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

 It is currently 20 Feb 2019, 16:06

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# Three math classes: X, Y, and Z, take an algebra test.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53020
Three math classes: X, Y, and Z, take an algebra test.  [#permalink]

### Show Tags

28 Jan 2019, 05:05
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:55) correct 38% (02:08) wrong based on 18 sessions

### HideShow timer Statistics

Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average score for all the three classes, taken together?

A. 81
B. 81.5
C. 82
D. 82.5
E. 84.5

_________________
Manager
Status: Manager
Joined: 27 Oct 2018
Posts: 161
Location: Malaysia
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Three math classes: X, Y, and Z, take an algebra test.  [#permalink]

### Show Tags

28 Jan 2019, 05:43
1
By using alligation, we can find that the ratio of students in each class x:y:z is 3:4:5

and the average = $$\frac{(3*83)+(4*76)+(5*85)}{3+4+5} = \frac{978}{12} = 81.5$$

B
Attachments

Untitled.png [ 11.57 KiB | Viewed 534 times ]

_________________

...Thanks for KUDOS

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2581
Re: Three math classes: X, Y, and Z, take an algebra test.  [#permalink]

### Show Tags

29 Jan 2019, 03:50

Solution

Given:
• The average score of class X = 83
• The average score of class Y = 76
• The average score of class Z = 85
• The average score of all students in X and Y together = 79
• The average score of all students in Y and Z together = 81

To find:
• The average score of all the three classes

Approach and Working:
• $$\frac{S_1}{X} = 83$$
o Implies, $$S_1 = 83X$$

• $$\frac{S_2}{Y} = 76$$
o Implies, $$S_2 = 76Y$$

• $$\frac{S_3}{Z} = 85$$
o Implies, $$S_3 = 85Z$$

$$\frac{(S_1 + S_2)}{(X + Y)} = 79$$
• Implies, $$S_1 + S_2 = 79X + 79Y$$
• Thus, 83X + 76Y = 79X + 79Y
• 4X = 3Y

$$\frac{(S_2 + S_3)}{(Y + Z)} = 81$$
• Implies, $$S_2 + S_3 = 81Y + 81Z$$
• Thus, 85Z + 76Y = 81Y + 81Z
• 4Z = 5Y

The average score of all the three classes = $$S_1 +S_2 + S_3/X + Y + Z = \frac{83X + 76Y + 85Z}{X + Y + Z}$$

• Therefore, total average score = ($$83 * \frac{3}{4} + 76 + 85 * \frac{5}{4})/ (\frac{3}{4}+ 1 + \frac{5}{4}) = \frac{163}{2} = 81.5$$

Hence, the correct answer is Option B

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Three math classes: X, Y, and Z, take an algebra test.   [#permalink] 29 Jan 2019, 03:50
Display posts from previous: Sort by