What is the ratio of the average

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 am; Thanked: 3 times; Followed by:2 members

What is the ratio of the average

by NandishSS » Thu Jan 12, 2017 5:47 am

What is the ratio of the average (arithmetic mean) weight of students in class A to the average weight of students in class B?

(1) The average weight of the students in class A is 60 kilograms.
(2) The average weight of the students in class A and class B combined is 80 kilograms

OA:E

Source:Math Revolution

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Thu Jan 12, 2017 6:08 am

NandishSS wrote:What is the ratio of the average (arithmetic mean) weight of students in class A to the average weight of students in class B?

(1) The average weight of the students in class A is 60 kilograms.
(2) The average weight of the students in class A and class B combined is 80 kilograms

Statements combined:

Total weight = (number of students)(average weight)

Case 1: 1 student in A, 1 student in B
Total weight of the 2 students = (number of students in A and B)(average weight in A and B) = (2)(80) = 160.
Weight of the 1 student in B = (total weight in A and B) - (total weight in A) = 160-60 = 100.
Resulting ratio:
(average for A)/(average for B) = 60/100 = 3/5.

Case 2: 2 students in A, 1 student in B
Total weight of the 3 students = (number of students in A and B)(average weight in A and B) = (3)(80) = 240.
Total weight of the 2 students in A = (number of students in A)(average weight in A) = (2)(60) = 120.
Weight of the 1 student in B = (total weight in A and B) - (total weight in A) = 240-120 = 120.
Resulting ratio:
(average for A)/(average for B) = 60/120 = 1/2.

Since different ratios are possible, the two statements combined are INSUFFICIENT.

The correct answer is E.

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Jan 12, 2017 10:06 pm

NandishSS wrote:What is the ratio of the average (arithmetic mean) weight of students in class A to the average weight of students in class B?

(1) The average weight of the students in class A is 60 kilograms.
(2) The average weight of the students in class A and class B combined is 80 kilograms

OA:E

Source:Math Revolution

It is quite obvious that each statement itself cannot alone be sufficient. Let us combine them.

S1 & S2: Say, Class A has only one student, whose weight is 60 (given); and class B has x number of students whose average weight is B kg.

Thus, 1*60 + x*B = (1+x)*80.

=> B = 20+80x

We want the value of A/B. We cannot get it as the value of B is not known. Insufficient.

Answer: E

Hope this helps!

-Jay
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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 am; Thanked: 14 times; Followed by:5 members

by Mo2men » Fri Jan 13, 2017 3:11 pm

GMATGuruNY wrote:
NandishSS wrote:What is the ratio of the average (arithmetic mean) weight of students in class A to the average weight of students in class B?

(1) The average weight of the students in class A is 60 kilograms.
(2) The average weight of the students in class A and class B combined is 80 kilograms
Statements combined:

Total weight = (number of students)(average weight)

Case 1: 1 student in A, 1 student in B
Total weight of the 2 students = (number of students in A and B)(average weight in A and B) = (2)(80) = 160.
Weight of the 1 student in B = (total weight in A and B) - (total weight in A) = 160-60 = 100.
Resulting ratio:
(average for A)/(average for B) = 60/100 = 3/5.

Case 2: 2 students in A, 1 student in B
Total weight of the 3 students = (number of students in A and B)(average weight in A and B) = (3)(80) = 240.
Total weight of the 2 students in A = (number of students in A)(average weight in A) = (2)(60) = 120.
Weight of the 1 student in B = (total weight in A and B) - (total weight in A) = 240-120 = 120.
Resulting ratio:
(average for A)/(average for B) = 60/120 = 1/2.

Since different ratios are possible, the two statements combined are INSUFFICIENT.

The correct answer is E.

Dear GMATGuru,

Your solution sis perfect but I want to know where I go wrong with mine please.

The average weight of the students in class A = A
The average weight of the students in class B = B

Combined statements 1 & 2:

Dividing Statement 2 over statement 1

(A+B)/A = 80/60

Then A=60 & B=20

A/B= 3/1

Then answer should be C.

Can you help please??

Thanks in advance

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Jan 14, 2017 3:48 am

Mo2men wrote:[Dear GMATGuru,

Your solution sis perfect but I want to know where I go wrong with mine please.

The average weight of the students in class A = A
The average weight of the students in class B = B

Combined statements 1 & 2:

Dividing Statement 2 over statement 1

(A+B)/A = 80/60

Then A=60 & B=20

A/B= 3/1

Then answer should be C.

Can you help please??

