CR - demonstrated byt he case of Tribinia's coal industry.

[anoo_anand]

That the application of new technology can increase the productivity of
existing coal mines is demonstrated byt he case of Tribinia's coal industry.
Coal output per miner in Tribinia is double what it was five years ago, even
though no new mines have opened.

Which of the following can be properly concluded from the statement about
coal output per miner in the passage?

A. If the number of miners working in Tribian coal mines has remained
constant in the past five years, Tribinia's total coal production has
doubled in that period of time.

B. Any individual Tribian coal mine that achieved an increase in overall
output in the past five years has also experienced an increase in output per
minor.

C. If any new coal mines had opened in Tribiniain the past five years, then
the increase in output per miner would have been even greater than it
actually was.

D. If any individual Tribinian coal mine has not increased its output per
miner in the past five years, then that mine's overall output has declined
or remained constant.

E. In Tribinia the cost of producing a given quantity of coal has declined
over the past five years.



Questions is: Why D is wrong and B right ?

The increase in output per miner can aso be due to removing miners ? i.e. decreasing the number of miners then also we will get the same result.

However in D we are sure that if the output per miner did not increase then the output aso will not increase.

How does one solve in the test questions like this .

[RonPurewal]

you should go double-check the answer to this one; it should be (a).

explanations:

That the application of new technology can increase the productivity of
existing coal mines is demonstrated byt he case of Tribinia's coal industry.
Coal output per miner in Tribinia is double what it was five years ago, even
though no new mines have opened.

simplify!

ALL this really says is:
the average coal output per miner, for ALL of tribinia, has doubled over the last 5 years.
that's it.
this means that there could be vast differences between miners; this is only a national average. in particular, it is totally possible that some miners, and some mines, are LESS productive than they were 5 years ago.

...and no new mines have opened.
however, the existing miners could have added, or laid off, miners. there is no information in the passage about the # of workers at each mine.
in fact, there could now be 100 times as many miners as there were before, at every mine.
or 1% as many as before. we have no idea at all.

Which of the following can be properly concluded from the statement about
coal output per miner in the passage?

remember what "properly concluded" (or "draw the conclusion" in general) means.
you have to PROVE THE STATEMENT!

A. If the number of miners working in Tribian coal mines has remained
constant in the past five years, Tribinia's total coal production has
doubled in that period of time.

CORRECT ANSWER

this choice deals with the WHOLE NATION of tribinia, so we can use the quoted statistic.
5 years ago, there were N number of miners, and their production rate was X units of coal per miner. that's a total of NX.
now, there are still N number of miners, but their production has increased to 2X units of coal per miner. that's a total of 2NX.

proved.

(also notice that this choice, alone among ALL the choices, fixes that pesky number-of-miners issue.)

B. Any individual Tribian coal mine that achieved an increase in overall
output in the past five years has also experienced an increase in output per
minor.

nope.

see above -- you can't assume that the NATIONAL trend applies to INDIVIDUAL mines.

also, see above again -- it's entirely possible that this result could have come from adding miners to the mine's work force.

can't prove the statement.

C. If any new coal mines had opened in Tribiniain the past five years, then
the increase in output per miner would have been even greater than it
actually was.

totally hypothetical. no grounds whatsoever to prove (or disprove) this one.

D. If any individual Tribinian coal mine has not increased its output per
miner in the past five years, then that mine's overall output has declined
or remained constant.

nope.

see above -- it's possible that the mines added workers.

if a mine added workers, then its TOTAL OUTPUT could increase despite a decrease in the per-worker output.
(i.e., think about 100 workers producing 3 units each, vs. 200 workers producing 2 units each.)

can't prove the statement.

E. In Tribinia the cost of producing a given quantity of coal has declined
over the past five years.

totally unrelated to anything in the passage.

the answer should be (a) -- please check again.

[saptadeepc]

Hi Ron,

Sorry to bump on this thread after such a long time.

I agree with the answer that you have provided, but I want to clarify something in option 'C'

According to the Question, it is given that :-
Coal output per miner in Tribnia is double what it was five years ago, even though no new mines have opened.

this means, if there were new mines, productivity would have increased.

Option 'C' says,

C. If any new coal mines had opened in Tribnia in the past five years, then the increase in output per miner would have been even greater than it actually was.

Please clarify, why is this not even related to the question at hand ?

I thought it is a contender, but a weak one coz 'A' is much stronger than this one.

[RonPurewal]

C. If any new coal mines had opened in Tribnia in the past five years, then the increase in output per miner would have been even greater than it actually was.

Please clarify, why is this not even related to the question at hand ?

I thought it is a contender, but a weak one coz 'A' is much stronger than this one.

it's not "irrelevant"; it's actually flat-out wrong. notice that it's talking about an increase in the coal output *per miner*, not an increase in the total numerical output of coal.
if a new mine were inefficient (i.e., produced a low amount of coal per miner), then it could actually *decrease* the average output of coal per miner.
if you don't see why this is the case, play around with some numbers. it may perhaps be instructive to open your theoretical new mine with an output of 0, and see what happens to the coal per miner overall.

[saptadeepc]

C. If any new coal mines had opened in Tribnia in the past five years, then the increase in output per miner would have been even greater than it actually was.

Please clarify, why is this not even related to the question at hand ?

I thought it is a contender, but a weak one coz 'A' is much stronger than this one.

it's not "irrelevant"; it's actually flat-out wrong. notice that it's talking about an increase in the coal output *per miner*, not an increase in the total numerical output of coal.
if a new mine were inefficient (i.e., produced a low amount of coal per miner), then it could actually *decrease* the average output of coal per miner.
if you don't see why this is the case, play around with some numbers. it may perhaps be instructive to open your theoretical new mine with an output of 0, and see what happens to the coal per miner overall.

