The ABC Reservoir on Clear River is used to prevent flooding in downst

Question

The ABC Reservoir on Clear River is used to prevent flooding in downstream cities and to provide a recreation area for fishing, swimming and boating. Engineers control the depth of the reservoir by controlling the outflow rate - the rate at which water flows out of the reservoir. The inflow rate - the rate at which water flows into the reservoir - is uncontrolled and varies. The engineers use a computer model to predict the inflow rate. It is considered a rare event for the actual average inflow to differ from the model's prediction by more than 4% of the prediction.

The reservoir depth decreases whenever the outflow exceeds the inflow. Similarly, the reservoir depth increases whenever the inflow exceeds the outflow. Whenever possible, the engineers are expected to keep the reservoir depth within a certain 23 meter allowable range - high enough to support recreational activities and not above the reservoir's maximum allowable depth - and to keep the outflow rates within a certain 25 cubic meters per second (m3/s) allowable range. The engineers have never failed to satisfy these constraints.

HarshavardhanR · Accepted Answer

Q1:
We need to select "Yes" if the statement suggests long-term negative impact on the ability to stay within the given constraints (depth and/or outflow rate).

S1: An upstream water division project on the Clear River permanently reduces the average inflow to the reservoir by 50m3/s

Yes. This could have a serious impact. Let's understand why.

Remember that the engineers control the depth by varying the outflow rate.

If they want to increase the depth, they lower the outflow rate to a point below inflow rate (max lower limit being 85 m3/s).
If they want to decrease the depth, they increase the outflow rate to a point above inflow rate (max higher limit being 110 m3/s).

For the engineers to be able to do the above, the inflow rate has to be between 85 m3/s and 110 m3/s.

Examples to understand this

- If the inflow rate was, say, 111 m3/s, then, within these constraints (85 to 110 m3/s), there is no way to reduce depth (inflow always > outflow)
- if the inflow rate was, on average, 84 m3/s, then, within these constraints (85 to 110 m3/s), there is no way to increase depth (inflow always < outflow)

Thus, we can say that even the inflow rate will be somewhere between 85 m3/s and 110 m3/s, because only then can the engineers control depth in all scenarios using the given outflow range.

Even in the data for inflow rates from the 7-day period, we can see that inflow rates are within this range.

An example of how the engineers control the depth

- if the inflow rate was, on average, 100 m3/s, then,

1) If engineers want to increase the depth, they can bring down outflow rate to below 100 m3/s (but not below 85 m3/s).
2) If they want to decrease the depth, they can increase outflow rate to above 100 m3/s (but not above 110 m3/s).

But what if the average inflow rate has been permanently reduced by 50 m3/s?

Example: New inflow rate is 100 - 50 = 50 m3/s.

Then, the engineers would not be able to control the depth of the reservoir with the constraints (85 to 110 m3/s).

Inflow would always be < outflow. No way to control depth.

Whether the average inflow rate is 85.1 m3/s or 109.9 m3/s, a reduction of 50 takes it to such a low point that the engineers would not be able to stay within the set constraints to control depth.

Thus Statement 1 suggests a clear long-term negative impact on the engineers' ability to stay within the given constraints. Hence, YES.

S2: An equipment failure prevents engineers from increasing the reservoir's outflow for 12 hours

Remember - we are looking for long-term negative impact. This seems to be a problem that can get fixed in 12 hours. The engineers may even get lucky in the sense that during this failure, there may be no actual need to increase outflow!

While there could be some short-term negative impact, there is nothing to suggest long-term negative impact. No.

S3: A new source of funding allows the engineers to purchase additional computers to increase the speed and accuracy of the model's prediction.

Better model -> better prediction -> better choices of outflow rate, perhaps. This does not really suggest that the new outflow rates/depths will go beyond the set constraints. It is a stretch to say that a better model will have a negative long-term impact on the ability to stay within the constraints.

Hope this helps.

___
Harsha

HarshavardhanR · Answer

Q2  
 Given  Model Predictions : 
Current Depth: 217m
By Next Day: 217 + 1 = 218m
Next Two days: 218m (will remain at this depth)

Question:  For each of the statements, say "Yes" if it is true. Else, "No".

