GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2019, 08:00

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In the first half of last year, a team won 60 percent of the games it

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55668
In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

09 May 2018, 00:55
00:00

Difficulty:

65% (hard)

Question Stats:

64% (01:50) correct 36% (02:17) wrong based on 124 sessions

### HideShow timer Statistics

In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60

B) 70

C) 80

D) 90

E) 100

_________________
Manager
Joined: 30 May 2017
Posts: 138
Location: United States
Schools: HBS '21
GMAT 1: 690 Q50 V32
GRE 1: Q168 V164
GPA: 3.57
In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

09 May 2018, 12:12
2
x = number of games in the first half of last year
putting the questions into words.
0.6x+3=0.5(x+20)
0.6x+3=0.5x+10
0.1x=7
x=70

The total game played is number of games in the first half of last year + number of games in the second half of last year = 70+20 =90

Hence, option D = 90 is the answer.
_________________
Kindly press the +1Kudos if you like the explanation. Thanks a lot!!!
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6566
Location: United States (CA)
Re: In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

05 Jul 2018, 16:47
Bunuel wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60

B) 70

C) 80

D) 90

E) 100

We can n = the number of games played in the first half. Thus, we see that 0.6n is the number of games won in the first half of the year and (0.6n + 3) is the total number of games won for the entire year. We also see that (n + 20) is the total number of games played during the entire year Thus, we can create the equation:

(0.6n + 3)/(n + 20) = 1/2

2(0.6n + 3) = n + 20

1.2n + 6 = n + 20

0.2n = 14

n = 70

Therefore, they played a total of 70 + 20 = 90 games last year.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Math Expert
Joined: 02 Aug 2009
Posts: 7757
In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

05 Jul 2018, 19:09
1
Bunuel wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60

B) 70

C) 80

D) 90

E) 100

Alternate ways:-

1) logical - short and crisp

Had the team won 12 out of team they would have remained at 60%.
BUT they win 12-3=9 matches less
Loss of 9 matches - winning % drops from 60% to 50%
so 10% of total matches including 20 played in second half = 9
total = $$9*\frac{100}{10}=90$$

2) substitute-
check from centre value
c) 80
so 60% of 60 + 3 = 36+3=39
It is NOT 50% of 80 or rather < 50%, so look for higher TOTAL
d) 90
so 60% of 70 + 3 = 42+3=45
It is 50% of 90

Algebraic method
let the initial games be x, so 60% of x = 0.6x
so Total games = x+20 and games won = 0.6x+3
as per info given - $$0.5(x+20)=0.6x+3..........0.5x+10=0.6x+3..............0.1x=7........x=70$$so total = 70+20=90

Best way for you to do - SUBSTITUTE
logical method is best if you have mastered it

_________________
Director
Joined: 14 Dec 2017
Posts: 519
Location: India
Re: In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

05 Jul 2018, 23:07
Bunuel wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60

B) 70

C) 80

D) 90

E) 100

Given, First half winnings = 60%

Second half winnings = (3/20)*100 = 15%

Average winnings for the year = 50%

Let the total games played in the first half of the year = X

Using the Weighted Average / Alligation approach,

60%............50%...................15%

(50-15).........50%................(60-50)

We get, 35/10 = X/20

Hence, X = 70

Therefore Total # of games played for the year = 70 + 20 = 90

Thanks,
GyM
_________________
CEO
Joined: 12 Sep 2015
Posts: 3782
Re: In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

21 Sep 2018, 06:46
Top Contributor
Bunuel wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60

B) 70

C) 80

D) 90

E) 100

Let T = TOTAL number of games played last year

The team won 50 percent of the games it played last year
So, TOTAL NUMBER OF WINS = 0.5T

In the SECOND HALF of last year, the team played 20 games, winning 3 of them
Number of WINS IN SECOND HALF = 3

If the team plays 20 games in the SECOND HALF, then T - 20 = the number of games played in the FIRST HALF

In the first half of last year, a team won 60 percent of the games it played.
So, the team won 60% of the T - 20 games it played in the FIRST HALF
Number of WINS IN FIRST HALF = (0.6)(T - 20)

We know that: WINS IN FIRST HALF + WINS IN SECOND HALF = TOTAL NUMBER OF WINS
So: (0.6)(T - 20) + 3 = 0.5T
Expand: 0.6T - 12 + 3 = 0.5T
Simplify left side: 0.6T - 9 = 0.5T
Subtract 0.6T from both sides to get: -9 = -0.1T
Solve: T = 90

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936
Re: In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

21 Sep 2018, 07:12
Bunuel wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60

B) 70

C) 80

D) 90

E) 100

From the fact that 60% = 3/5 and 50% = 1/2, let´s call 10M the number of games played in the first half.
Besides that, do not forget (in the table below) that half (10M+20) equals 5M+10. Therefore:

$$\begin{array}{*{20}{c}} {} \\ {{1^{{\text{st}}}}\,{\text{half}}} \\ {{2^{{\text{nd}}}}\,{\text{half}}} \\ {{\text{Total}}} \end{array}\,\,\,\,\begin{array}{*{20}{c}} {{\text{won}}} \\ {\frac{3}{5}\left( {10M} \right) = \boxed{6M}} \\ {\boxed3} \\ {\boxed{5M + 10}} \end{array}\,\,\,\,\,\begin{array}{*{20}{c}} {{\text{lost}}} \\ {\frac{2}{5}\left( {10M} \right) = 4M} \\ {17} \\ {5M + 10} \end{array}\,\,\,\,\,\begin{array}{*{20}{c}} {{\text{Total}}} \\ {10M} \\ {20} \\ {10M + 20} \end{array}$$

$$? = 10M + 20$$

$$6M + 3 = 5M + 10\,\,\,\,\, \Rightarrow \,\,\,\,\,M = 7\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 90$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
VP
Joined: 09 Mar 2016
Posts: 1279
In the first half of last year, a team won 60 percent of the games it  [#permalink]

### Show Tags

21 Sep 2018, 09:11
Bunuel wrote:
In the first half of last year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year?

A) 60

B) 70

C) 80

D) 90

E) 100

let x be total number of games played

let y be total number of games won

1st half / games played =x / games won 0.6x

2nd half / games played = 20 / games won 3

total games won = 0.5x
---------------------------------------------------

total games played 20+x = ? (plug in the equation below)

total games won 0.6x +3 = 0.5x

0.6x +3 = 0.5(20+x)
x = 70

hence 20+70 = 90 i made it
In the first half of last year, a team won 60 percent of the games it   [#permalink] 21 Sep 2018, 09:11
Display posts from previous: Sort by