Worldwide paper industry---interesting inference

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Last year the worldwide paper industry used over twice as much fresh pulp (pulp made directly from raw plant fibers) as recycled pulp (pulp made from wastepaper). A paper-industry analyst has projected that by 2010 the industry will use at least as much recycled pulp annually as it does fresh pulp, while using a greater quantity of fresh pulp than it did last year.
If the information above is correct and the analyst's projections prove to be accurate, which of the following projections must also be accurate?
(A) In 2010 the paper industry will use at least twice as much recycled pulp as it did last years.
(B) In 2010 the paper industry will use at least twice as much total pulp as it did last year.
(C) In 2010 the paper industry will produce more paper from a given amount of pulp than it did last year.
(D) As compared with last year, in 2010 the paper industry will make more paper that contains only recycled pulp.
(E) As compared with last year, in 2010 the paper industry will make less paper that contains only fresh pulp.

Answer after some discussion.

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by bubbliiiiiiii » Tue Apr 12, 2011 3:36 am
IMO A.

I would have loved to choose D if it didnot contain the word 'only'.

OA and OE please.

Please correct me incase I am wrong.
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by HSPA » Tue Apr 12, 2011 3:40 am
last year : F1 = 2 R1 = 1
this year projection : R2 >= F2

R2 = 3 and R2 >= F2, R2+f2 >= 6

a) R1*2 = 3 false
b) 3*2 = 6

IMO B
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by sandy217 » Tue Apr 12, 2011 4:32 am
champmag wrote:Last year the worldwide paper industry used over twice as much fresh pulp (pulp made directly from raw plant fibers) as recycled pulp (pulp made from wastepaper). A paper-industry analyst has projected that by 2010 the industry will use at least as much recycled pulp annually as it does fresh pulp, while using a greater quantity of fresh pulp than it did last year.
If the information above is correct and the analyst's projections prove to be accurate, which of the following projections must also be accurate?
(A) In 2010 the paper industry will use at least twice as much recycled pulp as it did last years.
(B) In 2010 the paper industry will use at least twice as much total pulp as it did last year.
(C) In 2010 the paper industry will produce more paper from a given amount of pulp than it did last year.
(D) As compared with last year, in 2010 the paper industry will make more paper that contains only recycled pulp.
(E) As compared with last year, in 2010 the paper industry will make less paper that contains only fresh pulp.

Answer after some discussion.
IMO C
fresh pulp =2x
recycled pulp =x
2010
fresh pulp =y
recycled pulp = y

It is given y>2x (while using a greater quantity of fresh pulp than it did last year),
hence more pulp is used in manufacturing paper and more paper is possible(? ruling out unstated problems)

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by HSPA » Tue Apr 12, 2011 5:18 am
Hi Champmag,

Kindly provide OE for A and B...
I would be nice if we can get the right math..
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
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by sandy217 » Tue Apr 12, 2011 5:47 am
HSPA wrote:last year : F1 = 2 R1 = 1
this year projection : R2 >= F2

R2 = 3 and R2 >= F2, R2+f2 >= 6

a) R1*2 = 3 false
b) 3*2 = 6

IMO B

HSPA: did u assume that current year is 2009? I think we can't make that assumption !!

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by fitzgerald23 » Tue Apr 12, 2011 6:36 am
This is one of those you can answer using Math.

Current:
Rec. Pulp = R
Fresh Pulp = GT2R

Future:
Rec Pulp = GT2R+1
Fresh Pulp = GT2R+1

A. Correct. No matter what the amount of recycled pulp has to double. If the amount used currently is 10, then fresh pulp is GT20. Fresh pulp will increase in 2010 (lets say by 1 to be GT21), so for the recycled pulp to be the same level it as to grown by more than 10 which is more tan twice the current amount.

B. Incorrect. Not necessarily true. If it just grows by 1 and the initial market was 31 (21 F and 10 R) the new amount would be 44 (22 of both) which is not double.

C. Incorrect. They never give us the information to determine what is needed to make paper.

D. Incorrect. They never tell us the makeup of the paper.

E. Incorrect. Again they never tell us the makeup of the paper.

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by HSPA » Tue Apr 12, 2011 6:59 am
sandy217 wrote:
HSPA wrote:last year : F1 = 2 R1 = 1
this year projection : R2 >= F2

R2 = 3 and R2 >= F2, R2+f2 >= 6

a) R1*2 = 3 false
b) 3*2 = 6

IMO B

HSPA: did u assume that current year is 2009? I think we can't make that assumption !!
Thanks for pointing out sandy.. i took last year total pulp = this year recycle pulp.
That is how I got R2=3 (2F + 1R last year) :(
and based on analyst input I took R2=F2 = 3
So total pulp last = 3 and total pulp this year is 6... I need to hit gerald's input to find bug in my math
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
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by HSPA » Tue Apr 12, 2011 7:04 am
Gerald,

I have a question regarding your 'future' math: You took recycle = 2R+1, but paper can be recycled more than once so shouldnt it be 3R+1..

Sorry but I need your help to identify the bug in my math...
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
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by fitzgerald23 » Tue Apr 12, 2011 7:44 am
HSPA wrote:Gerald,

I have a question regarding your 'future' math: You took recycle = 2R+1, but paper can be recycled more than once so shouldnt it be 3R+1..

Sorry but I need your help to identify the bug in my math...
Last years paper has no bearing on how much pulp the industry is using. Te paper is a finished product whereas the pulp is the raw material. In your original post your math was basically correct (in this case the greater than parts really play no role). I think you just interpreted the choices wrong.

What A is asking is if it will be at least double. You seemed to take it as exactly double. You started with 1 recycled pulp and it grew to 3. That is triple the amount from last year, which satisfies the criteria that at least twice as much is used. For B you just happened to choose numbers that made it positive (3 and 6), but other numbers will make it false. Here is the walkthrough I would do:

Last year the worldwide paper industry used over twice as much fresh pulp (pulp made directly from raw plant fibers) as recycled pulp (pulp made from wastepape


So what this tells us here is that the current level use of fresh pulp is more than two times as much as recycled pulp. In your example you used R = 1. In that case F= GT2, lets just say 2.1.

by 2010 the industry will use at least as much recycled pulp annually as it does fresh pulp, while using a greater quantity of fresh pulp than it did last year


The first thing you have to see is that the use of fresh pulp is going to increase in 2010 over the prior levels. We said it was at 2.1 before. That means the minimum will have to be greater than that. I used a "+1" in my example to keep all the work with whole numbers but lets say its 2.2 to minimize it.

Now the first part tells us that in 2010 the industry will use at least as much pulp in 2010 as it does fresh pulp in 2010. So our recycled pulp in 2010 has to equal no less than 2.2.

If you add those together you can eliminate B. 4.4 (the future total use) is not 2 times greater than 3.1 (the current use). However, there is no set of numbers that can be used that will not make the quantity of R not double in order to meet the new level of fresh pulp usage.