S1  -> The predictions indicate that the reservoir's depth will be sufficient for recreational activities.

The constraint for depth is 195m to 218m. As long as the depth stays in this range, the depth is OK for recreational activities. In all these days, depth is 217 to 218m, sufficient for recreational activities. YES.

S2  -> The predictions indicate that the reservoir will reach its maximum allowable depth.

The upper limit is 218m. Clearly, as per the predictions, the maximum allowable depth (218m) is being reached. YES.

S3  -> The predictions indicate that the reservoir will exceed its maximum depth.

These predictions indicate that the depth will reach 218m but not anything more. It is reaching the maximum depth but not exceeding it. NO.

Q3  
Question: Given the data from the model (Day 1 to Day 7), on which day (among the options) was average outflow greater than average inflow?

Let's think about this ->  What would happen if, on a certain day, outflow rate was  lesser  than inflow rate?

On that day -> More water would be coming in than going out. Thus the depth of water would see an increase from previous day's measurement.

Similarly,  What would happen if, on a certain day, outflow rate was  more  than inflow rate?

On that day -> More water would be going out than coming in. Thus the depth of water would see a decrease from previous day's measurement.

We need to find on what day the outflow is more than inflow. That would be the day(s) when we see a reduction in the water level.

Now, look at the graph.
- On Day 2, we see an increase in depth from day 1. This means that inflow>outflow.
- On Day 3, we see an increase in depth from day 2. This means that inflow>outflow.
- On Day 4, we see an increase in depth from day 3. This means that inflow>outflow.
 - On Day 5, we see a decrease in depth from Day 4. This means that outflow>inflow.
- On Day 6, we see a decrease in depth from Day 5. This means that outflow>inflow. 
- On Day 7, we see an increase in depth from Day 6. This means that inflow>outflow.

Day 5 and Day 6 are both valid answers. We say Day 5 as a choice. It is the correct answer.

___
Harsha

Ankit__7182 · Answer

Bunuel   bb   GMATNinja 
I have an issue with the question language. To arrive at this answer we need to consider depth=height, which is not true. I was comfortable with whole data set with my understanding of depth as defined below, except in this question. Does GMAT leave such loopholes ? 
Please update if I am wrong here or how to avoid/tackle such loose words' meaning

Depth usually refers to something that extends downward or beneath grade . Conversely height, refers to something that extends upward, above ground or grade.

HarshavardhanR · Answer

Hi Ankit__7182 Replying to this one as you are referring to my explanation. In my explanation of Q3, I used depth/height interchangeably (quite by accident!) - your point is legit as per me ; there is a tiny difference between the two. Thanks for pointing this out - I am happy to use "depth" consistently.

My personal take on this (happy to be corrected by better experts!) : Though the point of initial reference (say, ground) may be different, both height and depth describe the same thing in this contex t. Unless we are dealing with a situation where the point of initial reference matters, the height of water in a reservoir is the same as depth of water in a reservoir. When we are talking about the depth changing as a result of outflow vs. inflow, we are concerned with the actual amount of water and therefore the magnitude of length (call it depth or height) changing. Whether one is looking at the water from the base of the reservoir (height) or from the surface water level (depth) will not impact this magnitude. In any case, (1) - The question language uses "depth" consistently, from what I see. (2) - More important -> Even if depth and height cannot be used interchangeably here, why would one have to consider depth = height to answer any of these 3 questions? For instance, in Q3, from what I see , the logic remains the same. If outflow rate > inflow rate on a particular day, one can expect to see a reduction in the depth of water in the reservoir by the End-Of-Day. Conversely, if inflow rate > outflow rate on a particular day, one can expect to see an increase in the depth of water in the reservoir by the End-Of-Day. Cheers, Harsha

NoeticImbecile · Answer

In Q3, although level of water on day 1 is least and day 5 is second least, are we selecting day 5, as for day 1 we cant compare how much its depth increased or decreased when compared with the preceding day (day0)

HarshavardhanR · Answer

Hi  NoeticImbecile ,

Yep - correct!

