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

 It is currently 14 Oct 2019, 08:40 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  What is the ratio of the average (arithmetic mean) height of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 12 Aug 2004
Posts: 7
What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

9
1
70 00:00

Difficulty:   35% (medium)

Question Stats: 65% (01:21) correct 35% (01:11) wrong based on 2196 sessions

HideShow timer Statistics

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.
Math Expert V
Joined: 02 Sep 2009
Posts: 58316
What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

26
22
What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

Average height of students in class X: $$x_{average}=\frac{sum \ of \ the \ heights \ in \ X}{n}$$, where $$n$$ is the # of students in class X;

Average height of students in class Y: $$y_{average}=\frac{sum \ of \ the \ heights \ in \ Y}{m}$$, where $$m$$ is the # of students in class Y.

Question: $$\frac{x_{average}}{y_{average}}=?$$

Each statement alone is clearly insufficient.

From (1): $$x_{average}=120$$;
From (2): $$126=\frac{x_{average}*n+y_{average}*m}{n+m}$$;

Above information is not sufficient to calculate $$y_{average}$$, so we can not get the ratio. If you try different values for $$m$$ and $$n$$ you'll get different values of $$y_{average}$$

_________________
General Discussion
Senior Manager  Joined: 19 Oct 2004
Posts: 282
Location: Missouri, USA

Show Tags

1
2
it is E according to me.. lemme try and explain.

let x and y be the average height of the classes X and Y respectively.

from statement 1--- x=120, y not known, hence insufficient.

from statement 2---- x+y=126, which is insufficient too..

now combining both, we get
SINCE the AVERAGE height of Classes X and Y combines is 126, total height is 126*2= 252 right? (for eg, there are two numbers 2 and 4. their average is 3. so 3*2=6 which is the SUM of the two numbers).
now we CANNOT subtract 120 from 252, because 252 is NOT the average anymore, but the TOTAL HEIGHT. and 120 is the average. So they cannot be subtracted.

Hence, I go with E.
_________________
Let's get it right!!!!
Intern  Joined: 02 Nov 2004
Posts: 11

Show Tags

1
2
What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
(1) The average height of the students in class X is 120 centimeters.

Let say total height of class x is k and total students is m so;

k/m=120 insufficient

(2) The average height of the students in class X and class Y combined is 126 centimeters.

Let say total height of class y is n and total students is r so;

(k+y)/(m+r) = 126

k/(m+r) + y/(m+r) = 126

if we combined 1 and 2 there is nothing

so I say e is the correct
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: DS - average height of students  [#permalink]

Show Tags

5
1
What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?
(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

OA will follow. Thank you.

The question deals with weighted averages since the number of students in the two classes might be different. So you cannot say that 126 will be the average of 120 and 132. I suggest you to read up on weighted averages. That will make this question seem straightforward.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

7
1
Hi All,

When a 'weighted average' question does NOT tell you the number of entities/items involved, you can TEST VALUES to prove if there's more than one possible way to get to that average.

Here, we're asked for the ratio of the average height in Class X to the average height in Class Y. We are told NOTHING about the respective number of students in each class.

Fact 1: The average height in Class X is 120cm.

This tells us nothing about the average height in Class Y.
Fact 1 is INSUFFICIENT

Fact 2: The average height of all students in both Classes (combined) is 126cm.

IF....
Each class has 2 students in it, the average heights could be....
Class X = 126cm
Class Y = 126cm
The answer to the question is 126:126 = 1:1

Class X = 125cm
Class Y = 127cm
The answer to the question is 125:127
Fact 2 is INSUFFICIENT

Combined, we know....
The average height in Class X = 120cm
The average height of both classes = 126cm
We DON'T KNOW the number of students in each class though...

IF...
Each class has 2 students in it
The average of Class X = 120cm
The average of Class Y = 132cm
The answer to the question is 120:132

IF....
Class X has 2 students and Class Y has just 1 student
The average of Class X = 120cm
The average of Class Y = 138cm
The answer to the question is 120:138
Combined, INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________
Intern  S
Joined: 10 Jun 2016
Posts: 45
Schools: IIM-A"19
Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

Hello All,

The Answer for me is E.

