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

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.

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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­To solve this question, let us deploy IMS's four-step technique.

STEP #1 -> IDENTIFY THE QUESTION TYPE

Let us read the question stem to identify the question type.
The stem indicates an inference question.

STEP #2 -> X-RAY THE PASSAGE

In an inference question, it is a must to x-ray the passage and comprehend it. Let us therefore read the passage first and note the facts soon after.
FACT #1: A ten-year comparison between the United States and the Soviet Union in terms of crop yields per acre revealed that when only planted acreage is compared, Soviet yields were equal to 68 percent of United States yields.

FACT #2: When total agricultural acreage (planted acreage plus fallow acreage) is compared, however, Soviet yield was 114 percent of United States yield.

STEP #3 -> FRAME A SHADOW ANSWER

To frame a shadow answer, we need to know what the correct answer should do. In an inference question, the correct answer must be 100 percent validated by the information stated in the passage.

SHADOW ANSWER: An option that is fully validated by the stated facts in the passage.

STEP #4 -> ELIMINATE INCORRECT ANSWERS

Options that do not match the shadow answer can be eliminated.

A. A higher percentage of total agricultural acreage was fallow in the United States than in the Soviet Union. - MATCHES THE SHADOW ANSWER - Does the passage deal with percentage values? Yes, both the facts have percentage values! Does the passage talk of total agricultural acreage in the US and Soviet Union, and does it make a comparison between the United States and Soviet Union with respect to the percentage of total agricultural acreage? Yes! Does either fact talk of fallow acreage? Yes, fact #2 does! Do we have a reason to eliminate the option? No! - KEEP

B. The United States had more fallow acreage than planted acreage. - NOT A MATCH - Does the passage make a comparison between fallow acreage and planted acreage in the US? No! - ELIMINATE

C. Fewer total acres of available agricultural land were fallow in the Soviet Union than in the United States. - NOT A MATCH - Does the passage make a comparison between the Soviet Union and the United States with respect to total acres of available agricultural land? No! - ELIMINATE

D. The Soviet Union had more planted acreage than fallow acreage. - NOT A MATCH - Does the passage discuss total planted or fallow acreage in the Soviet Union? No! - ELIMINATE

E. The Soviet Union produced a greater volume of crops than the United States produced. - NOT A MATCH - Does the passage compare volume of crops in the Soviet Union and United States? No! - ELIMINATE

FINAL CHECK

Let us understand a few terms before we look at this inference question mathematically.

acreage = area of land in acres
fallow = unplanted

Now, let us say the planted area in the United States was 1000 acres.
Let us say the planted area in the Soviet Union was also 1000 acres.
Simply put, the planted acreage in both nations was 1000 acres.

As per fact #1, Soviet yields were equal to 68 percent of United States yields when planted acreage was compared.
Therefore, the United States had crop yields of 1000/1000 (1) while the Soviet Union's crop yields stood at 680/1000 (0.68).

Let us now say the United States had 1000 acres of fallow land as well.
The crop yields would then be 1000/2000 or 0.5 (Crop yields in planted area + Crop yield in fallow area ÷ planted acreage + fallow acreage); remember, since fallow land is unplanted, it cannot have any yield.

Now, Fact #2 mentions that Soviet yield was 114 percent of United States yield when total agricultural acreage was compared.
So, it was 114/100 x 0.5 = 1.14 x 0.5 = 0.57.

FACT CHECK: 0.57 (Soviet yield) is 114% of 0.5 (US yield) when total agricultural acreage is compared while Soviet yields (680) are equal to 68 percent of United States yields (1000) when planted acreage was compared.

Now, let us figure out the total agricultural acreage in the Soviet Union.

Planted acreage divided by total agricultural acreage will give us the yield, which is 0.57.
680 ÷ total agricultural acreage = 0.57
So, total agricultural acreage in the Soviet Union = 6800 ÷ 0.57 = about 1193.
Therefore, the fallow acreage in the Soviet Union would be total acreage minus planted acreage, that is 1193 - 1000 = 193.

The fallow acreage in the United States was 1000 acres, that is 50 percent of the total agricultural acreage.
The fallow acreage in the Soviet Union, however, was roughly 193 acres, about 16 percent of the total agricultural acreage.

Clearly, a higher percentage of total agricultural acreage was fallow in the United States than in the Soviet Union.

Hence, (A) is definitely the correct answer. ­