An apple farm installed a fish pond on its land to save money and

Question

https://gmatclub.com/forum/download/file.php?mode=view&id=51970 An apple farm installed a fish pond on its land to save money and increase potential revenue. Waste apples and other apple by-products are used to supplement the diet of the fish while the waste from the pond is used to fertilize the apple trees. Fish and apples are both sold for profit. The graph shows the total cost of fertilizer per 10 kg of apples that are sold as well as the total number of fish sold in each year. Use the drop-down menus to complete the statements in a manner consistent with the given information. The average amount by which the cost of fertilizer per 10 kg of apples sold decreased from year 1 to year 5 is, to the nearest power of 10, nearest to GRAPH_1_PLACEHOLDER dollars per 10 kg apples per year. After year 3, the rate of growth in the total number of fish sold per year was GRAPH_2_PLACEHOLDER ID: 100350 Fish Sales and Fertilizer Cost.JPG

mborski · Accepted Answer

Question 1 - Looking at the graph, the cost of fertilizer in year 1 was 0.05 dollars per 10 kg apples sold. In year 5, that number was 0.005. You could calculate the decrease each year in between and get an average, but just by looking at the graph, we can see we're dealing in hundredths. Therefore the answer is D. 0.01

I think they're trying to throw you off by having you pull numbers for fertilizer cost from the right hand "dollars per 10kg of apples sold" side of the graph.

Question 2. - On the graph, the total number of fish sold in year 3 was 2,000 and the total in year 4 was 3,000, an increase of 1,000 fish. However, from year 4 (total fish 3,000) to year 5 (total fish 3,500), the increase is only 500 fish. Since we're talking about  rate , an increase of 1,000 in a one year period, then an increase of only 500 the following year means that the rate is decreasing. Answer: B decreasing.

Can be a bit tricky if you only look at the black line as increasing, rather than comparing the  rate  of change.

mborski · Answer

The “ Power of 10 ” is any of the integer exponents of the number 10. In other words, the number of 10s indicated by the exponent, multiplied together.

For example: 10 to the 3rd power is 10 x 10 X 10 = 1,000.

If the exponent is greater than zero, written in long form, a power of 10 is the number 1 followed by  n  zeros.  N  being the exponent.
Example:  10^8  equals 1 with 8 zeros behind it --> 100,000,000

If the exponent is less than zero, written out, the power of 10 is 1 with  n  places  after  the decimal point.  N  again being the exponent.
Example:  10^{-3}  is 1 with three places after the decimal point --> 0.001

In this particular problem, they are asking you to find the answer “to the nearest power of ten” because all of the answer choices are listed in powers of ten. By looking at the graph, we see that in year 1, the cost of fertilizer (per 10 kg of apples) is 0.05 and in year 5, the cost is 0.005. To calculate the actual average, first get the total difference

0.05 – 0.005 = 0.045

And divide it by the number of years

0.045 / 5 = 0.009

So, 0.009 is the  true  average, but the question asks you to find the average  to the nearest power of 10 . 0.009 is not a power of 10, so we need to round up a bit. Hence, 0.01 is the answer.

That’s the very long answer. The short answer is, because this is an integrated reasoning question, they probably just want to make sure you can read a graph correctly. The trick is not to focus on the actual average (doing the exact math to calculate 0.009), but to look at the graph and estimate by about how much the cost is decreasing per year. The cost of fertilizer per 10 kg of apples sold is listed on the right-hand side of the graph. Over 5 years, each year, the cost seems to go down by about 0.01 dollars.

Apt0810 · Answer

1) D -0.01 since the change from 0.005 to 0.05
2) The rate of increase is decreasing from 3-4 and from 4-5

Posted from my mobile device

kntombat · Answer

According to my understanding,
 The answer to question 1 should be option D , as the average of the decrease of the amount by which the cost of fertilizer per 10 kg of apples sold to the nearest power of 10 would be 0.01. Someone can try to calculate the value(I partially did it and on seeing the option knew D was the answer) or someone can just scan the graph look at the answer options and choose D to be the answer.

The answer to question 2 should be option B  i.e. decreasing, as from year 3 to year 4 the number of fish sold does increase but from year 4 to year 5, the value decreases.

Vegita · Answer

Hey there guys,

Could anyone please explain me what the phrase " the nearest power of 10 " means?

stoirar · Answer

Just curious, what if one where asked to solve for the average amount by which the cost of fertilizer per 10 kg of apples sold decreased from year 1 to year 5?

amount by which the cost of fertilizer per 10 kg of apples sold decreased from year 1 to year 5 = .05 - .005 = .045

divide by five to get average amount by which the cost of fertilizer per 10 kg of apples sold decreased from year 1 to year 5 so 0.045/5=.009.

do folks agree? I find it helpful to solve problems such as these then compare to answer choices

Trancv · Answer

The combo chart is misleading I think. GMAC should have used 2 separate charts instead for better readability.

