Source: Official Guide Revised GRE 1st Ed. Part 4; Set 6; #2

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A ten-year comparison between the United States

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. When total agricultural acreage (planted acreage plus fallow acreage) is compared, however, Soviet yield was 114 percent of United States yield. From the information above, which of the following can be most reliably inferred about United States and Soviet agriculture during the ten-year period? A higher percentage of total agricultural acreage was fallow in the United States than in the Soviet Union., The United States had more fallow acreage than planted acreage., Fewer total acres of available agricultural land were fallow in the Soviet Union than in the United States., The Soviet Union had more planted acreage than fallow acreage., The Soviet Union produced a greater volume of crops than the United States produced.

6 Explanations

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Zhenghui Li

For me, the fastest method may be a mathematical one.
In this question, the total yield of tow countries do not change in two comparison.
Say yield per acre of US when compared with planted acreage is X, then that of SU will be 0.68X
Thus total yield of US : X * planted area of US
total yield of SU: 0.68X * planted area of SU

Then let us do the second comparison, divide the total yield by total area. We will have an equation:
1.14 * (X * planted area of US / total agri area of US) = 0.68X * planted area of SU / total agri area of SU
We can then substitute X and get
planted area of US / total agri area of US = (0.68/1.14) * (planted area of SU / total agri area of SU)

That means the percentage of US acres that are planted acreage is lower than SU, thus the percentage of US acres that are fallow is higher.

I hope this would help. ^ ^

Jun 21, 2018 • Comment

David Recine, Magoosh Tutor

Thanks for sharing that, Zhenghui. :) For those who are confident in Quant but sometimes have doubts in Verbal, it's always good to look for a way to use math strengths in CR. And there are a number of other CR questions out there that can also be dealt with mathematically!

Jun 26, 2018 • Reply

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Xu Hongduo

I still get confused why not choose C but A. As shown in the paragraph, [US yield / US planted acres ] > [Soviet yield / Soviet planted acres ], but [US yield / (US planted acres + US fallow acres)] < [Soviet yield / (Soviet planted acres + Soviet fallow acres)]. Therefore, it is reasonable to draw a conclusion that [US fallow acres > Soviet fallow acres]. It could only be a larger amount of fallow acres in US compared to Soviet that pulls down the crop yields per acre because the other terms in the second inequality aren't changed.
However, we have no idea about the relationship between [US fallow acres/ (US planted acres + US fallow acres)] and [Soviet fallow acres/ (Soviet planted acres + Soviet fallow acres)] since we don't know for US planted acres and Soviet planted acres which amount is larger.

Feb 26, 2018 • Comment

Sam Kinsman, Magoosh Tutor

You're on the right track here, Xu. You are right that:

[US yield / (US planted acres + US fallow acres)] < [Soviet yield / (Soviet planted acres + Soviet fallow acres)]

Notice that this does not mean that [US fallow acres > Soviet fallow acres] in absolute terms. Instead, it means that the percentage of US acres that are fallow is greater than the percentage of Soviet acres that are fallow.

Think of it like this: let's pretend that the US is a very, very small country. Its crop yield is 10 tonnes, and it has 1 planted acre and 4 fallow acres. So US yield per total acres is 10/5 = 2.

Now let's say the Soviet Union has a yield of 1000 tonnes, and 80 planted acres and 20 fallow acres. So its yield per total acres is 1000/100 = 10.

In this example, the US has a higher yield per planted acre than the Soviet Union, and the US has a lower yield per total acres than the Soviet Union (just like the question stated). The US has a higher percentage of fallow acres than the Soviet Union (80% vs 20%). But in terms of total amount of fallow acres, the Soviet Union has more fallow acres than the US.

So the information that we are given in the question does not mean [US fallow acres > Soviet fallow acres], but it does mean that the percentage of US acres that are fallow is greater than the percentage of Soviet acres that are fallow.

Mar 1, 2018 • Reply

Xu Hongduo

Thanks for your enlightening example! I got it! But it might be better if you assume a smaller number for crop yields in Soviet Union such as a number smaller than 800:)

Mar 10, 2018 • Reply

Sam Kinsman, Magoosh Tutor

Yes, we could do that too. The example would still work :)

Mar 14, 2018 • Reply

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Sam Adeniran

let's bring it home a little. let's assume that the planted acreage is represented by the size of a kitchen, and let's assume that the fallow land is the rest of the house. With respect to this question, we will operate under 2 assumptions:
Assumption 1-- the kitchen is the only useful part of the house and the rest of the house is useless.
Assumption 2-- the bigger the kitchen, the more the food comng out of it.

Now, the US has a bigger kitchen compared with the Soviet Union, so the amount of food coming out is bigger, let's assume the value of the food is 100. The Soviet Union has a smaller kitchen producing smaller food, let's assume the value of the food is 68. Therefore if we are only focusing on the kitchen which is the useful part of the house, The US has more food than the Soviet Union. (just like in the first part of the question, the US has more yield per acre than the Soviet Union).

Now that we've settled the kitchen, let's focus on the entire building. The US is a skyscraper while the Soviet Union is a studio apartment. Let's represent these two different buildings with hypothetical values.

US building (skscraper)= 1000
Soviet Union building (studio apartment)= 136

Now, let's compare the value of food coming out of the useful kitchen (planted acreage), with the size of the building (planted acreage + fallow land)

For the US= 100/1000= 0.1

For the Soviet Union= 68/136= 0.5

Therefore, Soviet Union > United states.

In the question Soviet Union's yield per acre is 114 percent of the United State's yield because it has a smaller fallow land (building= studio apartment) than the US (building= skyscraper).

