Throughout a certain decade in a European city, the mean monthly rent

Question

Throughout a certain decade in a European city, the mean monthly rents for studio apartments varied yearly, from a low of €804 to a high of €1,173. Those for one-bedroom apartments also varied yearly, from a low of €1,060 to a high of €1,497. But some individual studio apartments rented for as little as €420 in some years, and some one-bedroom apartments rented for up to €2,262. To visually assess how the ratio of mean monthly rents for studio apartments to those for one-bedroom apartments varied yearly over the decade, Maria requires a graph with the following characteristics. The graph will have two axes of equal length, with mean rents for one-bedroom apartments shown on the horizontal axis and mean rents for studio apartments shown on the vertical axis, and with the same scale on both axes. For each year, mean rents will be plotted as a point.

From the following options, select for Horizontal axis a range for the points on the horizontal axis and select for Vertical axis a range for the points on the vertical axis that together would satisfy Maria's requirements for the graph. Make only two selections, one in each column.

From the following options, select for  Horizontal axis  a range for the points on the horizontal axis and select for  Vertical axis  a range for the points on the vertical axis that together would satisfy Maria's requirements for the graph. Make only two selections, one in each column.

ID: 700224

egmat · Accepted Answer

This TPA question is a beautiful example of  how you take a simple concept such as scale of x and y axis  and  add layers of complexity  – one after another – to make it a rather difficult question that has all the hallmarks of creating a lot of anxiety in the test environment. But that is something that we are here to resolve.

Watch this video solution to understand how you should approach this question and read below to understand all the potential faltering points in this question.

https://www.youtube.com/watch?v=HaM2KECF4Mw

Faltering Point 1 – Could not draw the inference that the two specific data points are not to be plotted. 
 Faltering Point 2 – Could not extract all the conditions from the dataset about the two axes. 
 Faltering Point 3 – Could not order the conditions in the correct sequence for the most efficient processing. 
 Faltering Point 4 – Gave up on the question because of the sheer complexity of the dataset.

Understanding why you faltered is very important to decide how you need to fix these problems.

Let me know which faltering point(s) you stumbled on.

Happy Learning!
Payal

chetan2u · Answer

ckavya2691 ,

It is easy to get lost in the wordings. This is exactly what the intention of this question is. 
Throws a lot of data but seeks graph of a petticoat thing.

Graph is of mean monthly rents which are : the mean monthly rents for studio apartments varied yearly, from a low of €804 to a high of €1,173. Those for one-bedroom apartments also varied yearly, from a low of €1,060 to a high of €1,497.

The graph will have two axes of equal length, with  mean rents  for one-bedroom apartments shown on the horizontal axis and  mean rents  for studio apartments shown on the vertical axis, and with the same scale on both axes.

Now what about the additional values given?
But  some individual studio apartments rented  for as little as €420 in some years, and some one-bedroom apartments rented for up to €2,262.
These are some variations of some individual apartments and these will have impact on the mean monthly rents. Precisely, the reason why the mean monthly rents over years is spread over a given range. 
Whatever impact these outliers had to make has already been included in the mean monthly ranges of 804-1173 and 1069-1497.

We have to restrict our axes to the mean monthly ranges only and 0-1500 includes both 804-1173 and 1069-1497.

MartyMurray · Answer

Throughout a certain decade in a European city, the mean monthly rents for studio apartments varied yearly, from a low of €804 to a high of €1,173. Those for one-bedroom apartments also varied yearly, from a low of €1,060 to a high of €1,497. But some individual studio apartments rented for as little as €420 in some years, and some one-bedroom apartments rented for up to €2,262. To visually assess how the ratio of mean monthly rents for studio apartments to those for one-bedroom apartments varied yearly over the decade, Maria requires a graph with the following characteristics. The graph will have two axes of equal length, with mean rents for one-bedroom apartments shown on the horizontal axis and mean rents for studio apartments shown on the vertical axis, and with the same scale on both axes. For each year, mean rents will be plotted as a point.

From the following options, select for Horizontal axis a range for the points on the horizontal axis and select for Vertical axis a range for the points on the vertical axis that together would satisfy Maria's requirements for the graph. Make only two selections, one in each column.

From the following options, select for Horizontal axis a range for the points on the horizontal axis and select for Vertical axis a range for the points on the vertical axis that together would satisfy Maria's requirements for the graph. Make only two selections, one in each column.

The graph must have the following characteristics:

- two axes of equal length

- mean rents for one-bedroom apartments shown on the horizontal axis

- mean rents for studio apartments shown on the vertical axis

- the same scale on both axes

- For each year, mean rents will be plotted as a point.

