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Yet another one on averages

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Yet another one on averages

by abhasjha » Mon Aug 26, 2013 11:22 am
Group A consist of x students and their total age is 221 and their average is a integer.when group A is merged with group B with twice the number of students (number of students between 30 and 40 ) average age of B is reduced by 1. What is the original average of B ?
(a) 14
(b) 15
(c) 16
(d) none of these
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by [email protected] » Mon Aug 26, 2013 12:24 pm
Hi abhasjha,

The average formula question that you've listed here is NOT how the GMAT would pose the question. That having been said, the average formula is a standard formula, so here's how you would solve the problem:

Group A has x students with a total age of 221 and the average is AN INTEGER.

221/x = INTEGER

Since the average is an integer, there can't be that many possible values for x. In fact, there are only two possible values: 13 or 17

Group B has twice the number of students as Group A AND that total is between 30 and 40. There's only one option that fits: 34

So,
Group A = 17 students
Group B = 34 students

Combining groups, we're told that the average of Group B is reduced by 1.

Just Group B:
Sum/34 = Z

Combined A and B:
(Sum+221)/(17+34) = Z - 1

Now, it's just a matter of doing algebra:

First equation: Sum = 34Z

Second equation: Sum +221 = 51Z - 51
Sum = 51Z - 272

Set the equations equal:
34Z = 51Z - 272
272 = 17Z
16 = Z

Final Answer: C

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by GMATGuruNY » Mon Aug 26, 2013 12:26 pm
abhasjha wrote:Group A consist of x students and their total age is 221 and their average is a integer.when group A is merged with group B with twice the number of students (number of students between 30 and 40 ) average age of B is reduced by 1. What is the original average of B ?
(a) 14
(b) 15
(c) 16
(d) none of these
Total of the ages in Group A = (number of students)I(average age per student) = 221.
Since 221 = 13*17, the number of students in Group A must be 1, 13, or 17.
Since Group B has twice the number of students, and the number of students in Group B must be between 30 and 40, only one case is possible:
Number of students in Group A = 17.
Number of students in Group B = 2*17 = 34.

Since there are 17 students in Group A, and the sum of their ages = 221, the average age of the students in Group A = 13.

We can plug in the answers for the average age of the students in Group B.
When the groups are combined, there will be twice as many students from B as from A.
Thus, of every 3 students, 2 students will be from Group B, while 1 student will be Group A.
Implication:
To determine the average age when the groups are combined, we need only compute the average age when 2 students from B are combined with 1 student from A.

Answer choice D: 16
Here, the 2 students from Group B will have an average age of 16, while the 1 student from Group A will be 13 years old.
Average age for the 3 students = sum/number = [(2*16) + 13]/3 = 15.
(average age for Group B) - (average for the groups combined) = 16-15 = 1.
Success!

The correct answer is C.
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by rairavig » Tue Aug 27, 2013 12:31 am
from above it is clear that in group A we have 17 students and in group B 34 Students.
let us assume the total of the age of Group B students is "X"
now according to the Question:-
X/34 - (X+221 / 51) = 1
Gives X= 544
so the average age is Group B student before merging is 544/34 = 16 (Ans. C)
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