I hope this helped :)

Mar 11, 2017 • Comment

Navya Kollapally

Such a great example..thanks Sam :)

Jul 8, 2017 • Reply

MOHAMMED SAFIUL AZAM

Hello. Thanks a lot. However I still have confusion on a certain part of the passage. According to the texts "when total acreage is compared, however SU yield=114%of US yield". If I consider your example US=1000 then isn't it SU=114% of 1000 which makes it 1140 for SU and finally US(0.1)>SU(0.05). I would really appreciate your help here, thanks in advance :)

Mar 17, 2018 • Reply

Sam Kinsman, Magoosh Tutor

Keep in mind that when the passage mentions 114%, it is referring to yield (and not the amount of total acreage). It is saying that "when total acreage is compared, however SU yield=114%of US yield."

In the example above, the US yield is 100 / 1000 = 0.1. So the SU yield is greater than that. If the example used the exact numbers that the question does, the Soviet yield would have to be 114% of the US yield - so it would be 114% of 0.1, or 0.114.

Even though the example above does not use the exact numbers that the question does, it's a very nice illustration of how this question works.

Mar 21, 2018 • Reply

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chia hua Cheng

Why b and c are incorrect?

Apr 4, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi there :)

Happy to help. B states: "The US had more fallow acreage than planted acreage." In the passage, we're only told information comparing the US and the Soviet Union with which we cannot make any inferences about either country individually. On the other hand, C makes reference to actual amount of acres. However, in the passage, the yield per acre is being compared.

Both B and C can be proven by counter example. OlegC provides a counter example for each on this gmatclub thread about this question: http://gmatclub.com/forum/a-ten-year-comparison-between-the-us-and-the-soviet-union-in-7993.html

Hope this helps :)

Apr 15, 2016 • Reply

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Genevieve Valery

I initially had some trouble understanding this answer too. Thinking about it in the following way helped me. You have two jugs of juice. At first, jug A has a higher concentration of juice that jug B. After adding more water to both jugs, jug B now has a higher concentration of juice. Thus, more water must have been added to jug A than to jug B.

Jan 24, 2013 • Comment

Alvin John

Wow that explanation really helped Genevieve. I was having a tough time trying to understand this question. Thanks so much!!

Sep 19, 2013 • Reply

Abhipshito Bhattacharya

excellent explanation Jean .

Aug 1, 2016 • Reply

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Chris Lele, Magoosh Tutor

Oct 6, 2012 • Comment

Shubham Goel

I am not sure about this approach. I interpreted the question stating a ratio between the total agricultural acreage(fallow and planted) to be 1.14 and not between the percentage of planted land (after including the fallow land) to be 1.14. I am not sure where I made the mistake.

Nov 16, 2012 • Reply

Chris Lele, Magoosh Tutor

The key here is understanding the yield vs acreage. When only those acres that are planted are concerned, the U.S. has a great yield per acre.

When fallow land is taken into account, i.e., land that has zero yield, the numbers flip. Therefore, we can infer that the U.S. has far more fallow land to planted land than does Russia.

Hope that makes sense!

Nov 16, 2012 • Reply

Ramlah Merchant

I am having trouble understanding this. How did you translate the 114% in this and where did you get th 40% from? When I did the exact calculations I got Russia to have a higher percentage of fallow land. I took US's fallow land to be 200 and then the calculation I did was 68+x= 1.14 (300). x comes to be 274 which is a higher percentage of 342(68+274)than 300. Please help!

Sep 13, 2016 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Ramlah,

Happy to help :) First, let's talk about where 114% comes into play. This percentage compares the percentage of planted acreage to the total amount of land (planted + fallow acreage). In your calculations, you compared just the total land acreage.

Let's see the difference by looking at Chris's example:

US: 100 acres planted / (100 + 200) total acres
= 100/300 ~ 0.33 --> 33%
Soviet: 68 acres planted / (68+82) total acres
= 68/150 ~ 0.45 --> 45%

So, in this case, the Soviets have a higher percentage of acres planted per total acres than the US and the percent difference is actually greater than 114%:

(45 - 33) / 33 + 1 = 1.36*100% = 136%

And that's ok, because we're not using the exact numbers (we don't know them based on the prompt!) but rather using other numbers to show the same pattern.

I hope this clears up your doubts! :)

Sep 14, 2016 • Reply

Victor Yusuf

I think the biggest source of confusion here is that:

When the prompt says "when total agricultural acreage is compared" and then turns around and says "soviet YIELD was 114%" in the context of FALLOW (no yield) acreage and planted (actual 'yield resulting') acreage," it is no longer actually just mathematically comparing total agricultural acreages, even though that's what the wording says. The keywords, "fallow," "yield," have usurped that mathematical representation for "when total agricultural acreage is compared" to be "when ratio of planted acreage to total agricultural acreage is compared, Soviet's was 114%."

I guess that's why it's a verbal question and not a math one? Haha. They are really just testing the meaning of the words "fallow" and "yield." :) Even though it is still heavily mathematically jargoned though.

Oct 18, 2016 • Reply

Sam Kinsman, Magoosh Tutor

Hi Victor,

Actually, the question is not comparing the ratio of planted acreage to total agricultural acreage. Instead, it is saying that if we measure crop yields as yield / (planted acres AND fallow acres), Soviet yield was 114 percent of United States yield. In other words, the following comparison is being made:

[US yield / (US planted acres + US fallow acres)] < [Soviet yield / (Soviet planted acres + Soviet fallow acres)]

Oct 19, 2016 • Reply