Hi Ron,

thanks for the reply. I completely understand that 'A' is the best and 'A' can be proved to be true 100 percent of times.

what made me think was the keyword "even though", which brings in a contrast.

I 'am quoting an example on my understanding, please correct me if I m wrong. ( I try to understand everything from a layman's level )

For example
I got wet, even though it dint rain -- this sentence will CONCLUDE
THAT
I got wet due to something else BUT NOT RAIN
AND NOT THAT
If it rains, I will get wet.

[RonPurewal]

For example
I got wet, even though it dint rain -- this sentence will CONCLUDE
THAT
I got wet due to something else BUT NOT RAIN
AND NOT THAT
If it rains, I will get wet.

in the context of a problem like this one, this is correct -- on conclusion problems, you don't want to draw any inferences that are not logically sound. (a.k.a. you want to use "robot thinking")

note that this sort of strict logic is absolutely limited to conclusion problems -- you'll get in big trouble if you think that strengthening/weakening or "explain the situation" problems are as strictly logical as this type.

[K. Ali]

Manhattan Staff

You says "remember what "properly concluded" (or "draw the conclusion" in general) means.
you have to PROVE THE STATEMENT!"

My question is which statement I have to prove ?
Whether the question statement or the answer choice statement?

Thanks

[agarwalmanoj2000]

Kamilriz,

We should be able to prove the answer choice statement that we select as answer.

[tim]

thanks!

[jasonma.hp]

Hello, Ron! Good day!
For A, does 'in that period of time' mean 'in last five years'?
Let us assume that coal output per miner is 10, and output per miner of five years ago was 5. However if coal outputs of per miner in last 3 years were 2,1,1, and the number of miners remained constant, the total coal production will be 19, not 50. Please kindly help and let me know what is my wrong? Thanks a lot!

[RonPurewal]

i'm not following you-- i don't understand what those numbers represent, nor can i tell what you're doing with them.

in any case, it seems you're overcomplicating the issue.

the prompt is just telling us that C/M has doubled (where C = coal output and M = number of miners).

choice A says that, if M has not changed, then we know C has doubled. that's a mathematical fact.

[sw001]

Hello Ron,

I have some doubts on the solution of this answer choice -

For Answer choice A - What is given in the passage is that miners are constant. How can we be sure that total production of coal mines has doubled? There could be some coal mines that could have shut down. Thus, decreasing the overall production - as passage says there are no new coal mines, but doesnt say the coal mines are constant in number, they can always decrease in number.

For choice B - It says that if any individual coal mine has increase in output, it has also experienced an increase in output per miner. An increase in output per miner is given in the passage that it has doubled. Thus, we know for sure that it has doubled or increased - thus it would be increased per individual mine as well.

Also - I have seen in other CR problems that argument talks about a group as a whole and correct answer choice has inferred something about a subset of the group. Thus, if here the answer choice is talking about an individual coal mine. Why are we excluding that as an option? We can always talk about subset of the group, as same rule should apply to the subset of the group as to the overall group.

Thank you for your time!

That the application of new technology can increase the productivity of
existing coal mines is demonstrated byt he case of Tribinia's coal industry.
Coal output per miner in Tribinia is double what it was five years ago, even
though no new mines have opened.

Which of the following can be properly concluded from the statement about
coal output per miner in the passage?

A. If the number of miners working in Tribian coal mines has remained
constant in the past five years, Tribinia's total coal production has
doubled in that period of time.

B. Any individual Tribian coal mine that achieved an increase in overall
output in the past five years has also experienced an increase in output per
minor.

C. If any new coal mines had opened in Tribiniain the past five years, then
the increase in output per miner would have been even greater than it
actually was.

D. If any individual Tribinian coal mine has not increased its output per
miner in the past five years, then that mine's overall output has declined
or remained constant.

E. In Tribinia the cost of producing a given quantity of coal has declined
over the past five years.



Questions is: Why D is wrong and B right ?

The increase in output per miner can aso be due to removing miners ? i.e. decreasing the number of miners then also we will get the same result.

However in D we are sure that if the output per miner did not increase then the output aso will not increase.

How does one solve in the test questions like this .

[RonPurewal]

Hello Ron,

I have some doubts on the solution of this answer choice -

For Answer choice A - What is given in the passage is that miners are constant. How can we be sure that total production of coal mines has doubled? There could be some coal mines that could have shut down. Thus, decreasing the overall production - as passage says there are no new coal mines, but doesnt say the coal mines are constant in number, they can always decrease in number.

the number of mines is not relevant.

only two variables are considered here:

first:
coal output, or, equivalently, coal production (= measured in tons, or cubic metres, or some other unit that measures AMOUNTS OF STUFF)
note that 'output' and 'production' are the same thing.
let's call this 'P'.

second:
number of miners
let's call this 'M'.

the passage says that the ratio P/M is twice the old value.

choice A says, "if M has not changed, then P must be twice as big as it was." it should be quite clear that this is true.

[RonPurewal]

For choice B - It says that if any individual coal mine has increase in output, it has also experienced an increase in output per miner.

nope.
we have no information at all about the number of miners.
we have nothing about the number of miners in the industry overall, nor do we have anything about the number of miners at individual mines.

if a mine hired more workers, this statement could quite well be false.

[RonPurewal]

We can always talk about subset of the group, as same rule should apply to the subset of the group as to the overall group.

i think i am misinterpreting the red thing.

to me, the red thing seems to say this: "Any numerical statement that's true for a larger group will automatically be true for ALL smaller sets chosen from those groups."
...but that's plainly false, so you must have meant something else.

what did you mean to say? could you perhaps express the idea in other terms?