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The Huffingdale All Boys School has produced a comprehensive set of Updated on: 24 Jan 2024, 12:42
Originally posted by gmatt1476 on 21 Apr 2020, 22:22.
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The Huffingdale All Boys School has produced a comprehensive set of running standards for young boys. These standards are based on data from young boys attending Huffingdale in good health conditions - as determined by a physician. The table displays the percentile distribution of time on a kilometer run for Huffingdale students at grade levels 1 through 5 according to the Huffingdale model. In a model population -- a large population of young students grade 1 through 5 that conforms to the Huffingdale running standards -- for n=5, 15, 50, 85, and 95, the nth percentile in running time for a given grade is the unique running time among boys of that grade level that is slower than or equal to n percent, and faster than or equal to (100 - n) percent, of running times for students of that grade level.
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His height is approximately 185% of his height in Grade 2.
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1. Consider an individual boy from a model population. Suppose that from grades 1 through 5, this boy's height is at the 50th percentile for his running time and his running time is at the 50th percentile for his grade level. Which one of the following statements must be true of the boy at Grade 5?
His grade level is at the 50th percentile for his running time.
His height is at the 50th percentile for his grade level.
His running time is at the 50th percentile for his height.
His height is approximately 130% of his height in Grade 2.
His height is approximately 185% of his height in Grade 2.
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His height is approximately 185% of his height in Grade 2.

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If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.: Yes If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.: Yes If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.: No
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2. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.
Yes No
If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.
If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.
If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.
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If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.: Yes If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.: Yes If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.: No

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3. A boy, John, selected at random from a model population runs a 10:50 kilometer. Another randomly selected boy, Peter, runs a 10:00 kilometer. Both boys measured 80cm tall. The difference in their percentiles in height among boys who run their respective speeds is most closest to
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If he is in the second grade or lower, the probability that his speed is slower than 11:00 is greater than 85%.: Yes If he runs at most a 9 minute kilometer (no faster), the probability that his height is less than 80cm is no greater than 50%.: No If he runs a 7:30 kilometer run, he is definitely in the 5th grade.: No
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4. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.
Yes No
If he is in the second grade or lower, the probability that his speed is slower than 11:00 is greater than 85%.
If he runs at most a 9 minute kilometer (no faster), the probability that his height is less than 80cm is no greater than 50%.
If he runs a 7:30 kilometer run, he is definitely in the 5th grade.
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If he is in the second grade or lower, the probability that his speed is slower than 11:00 is greater than 85%.: Yes If he runs at most a 9 minute kilometer (no faster), the probability that his height is less than 80cm is no greater than 50%.: No If he runs a 7:30 kilometer run, he is definitely in the 5th grade.: No

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Approximately 95% of boys at the same height are slower than Joshua.: No No more than 15% of boys at this grade level are slower than Joshua.: No Joshua's speed is faster than or equal to that of 50% of boys in the second grade.: No
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5. Joshua is a boy in the 3rd grade whose kilometer run time is 11:20 and whose height is 81cm. For each of the following statements, select Yes if, based on the given information, it must be true of Joshua relative to a model population. Otherwise, select No.
Yes No
Approximately 95% of boys at the same height are slower than Joshua.
No more than 15% of boys at this grade level are slower than Joshua.
Joshua's speed is faster than or equal to that of 50% of boys in the second grade.
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Approximately 95% of boys at the same height are slower than Joshua.: No No more than 15% of boys at this grade level are slower than Joshua.: No Joshua's speed is faster than or equal to that of 50% of boys in the second grade.: No

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At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's.: Yes At least 80% of boys at this grade level have running times within 90 seconds of Joshua's running time.: Yes Joshua's running time is faster than that of at most 5% of boys in the fourth grade.: No
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6. Joshua is a boy in grade 4 whose running time is 10:30 and whose height is 80cm. For each of the following statements, select Yes if, based on the given information, it must be true of Joshua relative to a model population. Otherwise, select No.
Yes No
At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's.
At least 80% of boys at this grade level have running times within 90 seconds of Joshua's running time.
Joshua's running time is faster than that of at most 5% of boys in the fourth grade.
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At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's.: Yes At least 80% of boys at this grade level have running times within 90 seconds of Joshua's running time.: Yes Joshua's running time is faster than that of at most 5% of boys in the fourth grade.: No

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Reading Tab 1:

What are percentiles? Say you get 99th percentile score in GMAT - it means your score is better than (or equal to - if defined so) than 99 people out of 100.

The question defined the percentile in running time.
"the nth percentile in running time for a given grade is the unique running time among boys of that grade level that is slower than or equal to n percent"

So consider 1st grade.
I say 95th percentile of running time is 13 mins 20 sec. It means the time of 13 mins 20 sec is slower than or equal to 95% of the times taken by first graders for 1 km run. So to be fast, one should have a low percentile.
Say fourth grader, 15th percentile, time taken is 9:20. It means that 9 mins 20 secs is slowe than or equal to 15% of the times taken by fourth graders for a 1 km run.

That is how you read this table.

Go to the second tab -

Height percentiles of running times.

Given: "the nth percentile in height for a given running time is the unique height among boys of that running time that is taller than or equal to n percent,"

So look at 500 on x axis. Among all boys who take 500 seconds to run a km, the boys at the 95th percentile in height has a height of about 137 cm and the boy at the 5th percentile has a height of about 112 cm.
Similarly for all other time taken.

Question 1.

Question 1. 1. Consider an individual boy from a model population. Suppose that from grades 1 through 5, this boy's height is at the 50th percentile for his running time and his running time is at the 50th percentile for his grade level. Which one of the following statements must be true of the boy at Grade 5?

His running time is at the 50th percentile for his grade level. I know how to decode this from table in tab 1. I can find his running times as per his grade.

First grade 12:59 (about 780 seconds)
Second grade 11:15 (about 675 seconds)
Third grade 10:50
Fourth grade 9:55
Fifth grade 8:21 (about 500 seconds)

Next, from the second graph, as per running time, I can find 50 percentile of height.
I do not have data for 780 seconds time (because the graph only tells about 500 secs to 700 secs) but I do have for 675 seconds.
At 675 secs (grade 2 time), the orange curve is at about 65 cm.
At 500 secs (grade 5 time), the orange curve is at 120 cm.
Double of 65 is 130 so 120 would be at about 185%.

Hence option (E) is correct - His height is approximately 185% of his height in Grade 2.
Option (D) automatically becomes wrong then.

Option (A): His grade level is at the 50th percentile for his running time.
What does grade level at 50th percentile even mean?

Option (B): His height is at the 50th percentile for his grade level.
We know the percentile of height for running time, not for grade level. If all boys of a specific running time (say 500 secs) are brought together, how do their heights vary is known through the graph. How the heights vary as per grades is not known.

Option (C): His running time is at the 50th percentile for his height.
We know the running time percentile for grade through the table in tab 1. The percentile of running time for height is not known. The graph in tab 2 gives percentile of height for running time, not the other way around. Percentiles shown are of height.

Answer: His height is approximately 185% of his height in Grade 2.
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The Huffingdale All Boys School has produced a comprehensive set of 02 Jun 2023, 21:08
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Discussion continued from the above post. This one contains explanations for problems 4, 5, and 6.



4. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

Quote:
If he is in the second grade or lower, the probability that his speed is slower than 11:00 is greater than 85%.
Show more

This problem works almost exactly like the first part of problem 2. If necessary, please see the discussion of that part (in my previous post) for a fuller explanation.

This time our pool contains first-graders and second-graders.
• For FIRST graders, 11:00 is faster than ALL the numbers in the table. So there is a greater than 95% probability that a FIRST-grader will be slower than this.
• For SECOND graders, 11:00 is between 5th and 15th percentile (nominally closer to 15th, but we can't determine that any more precisely). So the probability that a SECOND-grader will run faster than this is between 85% and 95%.

These are both greater than 85%, so their weighted average—however the weights actually work out (not determined in the problem)—will also be greater than 85%. The first statement is TRUE.


Quote:
If he runs at most a 9 minute kilometer (no faster), the probability that his height is less than 80cm is no greater than 50%.
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"No faster" means we're looking at the entire part of the graph to the RIGHT of 9 min = 540 sec.
Across that range, a height of 80cm varies from below 5th percentile (for times near 540 sec) to nearly 95th percentile (for the times where the graph cuts off at the right side).
Our target statistic here is a weighted average across that range, with unknown weights, so... we don't really know. Could work out to be just about anywhere between the two extremes just mentioned.
Second statement is NOT guaranteed to be true.

Quote:
If he runs a 7:30 kilometer run, he is definitely in the 5th grade.
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Here we need to remember that we DON'T have MAXIMUM OR MINIMUM times. The extreme times listed in the table are only the 5th and 95th percentile times, leaving the FASTEST 5% and the SLOWEST 5%—which lie totally outside the values in the table—unbounded.
We just don't know anything here. It's possible for THE VERY FASTEST runners in ANY grade to be faster than 7:30 here, so, [b[this statement definitely DOES NOT[/b] have to be true.)


Overall: Y, N, N for #4.



5. Joshua is a boy in the 3rd grade whose kilometer run time is 11:20 and whose height is 81cm..


Well, if we're going to be handling 3 separate statements about this kid Joshua, we may as well figure out whatever else we can about him upfront. Let's do that:

• From the table, Joshua's running time of 11:20 is somewhere between 50th and 85th percentile for his grade level. (Probably closer to 85th, but we can't go any more granular than what's in the table.)

• From the graph—looking at 11min 20sec = 680 seconds—Joshua's height of 81cm falls between the 85th and 95th percentile curves. So his height is between those percentiles for his running time.


On to the choices we go:


Quote:
Approximately 95% of boys at the same height are slower than Joshua.
Show more

The data don't speak to this point. We have information about boys HEIGHT percentiles FOR SPECIFIC RUNNING TIMES—NOT vice versa! You can't switch around the explanatory (x axis) and response (y axis) variables, in general, unless you have more givens that substantiate an ability to do so.

First statement NOT supported.


Quote:
No more than 15% of boys at this grade level are slower than Joshua.
Show more
First bullet point above says Joshua's running time is between 50th and 85th percentile for his grade level. Therefore, some proportion of the class BETWEEN 15% AND 50% are slower than Joshua.
Accordingly, this second statement is actually GUARANTEED to be FALSE. (The answer is No for any statement that's guaranteed false or is just undetermined, so this is stronger than we need to get our No—but it's still a No.)


Quote:
Joshua's speed is faster than or equal to that of 50% of boys in the second grade.
Show more

Oddly enough, this part is solved by the same piece of information that solves the previous part (another aspect of this problem that's very uncharacteristic for GMAC... Are we sure the source citation is correct?)
Somewhere between 15% and 50% of the boys in this grade level are SLOWER than Joshua. The rest of them—between 50% and 85%—are faster than Joshua. So no, Joshua can't outrun half or more of the class.

This one's also definitively FALSE.

No to all three parts.




6. Joshua is a boy in grade 4 whose running time is 10:30 and whose height is 80cm. For each of the following statements, select Yes if, based on the given information, it must be true of Joshua relative to a model population. Otherwise, select No.

This problem is functionally identical to the previous problem, just with different numbers. (Why is the name still Joshua...?) Accordingly, brief summaries this time.

We should again go ahead and find the rest of what we know for this boy:

• Once again, the running time is somewhere between 50th and 85th percentile for grade level. This is basically an exact functional copy of what happens in the previous part (probably closer to 85th, but we can't go any more granular).

• This time, though, the height is also between 50th and 85th percentiles (for the stated running time of 630 sec).

To the choices we go.

Quote:
At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's.
Show more

(N.B. "that of Joshua's" is ungrammatical—it should be either "that of Joshua" or just "Joshua's". Yet another reason to suspect that GMAC did not create this problem.)

In fact, somewhere between 50% and 85% of the boys who run that time are shorter than Joshua, so this first part is quite handily TRUE.


Quote:
At least 80% of boys at this grade level have running times within 90 seconds of Joshua's running time.
Show more

Joshua's time is 10min 30sec. "Within 90 seconds", therefore, means anywhere between 9 minutes and 12 minutes.
The 15th through 95th percentiles for fourth grade fall between these times. Eighty percent of the boys lie just between those two percentiles (and there could be even more boys between 9min and 12min who fall outside the 15th-95th percentiles, too).
This statement is also TRUE.


Quote:
Joshua's running time is faster than that of at most 5% of boys in the fourth grade.
Show more

Nope. He's faster than somewhere between 15% and 50% of the class. Third statement is FALSE.

Y, Y, N to the 6th and last problem.
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SKDEV
­I am bit confused here,
so for Q2,
If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.
this should be NO right? if exact 50th percentile is 10:50 for third grade, means he is slower than or equal to 50% of people,
so how more than 50% are faster than 10:50, should it be, faster than or equal to 10:50?
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Question 2.

2. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.

Look at TAB 1. He could be in 3rd, 4th or 5th grade. 10:50 is at exact 50 percentile in 3rd grade, but at more than 95 percentile in 4th and 5th grades. So if he is selected from third or higher grade, the probability that his speed is faster than 10:50 is greater than 50% for sure. It will lie between 50% and 95%.

Select YES

If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.

Look at TAB 2. He runs a kilometer is 10 minutes or less time. At 10 minute i.e. 600 secs time, a height of 73 cm is at 5 percentile (on the green line). For any time less than 10 minutes, 73 cm will be an even lower percentile (perhaps 1 or 2). So the probability that his height is up to 73cm is no greater than 5%.

Select YES

If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.

For 5th grade, 8 min lies between 15th and 50th percentile. Hence, it is not essential that he is faster than at least 95% of boys of his same grade level. It will not be true if he is in the 5th grade. For all other grades, this statement will hold.
But since we need the statement to hold for every grade, the statement is not correct.

Select NO
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1)E,since his running time at grade 5 is 501 seconds and his height would be 120 cm while at grade 2 it would be 65 cm ,which is 185% of the height at grade 5

2)a)Yes,12 out of 15 cases are there with speed greater than 10:50
b)Yes,the probability would be very low since the cases would be only seen in 15th and 5th percentile
c)No,since the case is true for fourth grade but not for fifth grade

3)E,For John the timing is 60*10+50= 650,while for Peter it is 60*10=600,now height for both is 80 cm so the percentile for John is 85th percentile,while for Peter it is not exactly 50 rather it is slight lower than 50 going roughly around 48-49 so the difference is 85-49=36,which is roughly 40th percentile

4)a)Yes,since 9 out of 10 cases have speed slower than 11:00 at second gry or lower
b)No,because for time > 9*60=540 the probability would be very much high and it would be greater than 50%
c)No,because for 5th grade the time is 7:20 and not 7:30,so the boy might not be there in 5th grade

5)a)No,95% are not slower rather they are faster than Joshua
b)No,More than 15% are slower than Joshua
c)No,since 3 out of 5 boys in second grade are faster than Joshua

6)a)Yes,since around 50 percentile the value is coming so more than 50% have a height less than equal to Joshua's
b)Yes,4 out of 5 cases have height within 90 seconds of Josh's
c)No,it is faster than those of 15% population so it is greater than 5%

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The Huffingdale All Boys School has produced a comprehensive set of 20 Mar 2023, 09:43
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Sajjad1994

1. Consider an individual boy from a model population. Suppose that from grades 1 through 5, this boy's height is at the 50th percentile for his running time and his running time is at the 50th percentile for his grade level. Which one of the following statements must be true of the boy at Grade 5?

A. His grade level is at the 50th percentile for his running time.
B. His height is at the 50th percentile for his grade level.
C. His running time is at the 50th percentile for his height.
D. His height is approximately 130% of his height in Grade 2.
E. His height is approximately 185% of his height in Grade 2.

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Can someone please explain how the OA is A for this?
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Apt0810
1)E,since his running time at grade 5 is 501 seconds and his height would be 120 cm while at grade 2 it would be 65 cm ,which is 185% of the height at grade 5

2)a)Yes,12 out of 15 cases are there with speed greater than 10:50
b)Yes,the probability would be very low since the cases would be only seen in 15th and 5th percentile
c)No,since the case is true for fourth grade but not for fifth grade

3)E,For John the timing is 60*10+50= 650,while for Peter it is 60*10=600,now height for both is 80 cm so the percentile for John is 85th percentile,while for Peter it is not exactly 50 rather it is slight lower than 50 going roughly around 48-49 so the difference is 85-49=36,which is roughly 40th percentile

4)a)Yes,since 9 out of 10 cases have speed slower than 11:00 at second gry or lower
b)No,because for time > 9*60=540 the probability would be very much high and it would be greater than 50%
c)No,because for 5th grade the time is 7:20 and not 7:30,so the boy might not be there in 5th grade

5)a)No,95% are not slower rather they are faster than Joshua
b)No,More than 15% are slower than Joshua
c)No,since 3 out of 5 boys in second grade are faster than Joshua

6)a)Yes,since around 50 percentile the value is coming so more than 50% have a height less than equal to Joshua's
b)Yes,4 out of 5 cases have height within 90 seconds of Josh's
c)No,it is faster than those of 15% population so it is greater than 5%

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I have a question regarding the 1st statement of the question 6.

As 'At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's', it could mean that 80% or 100% of boys with the same running time have a height that is less than or equal to that of Joshua's, am I right?
If yes, then the statement should be 'No'
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Sajjad1994

1. Consider an individual boy from a model population. Suppose that from grades 1 through 5, this boy's height is at the 50th percentile for his running time and his running time is at the 50th percentile for his grade level. Which one of the following statements must be true of the boy at Grade 5?

This problem requires the use of both graphs.

We can't use the first statement right away, because we don't have the boy's height or running time to start with.
But we can use the second statement: The boy's running time is the median (50th percentile) for 5th graders. We can find this in the table (first datagraphic): 8 minutes 21 seconds. That's 8·60 + 21 = 501 seconds.

Now go back to the second datagraphic. 501 seconds is approximately 500 seconds, which is the left-hand extreme of the graph. The boy's height is the y-coordinate of the 50th percentile there, which is 120 cm. (Lol that's only about 4 feet tall... awfully short for a fifth-grader!)

Let's see whether we can decide any of the answer choices:

Quote:
A. His grade level is at the 50th percentile for his running time.
This is impossible to decide, because we don't have distributions of the numbers of students by running time or by grade level. (Among other things, the value cited here could vary if the classes at different grade levels have different numbers of boys in them.)

Quote:
B. His height is at the 50th percentile for his grade level.
We don't have any information about heights by grade level, only heights by running time. This can't be decided.

Quote:
C. His running time is at the 50th percentile for his height.
We can't use this unless we have some data for which height is the explanatory (x axis) variable. We have no such data here, so this is unresolvable as well.


For D and E, we need the boy's 2nd grade height.
This just takes another jaunt through the same two steps. First, find the 50th percentile time for second grade (11 min 15 sec, or 675 sec). Then go to the graph with the curves and read off the boy's height: about 65 cm.
(LOL!! that's barely more than 2 feet! Literal newborns are almost 2 feet long, so this is an absolutely insane figure. It's very uncharacteristic of GMAC to create a problem with numbers that are absurd in the real world—I can only guess that this problem didn't go through as much editing as most of them do.)

Twice 65cm is 130cm, so the fifth-grade height of 120cm is just barely less than twice the second-grade height.

Quote:
D. His height is approximately 130% of his height in Grade 2.
Nah.

Quote:
E. His height is approximately 185% of his height in Grade 2.
Yeah.

It's E.

(The listed OA isn't correct here. Not sure what happened there, but the datum in choice A can't be found from the data we're given.)



2. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

Some of the wordings in these statements are a bit dodgy (see details below). In the upcoming Data Insights section—essentially, "IR goes to play in the big leagues"—I trust that the real exam problems will be more extensively edited, and thus more meticulously written for clarity, than the below.


Quote:
If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.

"Probability" is singular here, so the only possible interpretation of this statement is that the boy is chosen at random from a pool containing all third-, fourth-, AND fifth-graders. We're talking about a SINGLE probability, for that whole pool of boys from three grade levels combined.

What do we know about the 3 individual grades that combine to make the pool?
• 3rd grade: 10m50s is exactly the 50th percentile running time. So, according to the given info, EXACTLY HALF of 3rd graders run faster times than this.
• 4th grade: 10m50s is beyond 95th percentile running time. So MORE THAN 95% of boys in 4th grade run faster than this time.
• 5th grade: 10m50s is exactly the 50th percentile running time. So MORE THAN 95% of boys in 5th grade run faster than this time.

The OVERALL probability here, therefore, is some weighted average of 50%, something greater than 95%, and something else greater than 95%. This definitely has to be greater than 50% overall, so the first statement IS satisfied.


Quote:
If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.

This statement doesn't involve grade level, so we can disregard the table this time. We're only going to use the graph.

10 minutes is equal to 600 seconds."No slower" means we need to look at the part of the graph to the LEFT of 600 seconds.
Throughout that region of the graph, all of the curves are above 73cm the whole time (see previous comments about the utter ridiculousness of this height in the real world...)
The bottom curve is the 5th percentile, so the data points for 95% of the boys lie above that curve at any given x value. Since this bottom curve sits entirely above 73cm in the desired region, this statement is ALSO TRUE.


Quote:
If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.

This time our statement isn't about probability, and is instead about the boy's INDIVIDUAL GRADE LEVEL. Therefore, this statement is only "True" if it works for ALL FIVE GRADE LEVELS individually.
But if we look at the 5th graders, we see that 15% of them run times faster than 7min 53sec. This statement is therefore false if our boy happens to be in fifth grade, so it is not supported overall.


Yes, yes, no.


3. A boy, John, selected at random from a model population runs a 10:50 kilometer. Another randomly selected boy, Peter, runs a 10:00 kilometer. Both boys measured 80cm tall. The difference in their percentiles in height among boys who run their respective speeds is most closest to

This part is more concrete than the preceding ones, because we can actually find the specific values for both halves of the comparison (quite the contrast with Data Sufficiency, where, if you're asked for a difference or other relative value, you probably won't be able to find all of the individual component values separately).

John's time is 650 seconds. We go to x = 650 sec and locate a height of y = 80 cm—which lands pretty much right on the 85th percentile curve. JOHN = 85th percentile

Peter's time is 600 seconds. We go to x = 600 sec and locate a height of y = 80 cm—which lands slightly UNDER the 50th percentile curve. PETER = ≈40th percentile (we can't read this one with much accuracy; all we know is "somewhere between 15th and 50th percentiles").


But with these choices...

Quote:
A. 15%
B. 25%
C. 30%
D. 35%
E. 40%
Show more

... that's enough to give us E, because we'd get D by landing ON BOTH the 85th and 50th percentile curves (respectively for John and Peter). so we know it's more than D, and only E does that.


"Most closest"? Does the problem actually... say that? •_______•


Other 3 problems will follow in another post, just to keep a lid on the total volume in each post. Ron
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The Huffingdale All Boys School has produced a comprehensive set of 02 Jun 2023, 23:58
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RonPurewal


Quote:
At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's.

(N.B. "that of Joshua's" is ungrammatical—it should be either "that of Joshua" or just "Joshua's". Yet another reason to suspect that GMAC did not create this problem.)

In fact, somewhere between 50% and 85% of the boys who run that time are shorter than Joshua, so this first part is quite handily TRUE.

Show more

Hi RonPurewal, thank you so much for all details of explanation.

I have a question regarding the 1st statement of the question 6 quoted above.

As 'At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's', it could mean that 80% or 100% of boys with the same running time have a height that is less than or equal to that of Joshua's, am I right?
If yes, then the statement should be 'No'
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KarishmaB

Sajjad1994
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Attachment:
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Attachment:
2.jpg
­Responding to a pm:

Reading Tab 1:

What are percentiles? Say you get 99th percentile score in GMAT - it means your score is better than (or equal to - if defined so) than 99 people out of 100.

The question defined the percentile in running time.
"the nth percentile in running time for a given grade is the unique running time among boys of that grade level that is slower than or equal to n percent"

So consider 1st grade.
I say 95th percentile of running time is 13 mins 20 sec. It means the time of 13 mins 20 sec is slower than or equal to 95% of the times taken by first graders for 1 km run. So to be fast, one should have a low percentile.
Say fourth grader, 15th percentile, time taken is 9:20. It means that 9 mins 20 secs is slowe than or equal to 15% of the times taken by fourth graders for a 1 km run.

That is how you read this table.

Go to the second tab -

Height percentiles of running times.

Given: "the nth percentile in height for a given running time is the unique height among boys of that running time that is taller than or equal to n percent,"

So look at 500 on x axis. Among all boys who take 500 seconds to run a km, the boys at the 95th percentile in height has a height of about 137 cm and the boy at the 5th percentile has a height of about 112 cm.
Similarly for all other time taken.

Question 1.

Question 1. 1. Consider an individual boy from a model population. Suppose that from grades 1 through 5, this boy's height is at the 50th percentile for his running time and his running time is at the 50th percentile for his grade level. Which one of the following statements must be true of the boy at Grade 5?

His running time is at the 50th percentile for his grade level. I know how to decode this from table in tab 1. I can find his running times as per his grade.

First grade 12:59 (about 780 seconds)
Second grade 11:15 (about 675 seconds)
Third grade 10:50
Fourth grade 9:55
Fifth grade 8:21 (about 500 seconds)

Next, from the second graph, as per running time, I can find 50 percentile of height.
I do not have data for 780 seconds time (because the graph only tells about 500 secs to 700 secs) but I do have for 675 seconds.
At 675 secs (grade 2 time), the orange curve is at about 65 cm.
At 500 secs (grade 5 time), the orange curve is at 120 cm.
Double of 65 is 130 so 120 would be at about 185%.

Hence option (E) is correct - His height is approximately 185% of his height in Grade 2.
Option (D) automatically becomes wrong then.

Option (A): His grade level is at the 50th percentile for his running time.
What does grade level at 50th percentile even mean?

Option (B): His height is at the 50th percentile for his grade level.
We know the percentile of height for running time, not for grade level. If all boys of a specific running time (say 500 secs) are brought together, how do their heights vary is known through the graph. How the heights vary as per grades is not known.

Option (C): His running time is at the 50th percentile for his height.
We know the running time percentile for grade through the table in tab 1. The percentile of running time for height is not known. The graph in tab 2 gives percentile of height for running time, not the other way around. Percentiles shown are of height.

Answer: His height is approximately 185% of his height in Grade 2.
Show more
­I am bit confused here,
so for Q2,
If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.
this should be NO right? if exact 50th percentile is 10:50 for third grade, means he is slower than or equal to 50% of people,
so how more than 50% are faster than 10:50, should it be, faster than or equal to 10:50?
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Hi,
Can anyone kindly help with this query?
KarishmaB HarshavardhanR Sajjad1994 chetan2u

Thank you
jaky_nguyen

Hi RonPurewal, thank you so much for all details of explanation.

I have a question regarding the 1st statement of the question 6 quoted above.

As 'At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's', it could mean that 80% or 100% of boys with the same running time have a height that is less than or equal to that of Joshua's, am I right?
If yes, then the statement should be 'No'
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gchandana
Hi,
Can anyone kindly help with this query?
KarishmaB HarshavardhanR Sajjad1994 chetan2u

Thank you
jaky_nguyen

Hi RonPurewal, thank you so much for all details of explanation.

I have a question regarding the 1st statement of the question 6 quoted above.

As 'At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's', it could mean that 80% or 100% of boys with the same running time have a height that is less than or equal to that of Joshua's, am I right?
If yes, then the statement should be 'No'
Show more

There are at least 15% boys with height less than 80 cm means that the height of 15% boys is certainly less than 80 cm. It means this value cannot be 14% or 10% or 3% etc. This value is certainly 15% or more. Our data shows us that this value is more than 50%. It could be 55% or 61% or 70% or 80% etc.
In ALL these cases, this value is more than 15%. That is why the statement is true. What the actual value is irrelevant. In all cases, it is more than 15%.
That is why we select Yes
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KarishmaB
gchandana
Hi,
Can anyone kindly help with this query?
KarishmaB HarshavardhanR Sajjad1994 chetan2u

Thank you
jaky_nguyen

Hi RonPurewal, thank you so much for all details of explanation.

I have a question regarding the 1st statement of the question 6 quoted above.

As 'At least 15% of boys with the same running time have a height that is less than or equal to that of Joshua's', it could mean that 80% or 100% of boys with the same running time have a height that is less than or equal to that of Joshua's, am I right?
If yes, then the statement should be 'No'

There are at least 15% boys with height less than 80 cm means that the height of 15% boys is certainly less than 80 cm. It means this value cannot be 14% or 10% or 3% etc. This value is certainly 15% or more. Our data shows us that this value is more than 50%. It could be 55% or 61% or 70% or 80% etc.
In ALL these cases, this value is more than 15%. That is why the statement is true. What the actual value is irrelevant. In all cases, it is more than 15%.
That is why we select Yes
Show more
Oh, right, got it.
So in the same sense, the 2nd statement of the 6th question is also true.
At least 80% of the boys means that the % is greater than 80. And not worried about the actual value.
This makes so much more sense now.

Thank you so much KarishmaB :cry:
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Q4
3 why is it 40 and not 35
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The point (600, 80) is a little below the 50th percentile line so 40% would be the more accurate estimate.
kayarat600
Q4
3 why is it 40 and not 35
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But you can not be estimating that! We cannot comment on the percentile and the difference as long as point don't fall on the line. The answer should be 35
cheshire
The point (600, 80) is a little below the 50th percentile line so 40% would be the more accurate estimate.

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KarishmaB

Question 2.

2. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

If he is in the third grade or above, the probability that his speed is faster than 10:50 is greater than 50%.

Look at TAB 1. He could be in 3rd, 4th or 5th grade. 10:50 is at exact 50 percentile in 3rd grade, but at more than 95 percentile in 4th and 5th grades. So if he is selected from third or higher grade, the probability that his speed is faster than 10:50 is greater than 50% for sure. It will lie between 50% and 95%.

Select YES

If he runs at least a 10 minute kilometer run (no slower), the probability that his height is up to 73cm is no greater than 5%.

Look at TAB 2. He runs a kilometer is 10 minutes or less time. At 10 minute i.e. 600 secs time, a height of 73 cm is at 5 percentile (on the green line). For any time less than 10 minutes, 73 cm will be an even lower percentile (perhaps 1 or 2). So the probability that his height is up to 73cm is no greater than 5%.

Select YES

If he runs an 8 minute kilometer run, he is faster than at least 95% of boys of his same grade level.

For 5th grade, 8 min lies between 15th and 50th percentile. Hence, it is not essential that he is faster than at least 95% of boys of his same grade level. It will not be true if he is in the 5th grade. For all other grades, this statement will hold.
But since we need the statement to hold for every grade, the statement is not correct.

Select NO
Show more


Hello mam KarishmaB

But the question mentions that " AT LEAST 10 mints"
Isn't we need to look for 600 sec and beyond that.


thx
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CEO2021



Hello mam KarishmaB

But the question mentions that " AT LEAST 10 mints"
Isn't we need to look for 600 sec and beyond that.


thx
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At least a 10 min kilometer (no slower) means he covers at least a km in 10 minutes. He is not slower than that. So he could cover more distance in a km but he covers at least 1 km. It means he takes either 600 secs or LESS time than that. No slower tells us that he does NOT take more than 600 secs for a km.
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In question 2 part 2, how do u say probability is less than 5%. I mean u saw 5th percentile height yes for them it is but there are boys in 85th percentile with runtime of 9.07 and when u compare that height they would all be above 73 cms. And u cannot justify 5% since we do not actually know how many boys would be there in 85th percentile.
Kind of feel like people should stop making questions just for making them & ending up with poorly framed ques.
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I am not able to find your solutions for all the questions, please help
KarishmaB
Reading Tab 1:

What are percentiles? Say you get 99th percentile score in GMAT - it means your score is better than (or equal to - if defined so) than 99 people out of 100.

The question defined the percentile in running time.
"the nth percentile in running time for a given grade is the unique running time among boys of that grade level that is slower than or equal to n percent"

So consider 1st grade.
I say 95th percentile of running time is 13 mins 20 sec. It means the time of 13 mins 20 sec is slower than or equal to 95% of the times taken by first graders for 1 km run. So to be fast, one should have a low percentile.
Say fourth grader, 15th percentile, time taken is 9:20. It means that 9 mins 20 secs is slowe than or equal to 15% of the times taken by fourth graders for a 1 km run.

That is how you read this table.

Go to the second tab -

Height percentiles of running times.

Given: "the nth percentile in height for a given running time is the unique height among boys of that running time that is taller than or equal to n percent,"

So look at 500 on x axis. Among all boys who take 500 seconds to run a km, the boys at the 95th percentile in height has a height of about 137 cm and the boy at the 5th percentile has a height of about 112 cm.
Similarly for all other time taken.

Question 1.

Question 1. 1. Consider an individual boy from a model population. Suppose that from grades 1 through 5, this boy's height is at the 50th percentile for his running time and his running time is at the 50th percentile for his grade level. Which one of the following statements must be true of the boy at Grade 5?

His running time is at the 50th percentile for his grade level. I know how to decode this from table in tab 1. I can find his running times as per his grade.

First grade 12:59 (about 780 seconds)
Second grade 11:15 (about 675 seconds)
Third grade 10:50
Fourth grade 9:55
Fifth grade 8:21 (about 500 seconds)

Next, from the second graph, as per running time, I can find 50 percentile of height.
I do not have data for 780 seconds time (because the graph only tells about 500 secs to 700 secs) but I do have for 675 seconds.
At 675 secs (grade 2 time), the orange curve is at about 65 cm.
At 500 secs (grade 5 time), the orange curve is at 120 cm.
Double of 65 is 130 so 120 would be at about 185%.

Hence option (E) is correct - His height is approximately 185% of his height in Grade 2.
Option (D) automatically becomes wrong then.

Option (A): His grade level is at the 50th percentile for his running time.
What does grade level at 50th percentile even mean?

Option (B): His height is at the 50th percentile for his grade level.
We know the percentile of height for running time, not for grade level. If all boys of a specific running time (say 500 secs) are brought together, how do their heights vary is known through the graph. How the heights vary as per grades is not known.

Option (C): His running time is at the 50th percentile for his height.
We know the running time percentile for grade through the table in tab 1. The percentile of running time for height is not known. The graph in tab 2 gives percentile of height for running time, not the other way around. Percentiles shown are of height.

Answer: His height is approximately 185% of his height in Grade 2.
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