The World Health Organization (WHO) has produced a comprehensive set o

Question

The World Health Organization (WHO) has produced a comprehensive set of growth standards for children. These standards are based on studies of children living in 6 nations on 5 continents under optimal conditions with respect to health and nutrition.
Height-for-age
The table displays the percentil distribution of height, in centimeters, at 3-month intervals, for boys ages 2 through 5 according to the WHO model. In a model population -- a large population of boys ages 2 through 5 that conforms to the WHO growth standards -- for n = 3, 15, 50, 85, and 97, nth percentile in height for a given age is the unique height among boys of that age that is greater than or equal to n percent, and less than or equal to (100- n) percent, of heights of boys of that age

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Weight-for-height

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attach1.JPG [ 54.7 KiB | Viewed 54704 times ]

The graph shows the percentile distribution of weight, in kilograms, for heights from 80 cm to 120 cm, for boys ages 2 through 5, according to the WHO model. In a model population, for n = 3, 15, 50, 85, and 97, the nth percentile in weight for a given heigh is the unique weight among boys of that height that is greater than or equal to n percent, and less than or equal to (100 - n) percent, of weights of boys of that height.

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.

A If his age is exactly 4 years 0 months, the probability that his height is at exactly 99.0 cm is 15%
B. If he is 81 cm tall, he is shorter than at least 95% of boys his age.
C. If he is 120 cm tall, he weighs more than 97% of boys age 2 years 6 months.

Show Spoiler

A.no
B. yes
C. no

Sajjad1994 · Accepted Answer

Official Explanation

1. 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.

Using the table in Height-for-age standards, the 50th percentile height for boys aged 3 years 3 months is 98.0 cm, so 50% of boys this age are taller than this. For boys aged 3 years 6 months and older, the 50th percentile height is greater than 98.0 cm, so at least 50% of boys this age are taller than this. Moreover, for boys 4 years 0 months and older, the 15th percentile height exceeds 98.0 cm, so at these ages, at least 85% of boys are taller than 98.0 cm. Thus, for a boy selected at random from a model population whose age is greater than 3 years 3 months, the probability that his height is at least 98.0 cm is greater than 50%.

The correct answer is Yes.

Using Weight-for-height standards, the 3rd percentile weight for height 105 cm is just over 14 kg, and for heights greater than 105 cm, the 3rd percentile weight is greater than 14 kg. Thus, at most, 3% of the population of boys at least 105 cm tall has a weight of 14.0 kg or less. In particular, at most 3% of the population of boys at least 105 cm tall has a weight of exactly 14.0 kg.

The correct answer is Yes.

Using Height-for-age standards, the 85th percentile in height for boys 5 years 0 months is 114.8 cm. This means that a boy 114.8 cm tall is as tall or taller than 85% of boys aged 5 years 0 months. It does not follow that a boy 114.8 cm tall is necessarily taller than 85% of boys aged 5 years 0 months, so it is not necessarily true of a boy 114 cm tall, either.

The correct answer is No.

2. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy's weight is at the 97th percentile for his height and his height is at the 97th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (choice A).

The boy's weight is less than that of 97% of boys his height, and his height is less than that of 97% of boys his age, but it is impossible to tell where his weight falls among the weights of boys his age (choice B).

Likewise, knowing height-for-weight percentiles does not provide information about weight-for-height percentiles (choice C).

However, it is possible to approximate his height at each age and his weight at each height; thus it is possible to determine his weight at each age. Height-for-age standards indicates that at age 2 years 0 months, the boy was 92.9 cm tall, and at age 5 years 0 months, he was 118.7 cm tall. Weight-for-height standards indicates that the 97th percentile weight for boys 92.9 cm tall is approximately 16 kg, while the 97th percentile weight for boys 118.7 cm tall is between 26 kg and 27 kg. Thus his weight at age 5 years 0 months is roughly between 26/16 = 162 .5% and 27/16 = 168 .75%, or approximately 166%, of his weight at age 2 years 0 months.

The correct answer is D.

3. B is a boy aged 4 years 3 months whose height is 110 cm and whose weight is 19 kg. For each of the following statements, select Yes if, based on the given information, it must be true of B relative to a model population. Otherwise, select No.