The passage provides several values. However, the graph will show only mean rents. So, the only values that matter are the following:

Studio apartments:

a low of €804 to a high of €1,173

One-bedroom apartments:

a low of €1,060 to a high of €1,497

So, the axis for studio apartments must go at least from around 800 to around 1,200, and the axis for one-bedroom aparments must go at least from around 1,000 to around 1500.

€0 to €1,500

€400 to €1,100

€800 to €1,200

€1,000 to €2,300

€1,100 to €1,500

One of the characteristics of the graph is that it has two axes of equal length. Scanning the choices, we see that only two are of the same length: €800 to €1,200 and €1,100 to €1,500.

€800 to €1,200 would work for studio apartments since it allows for a low of €804 and a high of €1,173.

However, €1,100 to €1,500 does not work for one-bedroom apartments since it does not allow for the low of €1,060.

So, it must be the case that one of the choices works for both axes since only by using one choice for both can we get axes of equal length and include all the values.

(Also, by the way, if one choice works for both, that choice must be the correct answer since the question cannot be answerable in two ways.)

To have the points for all the values of mean rents, the axes must go at least from a low of around 800 to a high of around 1,500. The only choice that includes both of those values is €0 to €1,500.

So, the correct answer for both Horizontal axis and Vertical axis is €0 to €1,500.

Answer:  €0 to €1,500, €0 to €1,500

ckavya2691 · Answer

Thank you for the reply but there is also 1 statement in the question "and some one-bedroom apartments rented for up to €2,262.". How will this be accomodated in the given solution?

ckavya2691 · Answer

Got it, thank you!

GMATGuruNY · Answer

Mean monthly rents for one-bedroom apartments range from 1060 to 1497.
Answer choices that can accommodate this range:
  €0 to €1,500 --> axis length = 1500-0 = 1500  
€1,000 to €2,300 --> axis length = 2300-1000 = 1300

Mean monthly rents for studio apartments range from 804 to 1173.
Answer choices that can accommodate this range:
  €0 to €1,500 --> axis length = 1500-0 = 1500  
€800 to €1,200 --> axis length = 1200-800 = 400

Since the axis length in each case must be the same, only the option in blue is viable for each axis.

KarishmaB · Answer

This is the intent of the graph: 
 To visually assess how the ratio of mean monthly rents for studio apartments to those for one-bedroom apartments varied yearly over the decade,

It needs to asses the MEAN monthly rents so lowest and highest given rents are irrelevant.

Studio MEAN - low of €804 to a high of €1,173 - Vertical Axis

One Bedroom MEAN - low of €1,060 to a high of €1,497 - Horizontal Axis

Since both axis should have same length and scale, we need a range that could cover all the MEANs of both.

Only range 0 - 1500 covers both ranges, 804 to 1173 and 1060 to 1497.
ANSWER

Note that range 1000 - 2300 covers the One bedroom means but not the studio means.
And range 800 - 1200 covers the Studio means but not the One bedroom means.

ruis · Answer

Official answer:
Because both axes must be the same length and have the same scale, the range for both axes must start low enough to accommodate €804 and go high enough to accommodate €1,497. The range €0 to €1,500 accommodates both the low of €804 and the high of €1,497. Neither of the ranges €400 to €1,100 and €800 to €1,200 goes high enough to accommodate €1,497 and neither of the ranges €1,000 to €2,300 and €1,100 to €1,500 goes low enough to accommodate €804.

The correct answer is €0 to €1,500.

Gemmie · Answer

..............................range.....Studio (€804 - €1,173)..........1BR (€1,060 - €1,497) 
€0 to €1,500............€1500...... covered ..................................... covered 
€400 to €1,100........€700........not covered............................... not covered 
€800 to €1,200........€400........covered..................................... not covered 
€1,000 to €2,300.....€1300...... not covered ................................covered
€1,100 to €1,500.....€400........ not covered ................................ not covered

SudsMeister · Answer

Hi Karishma, thank you for the explanation, I have few further questions to check my understanding:

Does 'same scale' mean that the starting point should be same for both the axes? And I think the 'same length' means the range on both should be the same.

What if the question only mentioned same length and didn't say anything about scale? In that case, if the options also include: 800 - 1300 and 1000 - 1500, then can we select that as an answer?

Another question: what if the question mentions same length and scale, and options are: 0 - 1500, 300 - 1800, 800 - 1500. What would the correct answer be then?

cheshire · Answer

What does "same scale" mean? 
 
