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
What is the ratio of the average
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Statements combined: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
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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It is quite obvious that each statement itself cannot alone be sufficient. Let us combine them.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
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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Dear GMATGuru,GMATGuruNY wrote:Statements combined: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
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.
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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The portion in red misrepresents the information in Statement 2.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
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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GMATGuruNY wrote:The portion in red misrepresents the information in Statement 2.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
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??
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Correct.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.
The following equation is valid: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??
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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Working withMo2men 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??
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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Mo2men wrote: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.'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??
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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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.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 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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