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The penguins currently living on an island are of two types,

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The penguins currently living on an island are of two types, [#permalink] New post 29 May 2019, 13:38
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The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of the Chinstrap penguins on the island is 13.2 centimeters, and the range of the heights of the Gentoo penguins on the island is 15.4 centimeters.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island?

Indicate all such statements.

A The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
B The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.
C The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.


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Question: 15
Page: 170
Difficulty: hard
[Reveal] Spoiler: OA

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Re: The penguins currently living on an island are of two types, [#permalink] New post 29 May 2019, 14:50
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The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of the Chinstrap penguins on the island is 13.2 centimeters, and the range of the heights of the Gentoo penguins on the island is 15.4 centimeters.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island?

First, define the range algebraically do determine specifically what value(s) will be sufficient to definitively determine the range of all penguin heights.

So, the range will equal largest penguin - smallest penguin. Already, we know that tallest G - shortest G = 15.4 and that tallest C - shortest C = 13.2.

So, what is needed to determine the total range is the overlap of the two ranges or Tallest G - Shortest C or Tallest C - Shortest G.

Evaluate the choices to determine if any will provide the overlap of the ranges.

A The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.

Plug in the information algebraically to find that Tallest G = Tallest C + 5.8.

Therefore, the overall range is determined by Tallest C + 5.8 - Shortest C = 13.2 --> So, the overall range of Tallest G - Shortest C = 7.4, which is a definitive answer, so select Choice A.

B The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.

Median provides no information about the shortest or tallest, so eliminate Choice B.

C The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.

Average provides no information about the shortest or tallest, so eliminate Choice C, leaving only Choice A selected.
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Re: The penguins currently living on an island are of two types, [#permalink] New post 29 May 2019, 21:20
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There are several ways to tackle this question. One approach is to give a set of penguins such as {13.2 } and { 15.4}, then point out scenarios that each statement do not match.
Another approach is to solve the problem is general.
For example, in statement A, just give the max height is x, then find relations of the range to the max height.
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Re: The penguins currently living on an island are of two types, [#permalink] New post 18 Jun 2019, 07:58
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if C1 is min and C2 is the Max height of one type, And G2 is the Max and G1 is the Min height of another group]
C2-C1= Range=13.2, So C2=C1+13.2
G2-G1=15.4, So G2= G1 +15.4
G2-C2=5.8 ( difference of the two tallest of both groups)
So, G2-C1=overall Range
G2-C1-13.2=5.8
or G2-C1=5.8+13.2=19.00 which is the over all range .
Is this OK that C1 is the lowest of all?
In my opinion,
C2=C1+13.2 and G2= G1 +15.4
Also, G2-C2=5.8 meaning G1>C1.
So, G2-C1 is the overall range
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Re: The penguins currently living on an island are of two types, [#permalink] New post 23 May 2020, 05:08
MyGuruStefan wrote:
Quote:
The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of the Chinstrap penguins on the island is 13.2 centimeters, and the range of the heights of the Gentoo penguins on the island is 15.4 centimeters.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island?

First, define the range algebraically do determine specifically what value(s) will be sufficient to definitively determine the range of all penguin heights.

So, the range will equal largest penguin - smallest penguin. Already, we know that tallest G - shortest G = 15.4 and that tallest C - shortest C = 13.2.

So, what is needed to determine the total range is the overlap of the two ranges or Tallest G - Shortest C or Tallest C - Shortest G.

Evaluate the choices to determine if any will provide the overlap of the ranges.

A The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.

Plug in the information algebraically to find that Tallest G = Tallest C + 5.8.

Therefore, the overall range is determined by Tallest C + 5.8 - Shortest C = 13.2 --> So, the overall range of Tallest G - Shortest C = 7.4, which is a definitive answer, so select Choice A.

B The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.

Median provides no information about the shortest or tallest, so eliminate Choice B.

C The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.

Average provides no information about the shortest or tallest, so eliminate Choice C, leaving only Choice A selected.


thank you. but shouldn't the overall range equal 19?
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Re: The penguins currently living on an island are of two types, [#permalink] New post 26 May 2020, 18:08
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A lot of the answers on this seem overly complicated.

The key in this question is that you're given two sets of range data, and you're looking for the additional set of data that would "provide(s) sufficient additional information to determine the range of the heights of all". So you just need to be able to say that you can create the "master range" of all the data. You don't actually NEED to create that, though, or do any additional figuring out.

A provides a sufficient relationship between the two sets of range data to answer that question.
B and C give you median and average data that won't help with determining the range unless you had more information.

Answer is A.
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Re: The penguins currently living on an island are of two types, [#permalink] New post 28 May 2020, 03:54
Mudslide53 wrote:
A lot of the answers on this seem overly complicated.

The key in this question is that you're given two sets of range data, and you're looking for the additional set of data that would "provide(s) sufficient additional information to determine the range of the heights of all". So you just need to be able to say that you can create the "master range" of all the data. You don't actually NEED to create that, though, or do any additional figuring out.

A provides a sufficient relationship between the two sets of range data to answer that question.
B and C give you median and average data that won't help with determining the range unless you had more information.

Answer is A.



how does A provide sufficient info?
the range of the group is tallest - shortest in both groups
the tallest is in G, but we have no info about the shortest, it could be in C or G
Re: The penguins currently living on an island are of two types,   [#permalink] 28 May 2020, 03:54
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