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For the first 3 months of last year, the average daily rainfall in Lan

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For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 15 Aug 2017, 00:09
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For the first 3 months of last year, the average daily rainfall in Lancaster was 6cm. For last year as a whole, the average daily rainfall was 12cm. What was the average daily rainfall for the last 9 months of last year?

A. 14cm
B. 16cm
C. 18cm
D. 24cm
E. 30cm

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Re: For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 15 Aug 2017, 00:54
It has been given that the average daily rainfall in Lancaster for the first 3 months was 6 cm.
Similarly, the average for the entire year is given to be 12 cm.

Let x be the average daily rainfall for each of the last 9 months.

Forming an equation, \(\frac{3*6 + 9*x}{12} = 12\)
Cross multiplying,
\(18 + 9x = 144\)
\(9x = 126\)
\(x = 14\)

Therefore, the average daily rainfall for the last 9 months of last year is \(14(Option A)\)
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For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 15 Aug 2017, 15:21
Bunuel wrote:
For the first 3 months of last year, the average daily rainfall in Lancaster was 6cm. For last year as a whole, the average daily rainfall was 12cm. What was the average daily rainfall for the last 9 months of last year?

A. 14cm
B. 16cm
C. 18cm
D. 24cm
E. 30cm


|__A__|__n__|__S___|
|__6__|__3__|__18__|
|_12__|_12__|__144_|
|_14__|__9__|__126_|

12 months' sum - 3 months' sum = 9 months' sum for daily average rainfall

144 - 18 = 126 cm total (sum) for 9 months

S/n = A

126 cm/9 months = 14 cm per month average daily rainfall

Answer A
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Re: For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 18 Aug 2017, 08:14
Bunuel wrote:
For the first 3 months of last year, the average daily rainfall in Lancaster was 6cm. For last year as a whole, the average daily rainfall was 12cm. What was the average daily rainfall for the last 9 months of last year?

A. 14cm
B. 16cm
C. 18cm
D. 24cm
E. 30cm


Let’s assume that each month has exactly 30 days. For the first 3 months, there were 6 x 30 x 3 inches of rainfall, and for the entire year, there were 12 x 30 x 12 inches of rainfall.

Finally, for the last 9 months, the average daily rainfall was:

(12 x 30 x 12 - 6 x 30 x 3)/(30 x 9) = (12 x 12 - 6 x 3)/9 = 126/9 = 14 cm

Answer: A
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For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 18 Oct 2017, 03:41
JeffTargetTestPrep wrote:
Bunuel wrote:
For the first 3 months of last year, the average daily rainfall in Lancaster was 6cm. For last year as a whole, the average daily rainfall was 12cm. What was the average daily rainfall for the last 9 months of last year?

A. 14cm
B. 16cm
C. 18cm
D. 24cm
E. 30cm


Let’s assume that each month has exactly 30 days. For the first 3 months, there were 6 x 30 x 3 inches of rainfall, and for the entire year, there were 12 x 30 x 12 inches of rainfall.

Finally, for the last 9 months, the average daily rainfall was:

(12 x 30 x 12 - 6 x 30 x 3)/(30 x 9) = (12 x 12 - 6 x 3)/9 = 126/9 = 14 cm

Answer: A


Hi JeffTargetTestPrep,

I was confused in this question too! It doesn't say MONTHY average rather it says DAILY average. Hence we need to know the number of days in each month to find the total rainfall, just as you have done .
But how can we assume that each month has 30 days .

If the question was " The monthly average for the first 3 months was 6 cm" then it would be ok to do 6 *3 to get the total rainfall of the first 3 months. Would it not ?
Please let me know what do you feel.
Thanks.
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Re: For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 08 Nov 2017, 09:36
Top Contributor
Bunuel wrote:
For the first 3 months of last year, the average daily rainfall in Lancaster was 6cm. For last year as a whole, the average daily rainfall was 12cm. What was the average daily rainfall for the last 9 months of last year?

A. 14cm
B. 16cm
C. 18cm
D. 24cm
E. 30cm



For the first 3 months of last year, the average daily rainfall in Lancaster was 6 cm.
So, (sum of first 3 months)/3 = 6
Multiply both sides by 3 to get: Sum of first 3 months = 18

For last year as a whole, the average daily rainfall was 12 cm
So, (sum of all 12 months)/12 = 12
Multiply both sides by 12 to get: Sum of all 12 months = 144
We can write this as: (sum of first 3 months) + (sum of last 9 months) = 144
Rewrite as: (18) + (sum of last 9 months) = 144
Solve to get: sum of last 9 months = 126

So, average for last 9 months = (sum of last months)/9
= 126/9
= 14
= A

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Re: For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 08 Nov 2017, 10:19
Bunuel wrote:
For the first 3 months of last year, the average daily rainfall in Lancaster was 6cm. For last year as a whole, the average daily rainfall was 12cm. What was the average daily rainfall for the last 9 months of last year?

A. 14cm
B. 16cm
C. 18cm
D. 24cm
E. 30cm


So, 3*6 +9*x = 12*12

Or, 9x = 144 - 18

Or, x = 14

Thus, the answer must be (A) 14
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Re: For the first 3 months of last year, the average daily rainfall in Lan  [#permalink]

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New post 03 Dec 2017, 23:16
Bunuel wrote:
For the first 3 months of last year, the average daily rainfall in Lancaster was 6cm. For last year as a whole, the average daily rainfall was 12cm. What was the average daily rainfall for the last 9 months of last year?

A. 14cm
B. 16cm
C. 18cm
D. 24cm
E. 30cm


the easiest way you may like

12cm * 12 = 144cm
6cm * 3= 18cm

so, (144 - 18) = 126cm rainfall in 9 month
now, average daily rainfall for 9 month

126cm / 9
= 14cm

thanks
:cool:
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Re: For the first 3 months of last year, the average daily rainfall in Lan &nbs [#permalink] 03 Dec 2017, 23:16
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