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of height on the basis of weight, so it is impossible to determine the proportion of boys weighing 19 kg whose height is less than 110 cm.

The correct answer is No.

Using the table in Height-for-age standards, the 85th percentile in height for boys aged 4 years 3 months is 109.5 cm, so (100 − 85)%, or 15%, of boys aged 4 years 3 months are taller than 109.5 cm. Thus, at most 15% of boys of this age are taller than B's height of 110 cm.

The correct answer is Yes.

Using the table in Height-for-age standards, the 50th percentile in height for boys aged 5 years 0 months is 110.0 cm, which is the same height as B. Therefore, B's height is greater than or equal to that of (100 − 50)%, or 50%, of boys aged 5 years 0 months.

The correct answer is Yes.

4. B is a boy aged 4 years 3 months whose height is 110 cm and whose weight is 19 kg. For each of the following statements, select Yes if, based on the given information, it must be true of B relative to a model population. Otherwise, select No.

According to the graph in Weight-for-height standards, the 15th percentile in weight for a boy of height 110 cm is approximately 17 kg. Therefore, 17 kg is greater than or equal to the weight of 15% of boys of that height. But 17 kg is less than B's weight of 19 kg, so the percentage of boys whose weight is less than or equal to B's weight may be somewhat larger than 15%. Consequently, at least 15% of boys at B's height have a weight that is less than or equal to that of B.

The correct answer is Yes.

B's height is 110 cm, and 10% of 110 is equal to 11, so a boy is within 10% of B's height provided that he is between 99 cm and 121 cm tall. According to Height-for-age standards, for boys aged 4 years 3 months, 100.5 cm is the 15th percentile in height and 113.1 cm is the 97th percentile in height. Therefore, (97 − 15)%, or 82% of boys B's age have heights between 100.5 cm and 113.1 cm. Since 99 < 100.5 and 113.1 < 121, the heights of all these boys are within 10% of B's height, so at least 82%—and hence at least 80%—of boys B's age have heights within 10% of B's height.

The correct answer is Yes.

According to Height-for-age standards, for boys aged 4 years 0 months, the 97th percentile in height is 111.2 cm, so B's height of 110 cm is less than that of at least 3% of boys this age. If B's height were also less than that of at most 3% of boys this age, then 110 cm would have to be the 97th percentile in height for boys aged 4 years 0 months, which it is not.

The correct answer is No

5. 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.

Using Height-for-age standards for boys aged 4 years 0 months, the 15th percentile in height is 99.0 cm. Thus, 15% of boys of this age are 99.0 cm tall or shorter. Note that the 3rd percentile in height for boys of this age is 95.4 cm, so 3% of boys of this age are at this height or shorter. Therefore, (15 − 3)%, or 12% of boys aged 4 years 0 months have heights greater than 95.4 cm and less than or equal to 99.0 cm. The proportion of boys of this age whose height is exactly 99.0 cm must therefore be less than or equal to 12%, so the indicated probability is also less than or equal to 12%.

The correct answer is No.

Using Height-for-age standards, the 3rd percentile in height for ages from 2 years 0 months through 5 years 0 months is at least 81.4 cm. This means that a boy from a model population whose height is 81.4 cm is shorter than at least 97% of boys his age. Thus, a boy who is 81 cm tall is shorter than at least 97% of boys his age and thus shorter than at least 95% of boys his age.

The correct answer is Yes.

Weight-for-height standards provide a weight distribution for boys 120 cm tall; in particular, 97% of boys at this height weigh more than 18 kg. But a randomly selected boy at this height could conceivably weigh much less than 18 kg. Moreover, even if the boy's weight were known, a percentile distribution of weight for boys age 2 years 6 months is lacking, so it is impossible to answer the question based on the information provided.

The correct answer is No.

6. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy’s weight is at the 50th percentile for his height and his height is at the 50th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (option A). The boy's weight is less than that of 50% of boys his height, and his height is less than that of 50% of boys his age, but it is impossible to tell where his weight falls among the weights of boys his age (option B). Likewise, knowing height-for-weight percentiles does not provide information about weight-for-height percentiles (option C).