S-1) Insufficient as Avg X is given. No details for Y
S-2) Insufficient as Avg (X+Y) = 126
S-T) Insufficient. Consider a example with numbers. If X = {10,20,30,40 } Avg X= 25. Avg of Y = {25,50,75,90} = Avg Y = 60. But Avg (X+Y) = {10,20,30,40,25,50,75,90} = 340/8 = 42.50. So in general, I understand Avg X + Avg Y <> Avg (X+Y)

Thanks,
Hits
_________________
Thank You Very Much,
CoolKl
Success is the Journey from Knowing to Doing

A Kudo is a gesture, to express the effort helped. Thanks for your Kudos.
Senior Manager  P
Joined: 29 Jun 2017
Posts: 424
GPA: 4
WE: Engineering (Transportation)
Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

Class X. let total student x
Class Y let total student y

1) average ht of Class X =120 cms
as no info of x,y as well as avg ht of class Y AD gone Insufficient

2) Average ht combined of Class X and Y is 126
Now x and y are unknown , if they were known soln was possible but in this case B is gone

Combine

differential for Class X is 6cms on lesser side as avg ht both class is 126
but again we dont know x and y so we cant find out avg ht of Class y

Diff ht X x Nr of stud X = Diff ht Y x Nr student Y
6x= (Diff ht Y) * y. tooo manay unkowns C is gone

_________________
Give Kudos for correct answer and/or if you like the solution. S
Status: It's now or never
Joined: 10 Feb 2017
Posts: 178
Location: India
GMAT 1: 650 Q40 V39 GPA: 3
WE: Consulting (Consulting)
Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

St 1. Average height of students in Class X is 120 cms, Info on Class Y is not given. Hence, Insufficient.
St 2. Avg height of students in class X and Y combined is 126 cms. Now number of Class X students and Class Y students are not known, therefore cannot determine the target info. Hence, insufficient.

St 1 + 2: No new information is added, number of students in class X and Y are still unknown, therefore "E".

Hope this helps.
_________________

Threadmaster for B-school Discussions
Class of 2019: Mannheim Business School
Class 0f 2020: HHL Leipzig
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

We want to find the ratio of the average height of students in class X to the average height of students in class Y. If we know the average height of students in each class, then we can find the ratio.

Statement One Alone:

The average height of the students in class X is 120 centimeters.

Without knowing the average height of the students in class Y, we can’t determine the ratio of the average height of students in class X to the average height of students in class Y.

Statement one alone is not sufficient.

Statement Two Alone:

The average height of the students in class X and class Y combined is 126 centimeters.

Even knowing that the combined (overall) average of the two classes is 126 centimeters, without knowing the average height of the students in each class, we still can’t determine the ratio of the average height of students in class X to the average height of students in class Y.

Statement two alone is not sufficient.
Statements One and Two Together:

Using statements one and two together, we can create a weighted average equation using the following:

a = the number of students in class X

120 = the average height of the students in class X

b = the number of students in class Y

y = the average height of the students in class y

126 = (120a + yb)/(a + b)

Now multiply both sides of the equation by (a + b) to get

126a + 126b = 120a + yb

6a + 126b = yb

(6a + 126b)/b = y

We need to determine the ratio of the average height of the students in class X to the average height of the students in class Y, or 120/y. Since we cannot determine a value for y, we cannot answer the question.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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.

Director  V
Joined: 12 Feb 2015
Posts: 915
Re: What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

When we apply the weigthed average formula after combining St 1 and 2 we get an equation with 3 variables.

Clearly the information is not sufficient to find the required ratio. Correct Ans is OptionE
_________________
"Please hit +1 Kudos if you like this post" _________________
Manish "Only I can change my life. No one can do it for me"
Intern  B
Affiliations: National Institute of Technology, Durgapur
Joined: 22 Feb 2017
Posts: 38
Location: India
GPA: 3.6
WE: Engineering (Manufacturing)
What is the ratio of the average (arithmetic mean) height of  [#permalink]

Show Tags

1
What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

1st please clear your concept about mean from this example below-

Mean of 'N' elements of a set whose sum is 'S' = M = S/N
Mean of 'n' elements of another set whose sum is 's' = m = s/n

Now, average of all the elements 'N+n' would be, A = (S+s)/(N+n) ......eq(1)
Average of means of both the sets, a = (M+m)/2 = [S/N+s/n]/2 = [nS+Ns]/(2xnxN) .......eq(2)
In order for 'A' to be equal to 'a' , N=n, [for which A=a=(S+s)/2n OR (S+s)/2N]
Else, both 'A' & 'a' would have different value OR same value depending on values of 's' & 'S' => In order to solve this problem we need no. of students in class X as well as in class Y OR atleast whether they have same no. of students or not?

In this problem we are asked about eq(1) and not eq(2) ;
Those who opted for option (C) by solving the problem as =>(Xavg+Yavg)/2=126 are wrong as we don't know whether 'X' & 'Y' have equal no. of students/elements or not ;

Correct answer is option (E) .
_________________
GMAT date:- 21-12-2019

"Put your head down and work hard. Never wait for things to happen, make them happen for yourself through hard graft and not giving up"
-Chef Gordon Ramsey What is the ratio of the average (arithmetic mean) height of   [#permalink] 01 Dec 2018, 03:41
Display posts from previous: Sort by

What is the ratio of the average (arithmetic mean) height of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  