#24 - Each December 31 in Country Q, a tally is made of the

[Adam Tyson]

There's no need to assume there is a rollover, because the definition of the tally is provided for you: the total amount mined but not consumed. Pretend for a moment that 1980 was the first year any coal was mined, and they mined 10 tons that year. Imagine they consumed 8 tons that year. At the end of the year, the total amount "mined but not consumed" (read that phrase as a whole) is 2 tons. Now, in 1981 they mine another 10 tons. What is the total amount mined at that point? 20 tons. They consume 8 tons again, so now at the end of 1981 the total amount "mined but not consumed" is 4 tons. There's no assumption required - it's just reading the definition as it is, in plain English. Maybe you are reading into it something else, like "in that year"? Don't add to, subtract from, or otherwise alter that definition.

Now we get to some year (1991, let's say) where the tally (the total amount mined but not consumed) is lower than it was a year before. No matter what the numbers are for the amounts mined, consumed, or what exactly the tally was a year ago or is now, the only way that the total amount mined but not consumed would go down is if you consumed some of that prior year's tally. In other words, in 1991 you must have consumed more than you mined. If you mined a ton and consumed less than a ton, your tally would have gone up. If you consumed exactly that one ton, your tally would have stayed the same. Only by consuming more than that ton could your tally have gotten smaller.

By the way, "mined but not consumed" means the same thing as "mined and not consumed", and those both mean the leftover or surplus, the unused excess.

I hope that helps clear things up some for you.

[guilhermeb]

I am still having difficulty distinguishing between "year minus the amount consumed that year" and "the amount of coal, total, that the country has left over after consumption." Could you please show me that more clearly and why understanding the difference between the 1990 and 1991 ration is not important?

Thank you

[Adam Tyson]

I'll give it a try, guilhermeb!

The stimulus tells us that every December 31st, the country counts up all the coal that has been mined but which has not yet been consumed. Whatever they have is their "tally". There is nothing in the stimulus about when that coal was mined, or how much was mined, or how much was consumed. It's just about the total amount that was mined that is still available for consumption.

On December 31, 1991, the tally was lower than the tally a year before. We need to deduce something from that info.

We cannot tell anything about how much coal was mined in 1991, or about how much was consumed. We cannot tell anything about what those amounts were in relation to the amounts mined or consumed in other years. The only thing we know is that the tally has gone down. That means that no matter how much coal was mined in 1991, whether it was more than ever before or none at all, we must have used all of it up and then used some of the coal that had been mined in prior years. The only way the tally (think of it as the leftovers) can go down is if we consume more than we mine.

Maybe in 1990 we mined a million tons and used all million tons. The tally at the end of 1990 would have been the same as the tally at the end of 1989 - we used what we mined and didn't touch the leftovers. In 1991 we may have mined one ton, far less than we did the year before. In order for the tally at the end of that year to be lower than the year before, we would have to have used that one ton that we mined, plus at least some of the leftovers. There's no need to mine or consume more in 1991 than in 1990 - all that we need to is use more than we mined, whatever those figures may be.

[Preethi]

Thank you for sharing so much of information about tally. I am new to this field and I was looking for additional information. Glad that I found this thread. Keep sharing more of your thoughts.

[Mariam]

I picked D and eliminated B because it says that the amount of coal consumed was greater than the amount mined in 1991. I thought it was wrong because that would mean that there is no available coal supply. the stimulus says that the amount was lower but not there wasn't any. Please clarify!

[Adam Tyson]

Mariam, did you go through the earlier explanations in this thread? That tally at the end of the year includes anything left over from the prior year, because that is still coal that has been mined but not yet consumed. It is possible to consume more than you mine IF there is some leftover in the pile of coal from the prior year that you could tap into. There would have to be if the tally - that leftover - was smaller in 1991 than in 1990.

[alylespier]

I read through earlier posts in this thread and want to understand that the answer choices that are wrong are wrong because they compare years. B is correct because it only discusses 1991?

[Jeremy Press]

Hi alylespier,

Yes, exactly! The stimulus only gives us enough information to know about what happened in Country Q between December 31, 1990 (the tally was considerably higher), and December 31, 1991 (the tally was considerably lower). In other words, the stimulus gives us enough to conclude that a change occurred during 1991. We don't have information that would allow us to conclude anything about what happened in the country before December 31, 1990 (in other words, during 1990). So all answer choices that require such information, which is (A), (C), (D), and (E), are uncertain and we can eliminate them.

Hopefully this helps!

[menkenj]

I found this question to be helpful to write out the math of the stimulus.

(M1990 - C 1990 + M1991 - C1991 ) < (M1990-C1990)

The performing basic math. The M1990 and -C1990 are on both sides so those cancel out.
We are left with:

M1991 - C1991 < 0
M1991 < C 1991


I have been working on understanding which #% problems are best solved with basic math and which are not.
I haven't worked out a full fledged system yet but for this problem it really was the best way to solve it IMO.
The intuition of the above explanations are great too but for me personally I found the concreteness of the math much faster and easier to see.

[fk98]

Hi A,

The first statement in this stimulus is what often gives people trouble. It's deceptively tricky. What it tells us is that Country Q makes a tally of the total available coal supplies at the end of each year. That tally is NOT the amount mined minus the amount consumed. It's basically just how much coal they have on hand.

Let me give you an analogy. As an LSAT instructor, I carry a lot of pencils and I tend to lose them or give them away so I often need to buy more. Let's say I tally my pencil stock at the end of each year. At the end of 2012, I had 10 pencils. At the end of 2013, I had 4 pencils. Based on these facts, you really don't know anything about the specific amount of pencils I bought or lost in either year. All you know is that at the end of 2013, I had fewer pencils than I had in 2012. Maybe I didn't buy any pencils in 2013 but I lost 6 and that's why I'm only left with 4. Or maybe I bought 500 pencils in 2013 and I lost 506 of them and that's why I'm only left with 4. You have no idea. But what you do know is that I lost more than I bought in 2013 because I ended up with fewer pencils by the end of the year than I had at the start.

That same concept holds true here. We don't know specifically how much coal Country Q mined or consumed in 1991. We can't make any comparisons between 1991 and 1990 in terms of how much coal was mined and consumed in each year (which is what both answer choice (A) and (D) do). But we can say that if Country Q has less coal at the end of 1991 than it had at the start of 1991, they must have consumed more coal than they mined.

The "tally" concept is really what makes this a tricky concept. But once you figure out what that means, it isn't so bad

Hope this helps!

Best,
Kelsey

Hi Kelsey, this explanation makes so much sense thanks! So to clarify, if the value for 1990 was 10, then 1991 would start with 10, and then it doesn't matter if Q mined more or not that year because the value would still be less than what it was at the beginning, and thus in 1991 more was consumed than mined. Is this correct?