What can be approximated, however, is his height at each age and his weight at each height; thus, it is possible to know his weight at each age. Height-for-age standards indicates that at age 2 years 0 months, the boy was 87.1 cm tall, and at age 5 years 0 months, he was 110.0 cm tall. Weight-for-height standards indicates that the 50th percentile weight for boys 87.1 cm tall is approximately 12 kg, while the 50th percentile weight for boys 110.0 cm tall is approximately 18 kg. Thus, his weight at age 5 years 0 months is approximately 18/12 (100)%, or 150%, of his weight at age 2 years 0 months.

The correct answer is D.

KarishmaB · Answer

Here is the detailed discussion on this set:

https://www.youtube.com/watch?v=bql1Mw0gl_A

maybeam · Answer

The World Health Organization (WHO) has produced a comprehensive set of growth standards for children. These standards are based on studies of children living in 6 nations on 5 continents under optimal conditions with respect to health and nutrition.
Height-for-age
The table displays the percentil distribution of height, in centimeters, at 3-month intervals, for boys ages 2 through 5 according to the WHO model. In a model population -- a large population of boys ages 2 through 5 that conforms to the WHO growth standards -- for n = 3, 15, 50, 85, and 97, nth percentile in height for a given age is the unique height among boys of that age that is greater than or equal to n percent, and less than or equal to (100- n) percent, of heights of boys of that age

Attachment:

attach1.JPG [ 76.53 KiB | Viewed 54942 times ]

Weight-for-height

Attachment:

attach1.JPG [ 54.7 KiB | Viewed 54704 times ]

The graph shows the percentile distribution of weight, in kilograms, for heights from 80 cm to 120 cm, for boys ages 2 through 5, according to the WHO model. In a model population, for n = 3, 15, 50, 85, and 97, the nth percentile in weight for a given heigh is the unique weight among boys of that height that is greater than or equal to n percent, and less than or equal to (100 - n) percent, of weights of boys of that height.

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.

A If his age is exactly 4 years 0 months, the probability that his height is at exactly 99.0 cm is 15%
B. If he is 81 cm tall, he is shorter than at least 95% of boys his age.
C. If he is 120 cm tall, he weighs more than 97% of boys age 2 years 6 months.

Show Spoiler

A.no
B. yes
C. no

nisen20 · Answer

6. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy’s weight is at the 50th percentile for his height and his height is at the 50th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (option A).

Based on this explanation, the OA for Q2 CANNOT be A.

Q2 and Q6 are basically the same kind of questions. Here's OE for Q2:

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (choice A).

The boy's weight is less than that of 97% of boys his height, and his height is less than that of 97% of boys his age, but it is impossible to tell where his weight falls among the weights of boys his age (choice B).

Likewise, knowing height-for-weight percentiles does not provide information about weight-for-height percentiles (choice C).

However, it is possible to approximate his height at each age and his weight at each height; thus it is possible to determine his weight at each age. Height-for-age standards indicates that at age 2 years 0 months, the boy was 92.9 cm tall, and at age 5 years 0 months, he was 118.7 cm tall. Weight-for-height standards indicates that the 97th percentile weight for boys 92.9 cm tall is approximately 16 kg, while the 97th percentile weight for boys 118.7 cm tall is between 26 kg and 27 kg. Thus his weight at age 5 years 0 months is roughly between 26/16 = 162 .5% and 27/16 = 168 .75%, or approximately 166%, of his weight at age 2 years 0 months.

The correct answer is D.

sarkarsarbani · Answer

Sajjad1994   KarishmaB   bb   Bunuel   kevincan 
Hi,
How can we solve such difficult 805 level in actual exam under pressure?I am assuming we have to guesswork such questions.If I get all 805 level questions wrong in exam, how drastically will it impact my score?
Please suggest some tips on how to handle such questions
Thanks

kevincan · Answer

You won’t see many 805 level questions unless you are performing at a level above the 80-90th percentile, just as you won’t see many 205 level questions unless you are performing at a level below the 20th percentile. Just don’t get obsessed by any one question so that you have time to answer all of them.

