The graph provides data on coffee bean production by the top 12 farms

Question

https://gmatclub.com/forum/download/file.php?id=85795 The graph provides data on coffee bean production by the top 12 farms and all other producers combined in the Andean Valley in 2022. Select from each drop-down menu the option that creates the most accurate statement based on the information provided. For the top 12 coffee-producing farms in 2022, the GRAPH_1_PLACEHOLDER of the given production volumes was greater than the production of exactly half of these 12 farms. In 2022, the combined production of the three largest farms was GRAPH_2_PLACEHOLDER the production of the farm ranked 13th in size. GMAT-Club-Forum-nxip37x3.png

Bunuel · Accepted Answer

Dropdown 1:

The median of 12 values is the middle value, which is the average of the 6th and 7th. Here those are 750 and 700. Since these two values are not the same, the median must fall between them, and by definition it will be greater than the lower half of the values. So the median = (750 + 700)/2 = 725, which is greater than exactly six of the farms.

Why the others are wrong?

Mode is not correct because all values are distinct and the mode does not exist.

Range = 1200 − 500 = 700, which is greater than only five farms and equal to one, not strictly greater than half.

Standard deviation is not correct: the values lie between 500 and 1200, are fairly spread out, and the deviation will be well below 700, so it cannot be greater than half of the values.

Dropdown 2:

The combined production of the three largest farms is 1200 + 920 + 890 = 3010. The 13th largest farm must have production less than 500, because the 12th is 500. Even if the 13th were equal to 500, the ratio would be 3010/500, which is more than 6. Hence the correct choice is more than 6 times.

I29-158

sarveshkhonde · Answer

1.  Median 
Median of 12 farms is 725 (not included 13th farm named as Others (combined) which is 860).

725 is greater than exactly half of the 12 farms i.e. 6 farms.

2.  3.5 Times 
Sum of the three largest farms is 1,200 + 920 + 890 = 3,010, which is 3.5 times of 13th farm i.e. Others (combined) which is 860

860*3.5 = 3,010

crimson_king · Answer

Answer for Part 2 should be more than 6 times as the 12th largest is 500.So 13th largest would be less than 500 & the combined production of the top 3 producers is over 3000 (3010 to be exact) & 500*6 = 3000.

sarveshkhonde · Answer

Yes I have little doubt about that whether 13th farm should be Others (combined) 860 or should it be River 500, because Others (combined) is specifically given as the last one i.e. 13th in number in the image.

Bunuel · Answer

Others cannot be 13th farm. The 13th farm is among the other group.

findingmyself · Answer

Hi  Bunuel

I am confused in this part:  For the top 12 coffee-producing farms in 2022, the of the given production volumes was greater than the production of exactly half of these 12 farms.

By reading this, I understood that the measure which is (range, mode, median, SD) should be greater than half of the production value   (production of exactly half of these 12 farms.)   of 12 farms. This is not a possible scenario. How to interpret this question? What is it asking for that is not coming clearly? 
 Please help.

Bunuel · Answer

The question means this: take the 12 farms and consider the chosen measure. Then check how many of those 12 farms have production below that value. The wording is simply saying that the measure is greater than the production of exactly half of the farms, that is, greater than 6 farms’ outputs.

findingmyself · Answer

Thanks  Bunuel

I wrongly assumed from the wording that the measure should be greater than the total of exactly half of these farms which, anyway, makes no sense. Thanks for the clarification.

Elite097 · Answer

The median lies between 700 and 750 so the production of 6 of these farms is definitely lesser than the median

Total production of 3 farms =3000 which will be more than 6 times of production of 13th farm which will be lesser than 500

AbhishekP220108 · Answer

Hi Sarvesh, I think you have got the first one correct, and also you have shown a good sense of analysis; however, the approach to the second is wrong.

Let me explain, how to approach

1.   Median of 12 farms will be avg of 6th and 7th farms  
6th 700
7th 750

so Avg will be (700+750)/2 which is the Median of 12 farms i.e 725 and 725 is greater than exactly half of the 12 farms i.e. 6 farms.

2.   More than 6 times

Sum of top 3 farms is 1200+920+890=3010 and by looking at the graph we can see that 13th farm will be either 500 or lesser than that, assuming it same as 500, sum of top 3 i.e 3010 is 6.02 times higher than 13th.

Question why we are not taking 13th as other combined value, because it already defines that it is some of all other 12farms and by looking at trend, 13th will be either same as 12th value or less than that.

Hope this helps

Dereno · Answer

Question1:

Since all the values of the coffee production for the first 12 farms are unique. There cannot be Mode.

The range of the 12 farms = 1200 - 500 = 700. This range is greater than 660, 640, 600, 580, and 500. So only 5 values.

Let’s look for the median values, after arranging it in ascending values = (750+700)/2 = 725.

725 is greater than 700, 660, 640, 600, 580, and 500. so  Median is greater than EXACTLY 6 values .

Question 2:

In 2022, the combined production of the three largest farms was (Select : more     than 6 times/ 6 times/ 3.5 times / less than 3 times)      the production of the farm ranked 13th in size.

The combined production of the three largest farms = (1200+ 920+890) = 3010.

we are given the absolute values for 12 farms, and the 13th farm can take a value 500. Since, it’s not mentioned that these values are unique.

3010 = x * 500

x > 6

so,  MORE THAN 6 times .

The graph provides data on coffee bean production by the top 12 farms

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The graph provides data on coffee bean production by the top 12 farms

Prep Toolkit

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