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# A ten-year comparison between the United States and the Soviet Union i

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Re: A ten-year comparison between the United States and the Soviet Union i [#permalink]
Can someone please explain why A is correct?
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Re: A ten-year comparison between the United States and the Soviet Union i [#permalink]
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gargchetna19 wrote:
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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Re: A ten-year comparison between the United States and the Soviet Union i [#permalink]
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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.
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Re: A ten-year comparison between the United States and the Soviet Union i [#permalink]
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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.
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A ten-year comparison between the United States and the Soviet Union i [#permalink]
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gargchetna19 wrote:
Can someone please explain why A is correct?

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.

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Re: A ten-year comparison between the United States and the Soviet Union i [#permalink]
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Re: A ten-year comparison between the United States and the Soviet Union i [#permalink]
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