Can someone please explain why A is correct?

The key is to understand that we are asked about "crop yields per acre".

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Some thoughts on why (A) is not correct. Maybe someone prove me wrong.

Let planted acreage in USSR and USA = 1
Let fallow acreage in USSR and USA = 1
z1 = crop yield per acre on USSR fallow acreage
z2 = crop yield per acre on USA fallow acreage

Then, from the last sentence of the passage, we derive an equation:

(0.68*1 + z1*1) / (1+1) = [ (1*1 + z2*1) / (1+1) ] * 114/100
...
After algebraic arrangements, we get :
z1 = 13; z2 = 11 (one solution of many): crop yield on fallow acreage in USSR=13 > in USA=11.

So, it can not be (A): 1/(1+1) > 1/(1+1) - nonsense.

Fallow = 0 Yield.

Let R and US have the same agricultural land, say 100x.
US has yield of 1, Russia of 0.68.
So Us produces 100 units and Russia 68 Units.

Adding the fallow area that has yield = 0, we are told that Russia's total yield is now bigger than that of the US.
Russia's ratio --> production / (planted+fallow) is bigger than the US'.
The only way this can happen is if the US fallow land increases by a larger absolute amount than Russia's.

In other terms, the yield is more diluted in the US than in Russia, because the overall agricultural land comprises more fallow area.

Its A in IMO.
Please see the attached image.

In all other options no idea of P and F which is must so wrong

First reason, the passage only gives the proportional information, and only the choice A talks about proportional information. Others talk about absolute values, which we can’t infer from the information given from the passage.

Second reason, let’s see the calculation.

“In terms of crop yield per acre revealed that when only planted acreage is compared, S yields are equal to 68% of US”
Simply means that \(\frac{US’s Crops}{US’s Planted acre}>\frac{S’s Crops}{ S’s Planted acre}\)

“When total acerage is compared, S yields is 114% of US yields.”
Means that \(\frac{US’s Crops}{US’sP+F}<\frac{S’s Crops}{S’sP+F}\)

Therefore, since the numerators haven’t changed but denominators, to make the fraction of US smaller than S’s, US’s amount of Fallowed acreage should be bigger than that of S’s.

Thus, fallow acreage of US must be bigger than that of S’s.

Posted from my mobile device

Here is the quick & easy way to do this question

A A higher percentage of total agricultural acreage was fallow in the United States than in the Soviet Union.
- HOLD, no immediate reason to eliminate

B The United States had more fallow acreage than planted acreage.
- eliminate
- the text gives us no information about fallow vs planted acreage in the US or in the Soviet Union

C Fewer total acres of available agricultural land were fallow in the Soviet Union than in the United States.
- eliminate
- the text compares only yields per acre; we cannot infer anything about the number of acres

D The Soviet Union had more planted acreage than fallow acreage.
- eliminate
- the text gives us no information about fallow vs planted acreage in the US or in the Soviet Union

E The Soviet Union produced a greater volume of crops than the United States produced.
- eliminate
- the text compares only yields per acre; the text tells us nothing about the area under cultivation or the volume of crops

By Process of Elimination, the answer is A
A can be shown to be the answer by logic too (but why bother? )

PS: Let's try to avoid algebra in Critical Reasoning questions
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