Rytthhm · Answer

mborski

What the 5 observations of the difference for which you are calculating the average of the 5 years?

GMATCoachBen · Answer

Rytthhm   short video solution here (2:08):

https://www.youtube.com/watch?v=UpNuAi6RTWk

GMATCoachBen · Answer

Sajjad1994  I saw this one in OG 2023-2024, do you want to re-tag the source? It says "GMAT Pill" now. Thanks!

Elite097 · Answer

GMATCoachBen  shuld we not divide the change over the 5 years by 4 and not 5 since we have 4 values?

GMATCoachBen · Answer

Elite097  Yes, you are correct! I mentioned in the video that there are 4 decreases (year 1 to 2, year 2 to 3, year 3 to 4, and year 4 to 5).

However, it makes no difference here, since the answers are so spread out. It's very helpful to round and approximate when we see that the answers are spread out, or when the stem says "nearest to" or "approximately"!

SMQazi · Answer

the ask here isn't to solve anything, but interpret the graph by just looking at it.

simply consider "dollars per 10 kg apples sold" as points on the graph so .05 becomes 5, 0.04 becomes 4...

change between year 1 & 2 was 0.5 points, followed by 1.5, then 1 point, and lastly 1.5
Add the numbers and divide by 4 for average change.

=0.5+1.5+1+1.5 / 4
=1.13

now, revert back to decimals  0.011 * 10^2 , which is D.

2. If you read the prompt carefully, the ask is only after year 3.
So, between 3-4, it was 1000 fish, between 4-5, it reduced to 500, hence  decreases .

k11work · Answer

Average amount means slope of the graph :

Part 1:

A(1,0.05) - B(5,0.005)

Slope = 0.045/4 = 0.011
Thus, nearest power of 10 is 0.01.

Part 2:

Slope of the graph is decreasing per year after the 3rd year , thus decreasing.

SSKP · Answer

This was a very good question.

bhanu29 · Answer

The average amount by which the cost of fertilizer per 10 kg of apples sold decreased from year 1 to year 5 is, to the nearest power of 10, nearest to _____ dollars per 10 kg apples per year.
Cost of fertilizer in year 1 : 0.05
Cost of fertilizer in year 5: 0.005
Decrease = 0.05 - 0.005 = 0.045/5 = 0.009, This is nearest to 0.01

After year 3, the rate of growth in the total number of fish sold per year was ____

If you see the slope of line after year 3 it's decreasing (angle with x axis)
So rate of growth is decreasing

Correct Answer: 0.01, Decreasing

vartikg · Answer

are we to simply divide by 5 once we have figured out the change, which is 0.045. for average or it done any other way

JustKeepGoing · Answer

Hi  vartikg

Please note that right side y-axis of the graph denotes "cost per 10 kg of apples sold" which is actually average or mean itself (sum divided by quantity). 
Hence, Average change = 0.045 dollars per 10 kg apples.

However, we divided 0.045 by 5 (or a 4...doesn't matter here) because 1st prompt asked us to calculate the " dollars per 10 kg apples   per year"

No other way to solve the 1st prompt.

egmat · Answer

Hi vartikg,

Great question! You've correctly identified the total change as approximately  0.045  — that's the right first step. Now, the key detail is what you divide by.

Key Insight:  When calculating an average annual change FROM Year  1  TO Year  5 , you divide by the number of intervals between those years,  NOT  the number of years listed.

From Year  1  to Year  5 , the intervals are:
- Year  1  to Year  2  (interval  1 )
- Year  2  to Year  3  (interval  2 )
- Year  3  to Year  4  (interval  3 )
- Year  4  to Year  5  (interval  4 )

That gives us  4  intervals, not  5 .

So the calculation is:   0.045  /  4  =  0.01125

Now, the question asks for the answer to the nearest POWER of  10 . The powers of  10  in the dropdown are:  100 ,  10 ,  1 ,  0.01 ,  0.0001 .

0.01125  is closest to  0.01  (which is  10 ^ -2 ).

Here's the good news though — even if you had divided by  5  ( 0.045  /  5  =  0.009 ), you'd still get closest to  0.01  as a power of  10 . So for THIS particular question, both approaches give the same final answer. But conceptually,  dividing by  4  is the correct method .

The general rule:   Average annual change = Total change / (Final year - Starting year) . Think of it like fences and fence posts —  5  posts create only  4  gaps between them.

Answer: 0.01, Decreasing

An apple farm installed a fish pond on its land to save money and

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An apple farm installed a fish pond on its land to save money and

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