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

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

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

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.

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