Harrison is planting a flowerbed. So far he has added 20 pounds of mat

Question

Harrison is planting a flowerbed. So far he has added 20 pounds of material to the soil. The material added was composed of fertilizer and organic compost. He has a 20-pound bag of fertilizer and a 20-pound bag of organic compost and wants to add fertilizer and organic compost in amounts such that the total amount of material added to the soil will be half fertilizer and half organic compost.

In the table below, select a fractional portion of the bag of organic compost and a fractional portion of the bag of fertilizer that Harrison could add to the garden to achieve his goal.

Compost    Fertilizer     
      3/16  
      1/4  
      1/2  
      11/16  
      7/8  
      15/16

Original Answer from Princeton Review as follows:
The word problem provides that Harrison is planting a flowerbed that currently has 20 pounds of material in it – divided into Fertilizer (times 20, or 3.75 pounds) and Compost (3/16 times 20, or 16.25 pounds). He wants to add amounts of Fertilizer and Compost so that the total amount is evenly divided between Fertilizer and Compost. To do so, he needs to make up the difference between the amounts originally added, which is equal to 16.25 pounds less 3.75 pounds, or 12.5 pounds.

Since the answer choices are expressed as fractions of 20-pound bags of fertilizer, you need to select two fractions that differ by 12.5 pounds, or, expressed as a fraction, 10/16 of a 20-pound bag. Which 2 fractions differ by 10/16? (7/8)-(1/4)=5/8=10/16

Alternatively, you could calculate the number of pounds each answer choice represents, and look for a difference of 12.5 pounds.

Since more fertilizer is needed than compost to even out the amounts, the larger of the two fractions will be the correct response for Fertilizer, and the smaller of the two will be the correct response for Compost.

Try the first answer choice, 3/16. 3/16 plus 10/16 equals 13/16. Since 13/16 is not another answer choice, 3/16 is not a correct response.

Try the second answer choice, 1/4. 1/4 plus 10/16 can be restated as 4/16 plus 10/16 , which equals 14/16 , which reduces to 7/8. Since 7/8 is also an answer choice, 1/4 and 7/8 are the correct responses for Compost and Fertilizer, respectively, and no further testing of answer choices is necessary.

Compost: 1/4
Fertilizer: 7/8

I'm always having a hard time with these types of problems, but this one is particularly bad for me and I'm having a difficult time understanding the official Princeton Review explanation! I understand needing to find the difference between the two "current" amounts, but not sure what to do after that!

AndrewN · Answer

Hello,  nr2020 . I would love to see the Official Explanation for this one. Based on what I see on the screen, the question does not make sense to me either, and I am at least decent at IR questions. Is this a case in which you can only make one selection per column, and the same answer cannot be selected twice? I wonder if you have found a question that went to print too quickly—something I have observed in other third-party materials—and the end product is incomplete or does not resemble the original thought.

Please share the OE if you can. Thank you.

- Andrew

Kinshook · Answer

Let us assume that fertiliser already added is x pounds; where x is a positive number less than 20
Organic compost already added = 20 - x pounds

Let us assume that f1 fractional portion of the bag of organic compost and f2 fractional portion of the bag of fertilizer Harrison could add to the garden to achieve his goal.

x + 20f1 = 20 - x + 20f2
20 (f1-f2) = 20 - 2x = 2(10-x)
10(f1-f2) = 10-x
f1-f2 = 1 - x/10
since 0<x<20
-2<-x/10<0
-1<1-x/10<1
-1<f1-f2<1
|f1-f2|<1

Please share OE.

nr2020 · Answer

Hi  AndrewN

I've updated the original question (under the Answer spoiler) with the official explanation from Princeton Review. Thanks for your help!

AndrewN · Answer

Hello again,  nr2020 . Thank you for supplying that additional information. I can now say for sure that the question as presented above is seriously flawed, lacking the numbers we need to be able to calculate anything meaningful.

The  highlighted  part shows what is missing. In short, we need to know the ratio of fertilizer to compost in that initial  20 pounds of material . This question probably went to print too fast, and what was lost in the mix (pardon the pun) is problematic for students looking to strengthen their skills in the IR section.

My advice? Trust  official  questions. You might get 9/10 great questions from third-party sources, but that tenth one could be the one that gets in the way of your making genuine progress. If you cannot figure out the question  with  the numbers given, then that is another story.

- Andrew

Harrison is planting a flowerbed. So far he has added 20 pounds of mat

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