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At an elite baseball camp, 60% of players can bat both right-handed and left-handed.

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At an elite baseball camp, 60% of players can bat both right-handed and left-handed.

by BTGModeratorVI » Thu Jun 18, 2020 5:56 am

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At an elite baseball camp, 60% of players can bat both right-handed and left-handed. If 25% of the players who bat left-handed do not bat right-handed, what is the probability that a player selected at random does not bat left-handed?

A.15%
B. 20%
C. 25%
D. 30%
E. 40%

Answer: B
Source: Veritas Prep
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Re: At an elite baseball camp, 60% of players can bat both right-handed and left-handed.

by Brent@GMATPrepNow » Thu Jun 18, 2020 7:07 am
BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:56 am
 At an elite baseball camp, 60% of players can bat both right-handed and left-handed. If 25% of the players who bat left-handed do not bat right-handed, what is the probability that a player selected at random does not bat left-handed?

A.15%
B. 20%
C. 25%
D. 30%
E. 40%

Answer: B
Source: Veritas Prep
We can solve using the Double Matrix Method.

The Double Matrix Method can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of baseball players, and the two characteristics are:
- bats left-handed or DOESN'T bat left-handed
- bats right-handed or DOESN'T bat right-handed

NOTICE that the question does not ask us to find an actual number. It asks us to find a probability. This means we can assign whatever value we wish to the total number of couples.
So, let's say there are 100 players, which we'll add to our diagram:

Image

60% of players can bat both right-handed and left-handed
60% of 100 = 60, so 60 players can bat both right-handed AND left-handed .
Add that to the diagram to get:
Image

25% of the players who bat left-handed do not bat right-handed
Hmmm, we don't know the number of left-handed players, so we can't find 25% of that value.
So, let's assign a variable.
Let's let x = left-handed batters, and add it to our diagram:
Image
So, x of the 100 players bat left handed.

25% of the players who bat left-handed do not bat right-handed
If x players bat left-handed, then 25% of x do not bat right-handed.
In other words, 0.25x = number of players who do not bat right-handed
Add this to our diagram:
Image

At this point, we see that the two left-hand boxes add to x.
So, we can write the equation: 60 + 0.25x = x
Rearrange to get 60 = 0.75x
Rewrite 0.75 as fraction to get: 60 = (3/4)x
Multiply both sides by 4/3 to get: 80 = x
If x = 80, then we know that 80 of the 100 players bat left-handed.
This means that the remaining 20 players DO NOT bat left handed.
Image

So, P(player doesn't bat left-handed) = 20/100 = 20%

Answer: B

Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.
------------------------

NOTE: This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: At an elite baseball camp, 60% of players can bat both right-handed and left-handed.

by Scott@TargetTestPrep » Sun Jun 21, 2020 4:48 am
BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:56 am
 At an elite baseball camp, 60% of players can bat both right-handed and left-handed. If 25% of the players who bat left-handed do not bat right-handed, what is the probability that a player selected at random does not bat left-handed?

A.15%
B. 20%
C. 25%
D. 30%
E. 40%

Answer: B
Solution:

We can let the total number of players = 100. So we have 60 players who can bat both right-handed and left-handed. We can let x = the number of players who can only bat left-handed. Thus, 40 - x = the number of players who can only bat right handed. We are given that 25% of the players who bat left-handed do not bat right-handed, which means they can only bat left-handed. Therefore, we can create the equation:

0.25(x + 60) = x

x + 60 = 4x

60 = 3x

20 = x

So we have 20 players who can only bat left-handed and also 40 - 20 = 20 players who can only bat right handed. We are asked for the probability that a player selected at random does not bat left-handed, i.e., who can only bat right-handed. Therefore, that probability is 20/100 = 20%.

Answer: B

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