_________________

Kevin Armstrong
Gmatclasses
Madrid , Spain

Signature Read More

bb · Answer

If you get all 805 questions wrong but answer 795 questions crrectly, you will be just fine.

But you should not pick the world hardest question and wonder how to solve it if you have not mastered easy and medium ones... and if you have mastered those, then you will know how to solve this one. Start with crawling, walking, and only then running.

P.S. Very few people can solve these super hard questions and that's just fine - people still get high scores on the DI.

KarishmaB · Answer

The role of these questions in your prep is to teach you the unfamiliar or less tested or higher level concepts. With such a question in practice tests, you will be better prepared for a percentile based question in the actual and it will not seem as hard as this one. 
Also, in the actual test, you get questions which are quite do-able in the limited time you have. You will get a very hard question only if you are doing very well on the test. In that case missing the very hard question won't impact your score much so no need to worry about it as long as you don't waste too much time on it. The point is that we need to do the best as per our ability.

vanshikajain1606 · Answer

I took official mock 6 today and got MANY 805+ questions (Evidence-based medicine MSR and 4-5 805+ TPA) I could not solve them under time pressure and ended up wasting most time on them, with a 78 Score on DI! Not sure why was I getting such hard questions back to back. My target score is DI83. kevincan KarishmaB Can you please recommend what to do in such situation?

KarishmaB · Answer

Each mock is a learning experience. You learn timing and management strategies and find out the topics in which you have gaps. During the test you do not know the level of the question you are attempting. All you can do and should do is focus on the question in front of you, give it your best in limited time and then move ahead. Use the Review and Edit option as explained in this post: https://anaprep.com/purpose-of-review-a ... n-on-gmat/ Worry about nothing else. Which question to give you next is the algo's problem, not yours. You keep to the plan and you will get the best score as per current ability. After the mock, focus on the topics in which you made mistakes to improve the current ability.

arunbhati · Answer

Hi  Bunuel ,

Can you please explain solution of statement 1 of Q5

Bunuel · Answer

If his age is exactly 4 years 0 months, the probability that his height is at exactly 99.0 cm is 15%.
 
Use Tab 1, because the age is given and the statement asks about height.

At age 4 years 0 months, 99.0 cm is the 15th-percentile height. This means that  at least 15% of boys that age have heights no greater than 99.0 cm .

It does  not  mean that 15% of boys are  exactly  99.0 cm tall.

Answer:  No

Yes	No
		If his age is greater than 3 years 3 months, the probability that his height is at least 98.0 cm is greater than 50%.
		If he is at least 105 cm tall, the probability that his weight is 14.0 kg is no greater than 3%
		If he is 114 cm tall, he is taller than at least 85% of boys his age.

	His age is at the 97th percentile for his height.
	His weight is at the 97th percentile for his age.
	His height is at the 97th percentile for his weight.
	His weight is approximately 166% of his weight at age 2 years 0 months.
	His weight is approximately 197% of his weight at age 2 years 0 months.

Yes	No
		Approximately 50% of boys at the same weight are shorter than B.
		No more than 15% of boys at this age are taller than B.
		B's height is greater than or equal to that of 50% of boys aged 5 years 0 months.

Yes	No
		At least 15% of boys at the same height have a weight that is less than or equal to that of B
		At least 80% of boys at this age have heights within 10% of B's height.
		B's height is less than that of at most 3% of boys at age 4 years 0 months.

	His age is at the 50th percentile for his height.
	His weight is at the 50th percentile for his age.
	His height is at the 50th percentile for his weight.
	His weight is approximately 150% of his weight at age 2 years 0 months.
	His weight is approximately 200% of his weight at age 2 years 0 months.

The World Health Organization (WHO) has produced a comprehensive set o

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Yes	No
		If his age is exactly 4 years 0 months, the probability that his height is at exactly 99.0 cm is 15%
		If he is 81 cm tall, he is shorter than at least 95% of boys his age.
		If he is 120 cm tall, he weighs more than 97% of boys age 2 years 6 months.

GMAT Multi-Source Reasoning (MSR) Questions

The World Health Organization (WHO) has produced a comprehensive set o

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia