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Ratio of players

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Ratio of players

by gmattesttaker2 » Thu May 15, 2014 8:15 am
Hello,

For the following:

A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, one-third were left handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of left-handed players who were not at practice?

A) 1/3
B) 2/3
C) 5/7
D) 7/5
E) 3/2

OA: C


When I tried using algebra it took me some time before I got this correctly. I was thinking that plugging in numbers might be a bit easier and maybe less error prone here. I was just wondering how to find out which numbers to use for testing though. Thanks a lot.

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Sri
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by theCodeToGMAT » Thu May 15, 2014 8:37 am
No. of lefties = No. of Righties
Total be x

Present = 1/3 * x
Left Handed = 1/3 * 1/3 * x

To find: R(not present):left(not present)

Let x = 90
Present = 30
Lefties Present= 10
Lefties Absent = 45 - 10 = 35
Righties Present = 20
Righties Absent = 45-20 = 25

Ratio = 25:35 = 5:7
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by theCodeToGMAT » Thu May 15, 2014 8:38 am
gmattesttaker2 wrote:Hello,

When I tried using algebra it took me some time before I got this correctly. I was thinking that plugging in numbers might be a bit easier and maybe less error prone here. I was just wondering how to find out which numbers to use for testing though. Thanks a lot.

Regards,
Sri
We know that Left Handed present = 1/3 * 1/3 * x ... so consider x as a multiple of 9
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by moumi2013 » Thu May 15, 2014 9:00 am
I tried it the Arithmetic way.
Say Total number of students as 90 INSTEAD of 100 (because these were fractions like 2/3 ,1/3)

Right-handed=R
Left-handed=L

No. of R(Present+Absent)=No.of L(Present+Absent)=45

Absent=2/3*90=60
Present=90-60=30

Present(L)=1/3*30=10
Present(R)=30-10=20

So
Absent(L)=45-10=35
Absent(R)=45-20=25

Absent(R):Absent(L)=25:35=5:7 or 5/7
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by GMATGuruNY » Thu May 15, 2014 9:22 am
A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, one-third were left handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of left-handed players who were not at practice?

1/3
2/3
5/7
7/5
3/2

C
This is an EITHER/OR group question.
Each player is EITHER left-handed OR right-handed.
Each player is EITHER present OR absent.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let L = left-handed, R = right-handed, P = present, A = absent.
To get a good number for the total, multiply all of the DENOMINATORS of the fractions described in the problem.
An equal number of left-handed and right-handed players implies 1/2.
2/3 were absent.
Of the players who attended practice, 1/3 were left-handed.
Let the total = 2*3*3 = 18.
Here's the grid:
_______________L_______R_______Total

P:

A:

total:____________________________18
Now let's fill in the grid step by step.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

A certain ball team has an equal number of right- and left-handed players.
Two-thirds of the players were absent from practice.
_______________L_______R________Total

P:________________________________6

A:_______________________________12

total:__________9_______9_________18
Of the players at practice that day, one-third were left handed.
_______________L______R________Total

P:_____________2______4___________6

A:_______________________________12

total:__________9______9__________18
Complete the grid:
_______________L______R_________Total

P:_____________2______4__________6

A:_____________7______5_________12

total:__________9______9_________18
Answer the question:
(right-handed and absent)/(left-handed and absent) = 5/7.

The correct answer is C.
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by telberrak » Thu May 15, 2014 9:51 am
Let X be the number of players
Left Handed players = X/2
Right Handed players = X/2

Absent players = 2X/3
Present players = X/3 (1/3 are left handed)

Present left handed players = 1/3 * X/3 = X/9
Absent left handed players = X/2 - X/9 = 7X/18

Present Right handed players = X/3 -X/9 = 2X/9 (present players minus left handed)
Absent Right handed players = X/2 - 2X/9 = 5X/18 (total right handed players minus present right handed)


Ratio ==> Absent Right handed players/Absent left handed players

5X/18 / 7X/18 ==> 5X*18/7X*18 == > 5/7

Hope this helps
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by Brent@GMATPrepNow » Thu May 15, 2014 11:05 am
Mitch's Group Grid approach (aka 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 players, and the two characteristics are:
- left-handed or right-handed
- absent from practice or present at practice

These kinds of questions are VERY POPULAR on the GMAT, so be sure you know how to solve them.

To learn more about the Double Matrix Method (aka Group Grid), watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

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

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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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