Problem Solving

The Team-11 has played half of its due number of matches so far, out of which it has won 40 percent of the matches and lost the rest of these. Which of the following value could represent the possible number of the remaining matches the Team-11 must win in order to register an overall win percent of 60? Consider no ties.
A. 35
B. 30
C. 27
D. 24
E. 18


[spoiler]Made Up![/spoiler]

sanju09 wrote:The Team-11 has played half of its due number of matches so far, out of which it has won 40 percent of the matches and lost the rest of these. Which of the following value could represent the possible number of the remaining matches the Team-11 must win in order to register an overall win percent of 60? Consider no ties.
A. 36
B. 30
C. 27
D. 24
E. 18


[spoiler]Made Up![/spoiler]

total games played = g
half of total games played = 0.5g

The number of games won in the first half + the number of games won in the second half = 60% of the total games played
0.4(0.5g) + x(0.5g) = 0.6g
0.2g + 0.5xg = 0.6g
0.5x = 0.4
x = 4/5 - > therefore team has to win 80% of the remaining games

4/5 * number of games in the second half = whole number
check answer choices for which choice is a multiple of 5

[spoiler]Only B meets the criteria; ans = b[/spoiler]



[spoiler][/spoiler]

theCEO wrote:

sanju09 wrote:The Team-11 has played half of its due number of matches so far, out of which it has won 40 percent of the matches and lost the rest of these. Which of the following value could represent the possible number of the remaining matches the Team-11 must win in order to register an overall win percent of 60? Consider no ties.
A. 35
B. 30
C. 27
D. 24
E. 18


[spoiler]Made Up![/spoiler]

total games played = g
half of total games played = 0.5g

The number of games won in the first half + the number of games won in the second half = 60% of the total games played
0.4(0.5g) + x(0.5g) = 0.6g
0.2g + 0.5xg = 0.6g
0.5x = 0.4
x = 4/5 - > therefore team has to win 80% of the remaining games

4/5 * number of games in the second half = whole number and the answer as well
check answer choices for which choice is a multiple of 5

[spoiler]Only B meets the criteria; ans = b[/spoiler]



[spoiler][/spoiler]

Hi theCEO,

There's a typo in option A, this is 35 not 36. Edited.

Your work is good, but in the end it didn't address the real question, which is "the possible number of the remaining matches the Team-11 must win". It's correct that the possible answer is 4/5 of some total and is a whole number too, and it's also true that each half of the total is a multiple of 5, but we should better look for a multiple of 4 to answer the exact question instead of a multiple of 5 here.

sanju09 wrote:

theCEO wrote:

sanju09 wrote:The Team-11 has played half of its due number of matches so far, out of which it has won 40 percent of the matches and lost the rest of these. Which of the following value could represent the possible number of the remaining matches the Team-11 must win in order to register an overall win percent of 60? Consider no ties.
A. 35
B. 30
C. 27
D. 24
E. 18


[spoiler]Made Up![/spoiler]

total games played = g
half of total games played = 0.5g

The number of games won in the first half + the number of games won in the second half = 60% of the total games played
0.4(0.5g) + x(0.5g) = 0.6g
0.2g + 0.5xg = 0.6g
0.5x = 0.4
x = 4/5 - > therefore team has to win 80% of the remaining games

4/5 * number of games in the second half = whole number and the answer as well
check answer choices for which choice is a multiple of 5

[spoiler]Only B meets the criteria; ans = b[/spoiler]



[spoiler][/spoiler]

Hi theCEO,

There's a typo in option A, this is 35 not 36. Edited.

Your work is good, but in the end it didn't address the real question, which is "the possible number of the remaining matches the Team-11 must win". It's correct that the possible answer is 4/5 of some total and is a whole number too, and it's also true that each half of the total is a multiple of 5, but we should better look for a multiple of 4 to answer the exact question instead of a multiple of 5 here.

Hi sanju09,

I hate it when I don't answer questions properly! Thanks for the info. I will repost the full solution.

sanju09 wrote:The Team-11 has played half of its due number of matches so far, out of which it has won 40 percent of the matches and lost the rest of these. Which of the following value could represent the possible number of the remaining matches the Team-11 must win in order to register an overall win percent of 60? Consider no ties.
A. 35
B. 30
C. 27
D. 24
E. 18


[spoiler]Made Up![/spoiler]

total games played = g
half of total games played = (g/2) = 0.5g

The number of games won in the first half + the number of games won in the second half = 60% of the total games played
0.4(0.5g) + x(0.5g) = 0.6g
0.2g + 0.5xg = 0.6g
0.5x = 0.4
x = 4/5 - > therefore team has to win 80% of the remaining games

4/5 * number of games in the second half = whole number
4/5 * (g/2) = whole number; (g/2) also is a whole number
check each answer choice to see which produce a whole number when we have g/2

A. 35; 4/5 * (g/2) = 35; (g/2) = 43.75 -> not possible
B. 30; 4/5 * (g/2) = 30; (g/2) = 37.50 -> not possible
C. 27; 4/5 * (g/2) = 27; (g/2) = 33.75 -> not possible
D. 24; 4/5 * (g/2) = 24; (g/2) = 30 -> possible
E. 18; 4/5 * (g/2) = 18; (g/2) = 22.5 -> not possible

ans = d

Hi All ,

Can you please advise alternate approach?

