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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?

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.

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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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:

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.)

We don't have any information about heights by grade level, only heights by running time. This can't be decided.

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.

Nah.

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.



"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.



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.



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...

(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.

Hi nisen20

Could you kindly provide a screenshot to substantiate your assertion regarding the inaccurate official answer for question #1?

Thank you!

(A) His grade level is at the 50th percentile for his running time. grade level percentile for running time, clearly wrong
(B) His height is at the 50th percentile for his grade level. height percentile for grade level, clearly wrong
(C) His running time is at the 50th percentile for his height. running time percentile for height, clearly wrong

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

I don't have a screenshot, but I can explain.
The table in the first tab shows the running time percentile for grade level, and the graph in the second tab shows the height percentil for running time.

All three options, from A to C, are irrelevent to the given information, and cannot be deduced from it.
A B C are gone, and we are left with D and E which can be calculated.

Our lengend Ron's explanation is already there and I will steal it.
120/65 ≈ 1.84, approximately 185%

­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.

­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?