To determine if outflow on a certain day > inflow on a certain day, we have to see how depth changes from the previous day to that day. The absolute value of the depth (day 1 depth, day 5 depth, etc.) is irrelevant. The actual depth on any of these days may be super low, or super high - it doesn't matter.

The fact that Day 1 has the least depth does not matter. What matters is did the depth decrease from day 0 to day 1? We have no data for that here. But we do know that Day 5 and Day 6 saw a decrease in depth (from the graph!). This would mean that outflow > inflow.

Hope this helps!
___
Harsha

MBAToronto2024 · Answer

KarishmaB  
Q3. I was calculating the rates in the following manner.

Depth = Inflow - Outflow

Day 1: 200 = 95 - x, x = 105
Day 2: 200 = 95-x
....
Day 5: 204 = 105 - x, x = 99.

What's wrong with this approach? In the end, I realized that it's bs and selected Day 5.

KarishmaB · Answer

This is incorrect: Depth = Inflow - Outflow

Inflow - Outflow is "Change in Depth"

Imagine a bucket of water. If I add 10 ltrs to it and remove 15 litres from it, the depth of the water in the bucket will change by -5 litres i.e. it will reduce by 5 litres. I don't know what the actual depth of water in the bucket is.

By the end of Day 5, depth has reduced by 12 from end of previous day value. This means outflow > inflow. 
That is why day 5 is the answer.

KarishmaB · Answer

Question 1. For each of the following changes in conditions, select Yes if the information provided suggests that the change would have a negative long-term impact on the engineers' ability to stay within the given constraints. Otherwise, select No. What are the given constraints? Depth => 195 to 218 Outflow => 85 to 110 The depth has to be maintained within a range. This means that overall the average inflow and average outflow should match each other. Within these constraints, we would want the outflow to be about the average inflow so that the depth is maintained at around 200 long term. The constraints require the outflow to be around 100 on average which means that the inflow is also around 100 on average. An upstream water division project on the Clear River permanently reduces the average inflow to the reservoir by 503/s If the inflow reduces by 50 m^3/s, then the average inflow will go to around 50 m^s/s from the current around 100 m^3/s. Then the outflow should also be reduced to about 50 m^3/s but that doesn't lie within the range of given constraints. If the outflow is kept around 100 as it is now, then the depth of around 200 cannot be maintained. The depth will decrease. Hence the current constraints cannot be continued if the inflow reduces permanently by 50 m^3/s Select Yes An equipment failure prevents engineers from increasing the reservoir's outflow for 12 hours This is a temporary equipment failure causing issues for 12 hrs. The outflow rate will be maintained for 12 hrs. But long term, it will have no impact on the ability to maintain constraints. The equipment will be repaired and all will be back to normal. Select No A new source of funding allows the engineers to purchase additional computers to increase the speed and accuracy of the model's prediction. If inflow predictions become more accurate, it just means engineers will have better control to stay in the limits. It is good for maintaining constraints. Select No Question 2. Suppose that the reservoir depth is currently at 217 m. If the engineers maintain the current outflow rate, the inflow rates predicted by the model will cause the depth to increase by 1 m in the next day and remain at that depth for the following 2 days. For each of the following statements about the model's predictions, select Yes if the information provided suggests that the statement is true. Otherwise, select No Current depth = 217 m Next day depth = 218 m (increase of 1) Depth on next 2 days = 218 m This depth is within the constraints: Depth => 195 to 218 The predictions indicate that the reservoir's depth will be sufficient for recreational activities. Correct. This depth is sufficient for recreational activities. Select Yes The predictions indicate that the reservoir will reach its maximum allowable depth. Correct. This is the maximum allowable depth. Select Yes The predictions indicate that the reservoir will exceed its maximum depth. Not correct. It will not exceed 218 m Select No Question 3. Assuming the predictions made by the model about Days 1 through 7 were all accurate, on which one of the following days can it be most logically inferred that the average outflow was greater than the average inflow? The day on which outflow is greater than inflow, the depth of the reservoir will reduce. The graph gives is predicted end-of-day depths. End of Day 1 - 199 End of Day 2 - 202 End of Day 3 - 210 End of Day 4 - 215 End of Day 5 - 203 (On day 5, the depth decreased by 12 m so outflow > inflow) Select Day 5 Here is a discussion on how to solve MSR questions: https://youtu.be/xL631VXGjSg

Kavicogsci · Answer

The depth has to be maintained within a range. This means that overall the average inflow and average outflow should match each other. Within these constraints, we would want the outflow to be about the average inflow so that the depth is maintained at around 200 long term. The constraints require the outflow to be around 100 on average which means that the inflow is also around 100 on average.