Thanks in advance.

Thanks,

SJ

sanju09 wrote:The Team-11 has played half of its due number of matches so far, out of which it has won 40 percent of the matches and lost the rest of these. Which of the following value could represent the possible number of the remaining matches the Team-11 must win in order to register an overall win percent of 60? Consider no ties.
A. 35
B. 30
C. 27
D. 24
E. 18

Let F = the first half of the season and S = the second half of the season.

Percentage attributed to F = 40%.
Percentage attributed to S = x%.
Percentage attributed to the MIXTURE of F and S = 60%.

Since F and S each consist of an EQUAL NUMBER OF GAMES, the percentage for the MIXTURE -- 60% -- must be HALFWAY between the percentages for F and S (40% and x%).
Thus:
x% = 80% = 4/5.

Since (4/5)S must be an INTEGER VALUE, S must be a MULTIPLE OF 5:
S=5 --> number of wins = (4/5)(5) = 4.
S=10 --> number of wins = (4/5)(10) = 8.
S=15 --> number of wins = (4/5)(15) = 12.
The values in red imply that the number of wins in S must be a MULTIPLE OF 4.

The correct answer is D.

sanju09 wrote:The Team-11 has played half of its due number of matches so far, out of which it has won 40 percent of the matches and lost the rest of these. Which of the following value could represent the possible number of the remaining matches the Team-11 must win in order to register an overall win percent of 60? Consider no ties.
A. 35
B. 30
C. 27
D. 24
E. 18
[spoiler]Made Up![/spoiler]

Let, Matches played = 10
i.e. Total Matches = 2*10 = 20
Won = 4
Lost = 6
Minimum matches to win = x

Matches to be won = 12 out of 20
i.e. More matches to be won atleast = 12-4=8

i.e. Answer must be a multiple of 8

Answer: option D

Hi Mitch,

I did this question by 4 variable cross table method and I got answer = 40




|Played | Left |
-----|-----------|---------|-------
Won| 20 | M |60
------|-----------|---------|-------
Lost| 30 | |
-----|-----------|---------|-------
| 50 | 50 |100






From above value of M must be 40 to make it 60 won out of hundred.


Can you please tell me where I am making mistake.
-

vishalwin wrote:From above value of M must be 40 to make it 60 won out of hundred.
Can you please tell me where I am making mistake.

The question stems asks what COULD be the number of remaining games that are won.
In your solution, the total number of games = 100, with the result that the number of remaining games that are won = 40.
Implication:
The number of remaining games that are won COULD be 40.
But 40 is not among the answer choices.

To determine which of the five answer choices could be the number of remaining games that are won, test the LEAST POSSIBLE CASE.
Since 2/5 of the played games have been won, the least possible value for the number of played games = 5.
The following matrix is yielded:


Since 40% of the played games have been won, the number of played games that have been won = 40% of 5 = 2.
Since 60% of the total number of games are won, the total number of games that are won = 60% of 10 = 6.
The following matrix is yielded:

In the resulting matrix, the number of remaining games that are won = 4.

If the total number of games is multiplied by a factor of x, then the number of remaining games that are won will also be multiplied by a factor of x.
Implication:
The number of remaining games that are won = MULTIPLE OF 4.
Of the five answer choices, only D is a multiple of 4.

Hi Mitch,

How to choose if we have any other option like 36?

In the question it's not written to find out least possible but rather must be won.


Can you please help.

vishalwin wrote:Hi Mitch,

How to choose if we have any other option like 36?

In the question it's not written to find out least possible but rather must be won.


Can you please help.

The answer choices would not include both 24 and 36, since either is a viable option for the number of remaining games that are won.
Question stem: which of the following values could...
When the question stem includes the words in red, only ONE answer choice will be viable.
Here -- since the number of remaining games that are won must be a multiple of 4 -- the only viable answer choice is D.

The matrix method works, but I'd go for an equation instead, something like

(40% of the first half) + (x% of the second half) = 60% of the total

or

.4(m/2) + x(m/2) = .6m

so

x = .8

and the team must win 80% of its remaining matches.

Since the answer must be 80% of an integer, look for an answer that divides by 4. (80% = 4/5, so our number is a multiple of 4 and the total number of matches is a multiple of 5.) 24 is the only candidate, so we're done.