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lenagmat: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Oct 16, 2011 2:21 pmFollowed by: 1 member

by lenagmat » Tue Oct 18, 2011 9:08 am

If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?

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Source: Beat The GMAT — Problem Solving | Tue Oct 18, 2011 9:08 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Oct 18, 2011 9:13 am

lenagmat wrote:If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?

No, unless both groups have same number of members.

For example if 1st group has x members and 2nd group has y members, then total grade for the 1st group = 68.2x and total grade for 2nd group = 73.5y

Hence, average grade in two groups = (68.2x + 73.5y)/(x + y)

Only if x = y, then average = (68.2x + 73.5x)/(x + x) = (68.2 + 73.5)/2

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lenagmat: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Oct 16, 2011 2:21 pmFollowed by: 1 member

by lenagmat » Tue Oct 18, 2011 1:38 pm

Anurag@Gurome wrote:
lenagmat wrote:If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?
No, unless both groups have same number of members.

For example if 1st group has x members and 2nd group has y members, then total grade for the 1st group = 68.2x and total grade for 2nd group = 73.5y

Hence, average grade in two groups = (68.2x + 73.5y)/(x + y)

Only if x = y, then average = (68.2x + 73.5x)/(x + x) = (68.2 + 73.5)/2

I understood with x and y, and I am sure that you are completly right, but I don't understand taking numbers: (very simple ex.):
(2+6)/2=4 - Av.
(3+5+4)/3=4 - Av.

(Av.+Av.)/2=(4+4)/2=4
(2+6+3+5+4)/5=4

I just can not understand why both answers are the same.

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Tue Oct 18, 2011 2:12 pm

lenagmat wrote:
Anurag@Gurome wrote:
lenagmat wrote:If I know the average for one group, (for instance, the average grade for the first group = 68.2), and the average for the second group (for instance, the average grade for the second group = 73.5).
Could I say, that the average grade in two groups is - (68.2+73.5)/2 ?
And if not, why?
No, unless both groups have same number of members.

For example if 1st group has x members and 2nd group has y members, then total grade for the 1st group = 68.2x and total grade for 2nd group = 73.5y

Hence, average grade in two groups = (68.2x + 73.5y)/(x + y)

Only if x = y, then average = (68.2x + 73.5x)/(x + x) = (68.2 + 73.5)/2

I understood with x and y, and I am sure that you are completly right, but I don't understand taking numbers: (very simple ex.):
(2+6)/2=4 - Av.
(3+5+4)/3=4 - Av.

(Av.+Av.)/2=(4+4)/2=4
(2+6+3+5+4)/5=4

I just can not understand why both answers are the same.

It is just for THAT set of numbers(Where average1 = average 2), where you find that result equal.

Here is an example,
(2+6)/2 = 4
(98+99+100+101+102)/5 = 100

(avg1 + avg1)/2 = (100+4)/2 = 52
sum of numbers = (98+99+100+101+102+2+6)/7 = #72.59 which is not equal to 52 !

In simple words, the average of averages may not always be equal to the average of all the numbers.

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

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lenagmat: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Oct 16, 2011 2:21 pmFollowed by: 1 member

by lenagmat » Tue Oct 18, 2011 11:07 pm

Two groups in the class have passed the test. If the average grade for the first group was 68.2, and the average grade for the second group was 73.5, what was the average grade in two groups.

1). The first group had 20 more students than the second one
2). The first group has 3 time more students than the second one

Like I already know that average grade in two groups = (68.2x + 73.5y)/(x + y)
1). =(68.2(y+20)+ 73.5y))/(y+20+y)
And I can find Y.

But why B is the answer?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Oct 18, 2011 11:47 pm

lenagmat wrote:Two groups in the class have passed the test. If the average grade for the first group was 68.2, and the average grade for the second group was 73.5, what was the average grade in two groups.

1). The first group had 20 more students than the second one
2). The first group has 3 time more students than the second one

Say, number of students in group 1 and group 2 are x and y respectively.
Hence, average grade of two groups = (68.2x + 73.5y)/(x + y)

Statement 1: x = y + 20
Hence, required average = (68.2(y + 20) + 73.5y))/(y + 20 + y) = (141.7y + 1364)/(2y + 40)
But we don't know y.

NOT sufficient

Statement 1: x = y + 3y = 4y
Hence, required average = (68.2*(4y) + 73.5y))/(4y + y) = (4*68.2 + 73.5)/5
We can calculate the value of the above expression.

SUFFICIENT

The correct answer is B.

lenagmat wrote:Like I already know that average grade in two groups = (68.2x + 73.5y)/(x + y)
1). =(68.2(y+20)+ 73.5y))/(y+20+y)
And I can find Y. ----> How?

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lenagmat: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Oct 16, 2011 2:21 pmFollowed by: 1 member

by lenagmat » Wed Oct 19, 2011 1:17 am

Thank you very much.
And just for the future to make it completle clear for me:
If we have "X" and it is said:

Y 3 times more than X - than Y=3X+X, not Y=3X? (Because I thought all the time that it is y=3x).

Anurag@Gurome wrote:
lenagmat wrote:
Statement 1: x = y + 3y = 4y

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Oct 19, 2011 1:23 am

lenagmat wrote:...Y 3 times more than X - than Y=3X+X, not Y=3X?

When we say Y is 2 more than X, it means Y = X + 2
Similarly, when Y is 3 times more than X, then it means Y = X + 3 times X = X + 3X = 4X

Hope that helps.

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