An upstream water division project on the Clear River permanently reduces the average inflow to the reservoir by 503/s

If the inflow reduces by 50 m^3/s, then the average inflow will go to around 50 m^s/s from the current around 100 m^3/s. Then the outflow should also be reduced to about 50 m^3/s but that doesn't lie within the range of given constraints. If the outflow is kept around  100 as it is now, then the depth of  around  200 cannot be maintained. The depth will    decrease. Hence the current constraints cannot be continued if the inflow reduces permanently by 50 m^3/s
 
Didn't understand why are we taking avgs and why avg inflow needs to be close to avg outflow?

KarishmaB · Answer

The level has to be maintained with a range. If your output is consistently less than your input (even if by a small amount), the level will consistently reduce. After whatever days, weeks or months, the level will fall below the range in that case. Hence outflow needs to be kept close to the inflow.

blaze90210 · Answer

For Q2, I kept the following in mind from the first tab "It is considered a rare event for the actual average inflow to differ from the model's prediction by more than 4% of the prediction."

and eventually got the ans wrong

Please help me understand the context of the statement mentioned in tab 1 and how one should be able to eliminate it while answering Q2.

KarishmaB · Answer

That statement has no role to play in question 2. All statements of question 2 are based on predictions, not divergence from predictions. They all say what the predictions indicate, not what may actually happen. 
Every statement starts with:   The predictions indicate that ...

Aarya_San · Answer

By this logic, Day 4 to Day 5 also saw a decrease in water depth. Why won't the answer be day 4

HarshavardhanR · Answer

Hmm. Day 4 to Day 5 decrease means Day 5 saw a decrease,  not Day 4 . Perhaps you are looking at this graph simply in terms of math without picturizing what this means in real life. Let me try to help.

Imagine  the reservoir as a tank which has water. Imagine somebody measuring the depth every day at 11:59 PM (end of Day measurement).

Check Predictions tab, Figure-2.

- At the end of Day 3, the depth was 210m.
- At the end of Day 4, the depth was 215m.

So, when Day 4 started, the depth was 210m. When Day 4 ended, the depth was 215m.

So, through Day 4, 5m of extra water has accumulated in the tank. For this to happen, Inflow of water would have been > Outflow of water.

So, for Day 4, Inflow > Outflow.

- At the end of Day 4, the depth was 215m. 
- At the end of Day 5, the depth was 203m.

So, when Day 5 started, the depth was 215m. When Day 5 ended, the depth was 203m.

So, through Day 5, 12m of water was lost from the tank. For this to happen, Inflow of water would have been < Outflow of water.

So, for Day 5, Outflow > Inflow.

Hope you see this.

In essence,

- Day 4 to Day 5 saw a decrease in water depth. This tells us that on Day 5, Outflow > Inflow.
- Day 3 to Day 4 saw an increase in water depth. This tells us that on Day 4, Inflow > Outflow.

The ABC Reservoir on Clear River is used to prevent flooding in downst

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Yes	No
		An upstream water division project on the Clear River permanently reduces the average inflow to the reservoir by 50³/s
		An equipment failure prevents engineers from increasing the reservoir's outflow for 12 hours
		A new source of funding allows the engineers to purchase additional computers to increase the speed and accuracy of the model's prediction.

Yes	No
		The predictions indicate that the reservoir's depth will be sufficient for recreational activities.
		The predictions indicate that the reservoir will reach its maximum allowable depth.
		The predictions indicate that the reservoir will exceed its maximum depth.

GMAT Multi-Source Reasoning (MSR) Questions

The ABC Reservoir on Clear River is used to prevent flooding in downst

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards