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Updated on: 24 Jan 2024, 12:42
Originally posted by gmatt1476 on 21 Apr 2020, 22:22.
Last edited by Sajjad1994 on 24 Jan 2024, 12:42, edited 3 times in total.
Last edited by Sajjad1994 on 24 Jan 2024, 12:42, edited 3 times in total.
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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.
His height is approximately 185% of his height in Grade 2.
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:
42% (03:40) correct
58%
(03:45)
wrong
based on 1575
sessions
History
Date
Time
Result
Not Attempted Yet
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. |
ShowHide Answer
Official Answer
His height is approximately 185% of his height in Grade 2.
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
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:
38% (02:41) correct
62%
(02:49)
wrong
based on 1888
sessions
History
Date
Time
Result
Not Attempted Yet
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. |
ShowHide Answer
Official Answer
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
40%
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:
31% (01:40) correct
69%
(01:33)
wrong
based on 1709
sessions
History
Date
Time
Result
Not Attempted Yet
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
| 15% | |
| 25% | |
| 30% | |
| 35% | |
| 40% |
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
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:
31% (02:17) correct
69%
(02:21)
wrong
based on 1630
sessions
History
Date
Time
Result
Not Attempted Yet
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. |
ShowHide Answer
Official Answer
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
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
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:
40% (02:23) correct
60%
(02:16)
wrong
based on 1346
sessions
History
Date
Time
Result
Not Attempted Yet
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. |
ShowHide Answer
Official Answer
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
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
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:35) correct
50%
(02:37)
wrong
based on 1066
sessions
History
Date
Time
Result
Not Attempted Yet
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. |
ShowHide Answer
Official Answer
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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25 Apr 2024, 10:06
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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.
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.
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.
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.
"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.
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:
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.
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.)
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.
(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.
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.
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.
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:
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:
"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:
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:
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:
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:
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:
(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:
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:
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.
