7 = RHonly
but that must mean The Rest = 19 - 7 = 12. The Rest = the LHonly and Both batters, so L + B = 12.

We now have 3 equations:
R = 7
L + B = 12
L + R - B = 19

Start plugging.
L + 7 - B = 19
L - B = 12
and we also still know that L + B = 12
add the 2 equations and get:
2L = 24
L = 12. Sufficient!

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

thank you!

:-)

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Jamie Nelson
ManhattanGMAT Instructor

Thanks, I just was able to solve a similar problem thanks to this post! My friend Lenen and I where looking for the answer all day long.

glad to hear it!

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Tim Sanders
Manhattan GMAT Instructor