 Same scale → 1 unit on X-axis = 1 unit on Y-axis 
 So, both axes must have the same starting and ending values 
 Example:
 
 X-axis: €0 to €1500 
 Y-axis: €0 to €1500
  Valid (same scale and length)  
 X-axis: €300 to €1800 
 Y-axis: €0 to €1500
 Invalid (different starting point → different scale)

What does "same length" mean?

Same physical space (e.g., 10 cm for both axes) 
 Ranges must match, but starting values can differ 
 Example:
 
 X-axis: €800 to €1300 
 Y-axis: €1000 to €1500
  Valid for same length 
  Invalid if same scale is also required

If question mentions “same length” but NOT “same scale”:
 
 You can pick any pair with the same range 
 Example:
 
 €800 to €1300 
 €1000 to €1500
 Valid

If question mentions BOTH “same length” and “same scale”: 
 Only options with same start and end are valid
 Options:
 
 €0–€1500 -  Valid  
 €300–€1800 -  Invalid  
 €800–€1500 -  Invalid   
 Final Answer:  Only  €0–€1500  is valid if both scale and length are required

D3N0 · Answer

How is it true? 
The same scale only means that the difference between two points on the scale is the same. That means if we divide the axis scale points, then two sequential units are at the same distance. 
Example : if we step 1 unit up = $100 then 1 unit step sidewise = $100
It doesn't mean that the start and the end point are the same values. 
Why is this different in this case?

D3N0 · Answer

I am still confused. 
  As per my understanding, Same Scale only means that the difference between two points on the scale is the same. That means if we divide the axis scale points, then two sequential units are at the same distance from each other on both x an y axis. 
 lets say x1 x2 x3 x4 x5 are points on x axis and y1 y2 y3 y4 y5 are points on y axis 
 then x1-x2 = $100 and y1-y2 = $100 then it is same scale (isn't it) 
 and as there are x1 to x5 and y1 to y5 ($400 for length)

It doesn't mean that the start and the end points have to have the same values. 
  Why is this different in this case?   
  If you can please clarify this @KarishmaB

cheshire · Answer

“Same scale” here isn’t just about equal-sized tick increments (though that’s part of it); it means that a given data unit has to correspond to the same physical length on the X-axis as on the Y-axis. Since Maria also wants the two axes to be equal in length on the page, they must cover the same numeric span, necessitating the same starting and ending points.

D3N0 · Answer

I see that when we go with this approach, we have the answer, but I still couldn't find a source that confirms what you mentioned. (That same scale means starting points have to be similar). Everything I found says that they must use identical unit intervals. The same numeric span is not necessary.

cheshire · Answer

What “same scale” means here is the combination of two requirements that Maria explicitly asked for:
 
  Equal unit increments 
 
 One “tick” (e.g. €100) on the horizontal axis must represent exactly the same physical length on the page as one “tick” (€100) on the vertical axis. 
 This guarantees that a movement from €800 to €900 is visually the same distance left-to-right as bottom-to-top.  
 
  Axes of equal drawn length 
 
  Maria also wants the two axes themselves to be the  same total length  on the page. So that when you plot points, a circle of radius 1 cm around any point looks the same in all directions (you keep ignoring this).  
 If you gave the X-axis a span of €400–€1,500 (1,100 € range) but the Y-axis €0–€1,500 (1,500 € range), even though each €100 tick is “equal” in isolation, the X-axis would be shorter (11 ticks) than the Y-axis (15 ticks).  
  
Putting those together, the  only  way to satisfy both simultaneously is:
 
 Choose the  same tick size   and  
 Cover the  same total range  (same number of ticks) on both axes.  
Hence the axes must start and end at the same numeric values (€0 to €1,500 on both) so that:
 
 €100 on X is exactly as long as €100 on Y,  and  
 the overall X-axis drawn length equals the overall Y-axis drawn length.

You wont find word for word "they must cover the same numeric span and must have the same starting and end points." instead, these are simple logical conclusions you derive from the question and are key fundamentals that indicate your ability to to use logical reasoning

Throughout a certain decade in a European city, the mean monthly rent

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Horizontal axis	Vertical axis
		€0 to €1,500
		€400 to €1,100
		€800 to €1,200
		€1,000 to €2,300
		€1,100 to €1,500

GMAT Two-part Analysis (TPA) Questions

­Throughout a certain decade in a European city, the mean monthly rent

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards

Throughout a certain decade in a European city, the mean monthly rent