Thanks in advance

The portion in red misrepresents the information in Statement 2.
A+B = 80 implies that the SUM OF THE TWO AVERAGES is 80.
Not so.
Statements 2 indicates the following:
(sum of all the ages in A and B)/(total number of students in A and B) = 80.
Algebraically:
(60x + By)/(x+y) = 80, where x = the number of students in A and y = the number of students in B.
The two statements combined are INSUFFICIENT because the values of x and y are unknown.

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 am; Thanked: 14 times; Followed by:5 members

by Mo2men » Sat Jan 14, 2017 4:06 am

GMATGuruNY wrote:
Mo2men wrote:[Dear GMATGuru,

Your solution sis perfect but I want to know where I go wrong with mine please.

The average weight of the students in class A = A
The average weight of the students in class B = B

Combined statements 1 & 2:

Dividing Statement 2 over statement 1

(A+B)/A = 80/60

Then A=60 & B=20

A/B= 3/1

Then answer should be C.

Can you help please??

Thanks in advance
The portion in red misrepresents the information in Statement 2.
A+B = 80 implies that the SUM OF THE TWO AVERAGES is 80.
Not so.
Statements 2 indicates the following:
(sum of all the ages in A and B)/(total number of students in A and B) = 80.
Algebraically:
(60x + By)/(x+y) = 80, where x = the number of students in A and y = the number of students in B.
The two statements combined are INSUFFICIENT because the values of x and y are unknown.

Thanks Mitch

Can I say that the take away of this problem is:

when there are averages, I should not simple sum them.Instead, I should use the above equation
Total averages= (sum of all the ages in A and B)/(total number of students in A and B)??

Am I right??

Quote

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Jan 14, 2017 4:15 am

Mo2men wrote:Thanks Mitch

Can I say that the take away of this problem is:

when there are averages, I should not simple sum them.

Correct.

Instead, I should use the above equation
Total averages= (sum of all the ages in A and B)/(total number of students in A and B)??

Am I right??

The following equation is valid:
Average for A and B combined = (sum of all the ages in A and B)/(total number of students in A and B).
The following equation also is valid:
The average for A and B = (Ax + By)/(x+y), where x/y is the RATIO of the number of elements in A to the number of elements in B.
In the problem above, if we knew that A had twice as many students as B, the two statements combined would be sufficient.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pm; Location: East Bay all the way; Thanked: 625 times; Followed by:119 members; GMAT Score:780

by Matt@VeritasPrep » Wed Jan 18, 2017 6:15 pm

Mo2men wrote:Can I say that the take away of this problem is:

when there are averages, I should not simple sum them.Instead, I should use the above equation
Total averages= (sum of all the ages in A and B)/(total number of students in A and B)??

Am I right??

Working with

Sum = Average * Number is pretty helpful. Suppose you have x students in A and y students in B. Then you know

Sum of weights in A = 60 * x

Sum of weights in A and B = 80 * (x + y)

Then your ratio of (A and B) / A becomes 60x / (80x + 80y), or 3x/(4x + 4y), and it's plain that you can't reduce that to a proper ratio (integer over integer).

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Jan 18, 2017 9:26 pm

Mo2men wrote:
Can I say that the take away of this problem is:

when there are averages, I should not simple sum them.Instead, I should use the above equation
Total averages= (sum of all the ages in A and B)/(total number of students in A and B)??

Am I right??
It should be 'Average of total' and not 'Total averages.' 'Average of class A and class B combined' is one number that represents the average of class A and class B combined. Apt is 'Average of class A and class B combined.'

Average of class A and class B combined = (Sum of all the ages in class A and class B) / (Total number of students in class A and class B)

Average of class A and class B combined = [(Av. of A * # of students in A) + (Av. of B * # of students in B)] / (Total number of students in A and B)

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 7243; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jan 19, 2017 4:51 pm

NandishSS wrote:What is the ratio of the average (arithmetic mean) weight of students in class A to the average weight of students in class B?

(1) The average weight of the students in class A is 60 kilograms.
(2) The average weight of the students in class A and class B combined is 80 kilograms

We need to determine the ratio of the average weight of the students in class A to the average weight of students in class B.

We can define some variables:

a = the average weight of the students in class A

b = the average weight of the students in class B

x = the number of students in class A

y = the number of students in class B

Thus, we need to determine a/b.

Statement One Alone:

The average weight of the students in class A is 60 kilograms.

Although we know that a = 60, without knowing anything about variable b, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The average weight of the students in class A and class B combined is 80 kilograms.

Although we know the overall average weight, we do not have enough information to determine a value for a/b. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we can create the following equation for the average weight:

80 = (60x + by)/(x + y)

80x + 80y = 60x + by

20x + 80y = by

Since we cannot determine a unique value for b, we cannot determine a value for a/b.

Answer: E

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