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# What was the average (arithmetic mean) monthly rainfall

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What was the average (arithmetic mean) monthly rainfall [#permalink]  22 Jul 2003, 19:36
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What was the average (arithmetic mean) monthly rainfall during 1984 in region Y?

(1) In region Y the total rainfall for the first 6 months of 1984 was twice the total rainfall for the last 6 months of 1984.

(2) In region Y the average monthly rainfall for the first 6 months of 1984 was 2.31 inches more than the average monthly rainfall for the last 6 months of 1984.
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Re: What was the average (arithmetic mean) monthly rainfall [#permalink]  22 Jul 2003, 21:56
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average is (M1+M2+...+M12)/12, so we need a full sum of M1...12

(1) (M1+...+M6)=2*(M7+...+M12) - no absolute values, so it is out
(2) (M1+...+M6)/6=2.31+(M7+...+M12)/6 - no full sum either

combine: OK

Thus C
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Re: What was the average (arithmetic mean) monthly rainfall [#permalink]  22 Jul 2003, 22:13
C

(1) Could be any two numbers X and 2X
(2) Could be any two X and X + 2.31

Need to combine the two to get the first 6 months is 4.62 EACH and the second 6 months is 2.31 EACH. This is suff.
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Re: What was the average (arithmetic mean) monthly rainfall [#permalink]  15 Oct 2014, 02:41
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Re: What was the average (arithmetic mean) monthly rainfall [#permalink]  23 Feb 2015, 10:48
i dont understand how combining the two is sufficient. (2) says the first six months had a average of 2.31in more than the last 6 months, and (1) says first six months had twice as much as the second half, but how can you deduce the numbers from just that.

mciatto is saying first six months had 4.62in each and last six months had 2.31in each, but isnt that just an assumption. just cause (2) said its 2.31 more doesn't mean it is 2.31in. Or am i missing something
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Re: What was the average (arithmetic mean) monthly rainfall [#permalink]  23 Feb 2015, 11:11
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Curly05 wrote:
What was the average (arithmetic mean) monthly rainfall during 1984 in region Y?

(1) In region Y the total rainfall for the first 6 months of 1984 was twice the total rainfall for the last 6 months of 1984.

(2) In region Y the average monthly rainfall for the first 6 months of 1984 was 2.31 inches more than the average monthly rainfall for the last 6 months of 1984.

Let, monthly rainfall for 12 months are
A,B,C,D,E,F,G,H,I,J,K and L

Question : (A+B+C+D+E+F+G+H+I+J+K+L)/12 = ?

Statement 1: (A+B+C+D+E+F) = 2x(G+H+I+J+K+L)
No value for the sum of first/last 6 month is given theerfore
NOT SUFFICIENT

Statement 1: (A+B+C+D+E+F)/6 = [(G+H+I+J+K+L)/6] + 2.31
i.e. (A+B+C+D+E+F) = (G+H+I+J+K+L) + 13.86
But sum of all 12 months can't be calculated therefore
NOT SUFFICIENT

Combining the two statements:
(A+B+C+D+E+F) = (G+H+I+J+K+L) + 13.86
AND
(A+B+C+D+E+F) = 2x(G+H+I+J+K+L)

i.e. 2x(G+H+I+J+K+L) = (G+H+I+J+K+L) + 13.86
i.e. (G+H+I+J+K+L) = 13.86
i.e. (A+B+C+D+E+F) = 2x13.86 = 27.72
i.e. (A+B+C+D+E+F+G+H+I+J+K+L) = 27.72+13.86 = 41.58

i.e. Average of (A+B+C+D+E+F+G+H+I+J+K+L) = 41.58/12 = 3.465
SUFFICIENT

[Reveal] Spoiler:
C

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Re: What was the average (arithmetic mean) monthly rainfall [#permalink]  23 Feb 2015, 11:45
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Expert's post
Hi btan219,

When dealing with questions that include LOTS of variables, it often helps to make your variables as simple as possible (e.g., make 'groups' of them the same number, etc.).

Here, we're asked for the average monthly rain fall for the year 1984 in region Y. From this prompt, we would need to have information on ALL 12 months (the actual numbers, ratio data or equivalent) to answer this question.

Fact 1: In region Y the total rainfall for the first 6 months of 1984 was twice the total rainfall for the last 6 months of 1984.

This tells us NOTHING about the amount of rain that fell in any of the months. However, we can organize the information in a simple example:

First 6 months of the year: 2X rain per month
Last 6 months of the year: X rain per month
Fact 1 is INSUFFICIENT

Fact 2: In region Y the average monthly rainfall for the first 6 months of 1984 was 2.31 inches more than the average monthly rainfall for the last 6 months of 1984.

Again, this tells us NOTHING about the actual amount of rain that fell in any of the months. We can organize the information though....

First 6 months of the year: (Y + 2.31) inches per month
Last 6 months of the year: Y inches per month
Fact 2 is INSUFFICIENT

Combined, we know:
The average amount of rain that fell in the LAST 6 months = X = Y.
The average amount of rain that fell in the FIRST 6 months is 2X = X + 2.31
We can now solve for X.
X = 2.31, so we CAN answer the question.
Combined, SUFFICIENT.

[Reveal] Spoiler:
C

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Re: What was the average (arithmetic mean) monthly rainfall   [#permalink] 23 Feb 2015, 11:45
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