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Updated on: 03 Oct 2023, 02:34
Originally posted by Shrivathsan on 30 Sep 2016, 01:44.
Last edited by BottomJee on 03 Oct 2023, 02:34, edited 5 times in total.
Last edited by BottomJee on 03 Oct 2023, 02:34, edited 5 times in total.
Moved to new forum
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Increase
in demand: 25 Decrease
in supply: 15
in demand: 25 Decrease
in supply: 15
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
51% (03:40) correct
49%
(03:23)
wrong
based on 204
sessions
History
Date
Time
Result
Not Attempted Yet
The African country of Mbotekia has been the largest manufacturer of bread in Africa since the early 1900s. In fact, in 2006, 540 tonnes of bread were made, which was thrice the demand for bread in Mbotekia. However, civil war broke out in Mbotekia in 2006. Since then, the bread industry has been struggling and the supply of bread has been on the decline at a constant rate. On the other hand, due to influx of refugees and increasing population, the demand for bread has been increasing at a constant rate (the annual increase in demand is greater than the annual decrease in supply).
Economists predicted that in 2016, the demand for bread in Mbotekia will be, for the time time, greater than the supply.
In the table below, identify a rate of increase in demand for bread in Mbotekia (in tonnes per year), a rate of decrease of supply of bread in Mbotekia (in tonnes per year) in accordance with the economists’ prediction. Make only two selections, one in each column.
Economists predicted that in 2016, the demand for bread in Mbotekia will be, for the time time, greater than the supply.
In the table below, identify a rate of increase in demand for bread in Mbotekia (in tonnes per year), a rate of decrease of supply of bread in Mbotekia (in tonnes per year) in accordance with the economists’ prediction. Make only two selections, one in each column.
|
Increase in demand |
Decrease in supply |
------ |
| 40 | ||
| 35 | ||
| 30 | ||
| 25 | ||
| 15 |
ShowHide Answer
Official Answer
Increase
in demand: 25 Decrease
in supply: 15
in demand: 25 Decrease
in supply: 15
07 Oct 2016, 16:44
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Explanation:
Supply of bread in 2006 = 540 tonnes = 3 × Demand in 2006.
Thus, Demand = 540/ 3 = 180 tonnes.
Now, since 2006, supply is decreasing at some constant rate, let it be ‘x’ tonnes per year. And demand is increasing at some constant rate let it be ‘y’ tonnes per year.
Thus, in 2016 supply = 540 – 10x.
And demand = 180 + 10y.
As per prediction we know, in 2016, Demand > Supply.
(180 + 10y) > (540 – 10x)....(I)
Simplifying we get (y + x) > 36. (thus, looking at the options, we cannot take x and y both 15. As it will add up to 30 which is < 36.)
We are asked to find out x and y such that it satisfies the above condition.
Demand gets higher than supply in 2016, i.e. in 10 years. Means in 2015, Demand was not greater than supply. Thus, (180 + 9y) = (540 – 9x).....(II)
Thus, (y + x) = 40.
From the options, 25 and 15 satisfy the above two conditions.
Now, if we take y as 15 and x as 25. It does not satisfy (II)
Thus, y = 25 and x = 15.
~Consider giving Kudos if you like the solution. Be generous!
Supply of bread in 2006 = 540 tonnes = 3 × Demand in 2006.
Thus, Demand = 540/ 3 = 180 tonnes.
Now, since 2006, supply is decreasing at some constant rate, let it be ‘x’ tonnes per year. And demand is increasing at some constant rate let it be ‘y’ tonnes per year.
Thus, in 2016 supply = 540 – 10x.
And demand = 180 + 10y.
As per prediction we know, in 2016, Demand > Supply.
(180 + 10y) > (540 – 10x)....(I)
Simplifying we get (y + x) > 36. (thus, looking at the options, we cannot take x and y both 15. As it will add up to 30 which is < 36.)
We are asked to find out x and y such that it satisfies the above condition.
Demand gets higher than supply in 2016, i.e. in 10 years. Means in 2015, Demand was not greater than supply. Thus, (180 + 9y) = (540 – 9x).....(II)
Thus, (y + x) = 40.
From the options, 25 and 15 satisfy the above two conditions.
Now, if we take y as 15 and x as 25. It does not satisfy (II)
Thus, y = 25 and x = 15.
~Consider giving Kudos if you like the solution. Be generous!
07 Oct 2016, 16:03
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Shrivathsan
Dear Shrivathsan,
I'm happy to respond.
What is the source of this question? There are multiple problems with the question itself. The text contains a grammar mistake, the "due to" mistake:
"...due to the influx of refugees and the increasing population, the demand for bread has been increasing ... "
That would be wrong on GMAT SC.
Next, the prompt contains a crucial error:
...predicted that in 2016, the demand for bread will be, for the time time, greater than the supply.
I assume they mean for the "first time," but this makes the whole question garbled.
Typically, the numbers in the box would be in increasing order in a real GMAT problem.
Finally, something is funny about the answer provided.
Call the demand D and the supply S. In 2006, D = 180 and S = 540. The difference between them is 540 - 180 = 360. If the gap between them closed at exactly 36 per year, they would be equal in ten years, in 2016. The gap must close at slightly more than 36. What sum is slightly more than 36? Well, 15 + 25 is 40. The increase in D must be the larger one, so let's say D increase by 25 and S decreases by 15. In 2016, D = 180 + 250 = 430 and S = 540 - 150 = 390, so D > S in 2016. Check that this is the first time: in 2015, D = 430 - 25 = 405, and S = 390 + 15 = 405, so they would be equal. Thus, 2016 would be the first year in which D > S.
According to my calculations, we have to have:
D increase by 25
S decrease by 15
Those are answers of [C] & [J]. I don't agree at all with the answer posted.
I don't know what this source is, but if this problem is at all representative, I think you should set fire to the installation disc.
This is a poor question. Here's a set of six high quality 2PA questions:
GMAT Integrated Reasoning: Two-Part Analysis Practice Questions
Please let me know if you have any questions.
Mike
