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The penguins currently living on an island are of two types, Chinstrap 31 May 2019, 00:17
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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.What is the range of the heights of all the penguins on the island?

(1) The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
(2) 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.
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The penguins currently living on an island are of two types, Chinstrap 31 May 2019, 00:26
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Required is combined tallest - smallest penguin of both varieties.

Statement 1 says gentoo variety has the taller penguin of the two. If gentoo also has the smaller one then combined range is still 15.4 if not it can be higher. Inconclusive.

Statement 2 provides information on the median. It doesn’t provide information on tallest nor smallest penguin required for range.

Combined they are still insufficient to answer the question.

Hence option E

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The penguins currently living on an island are of two types, Chinstrap Updated on: 31 May 2019, 03:56
Originally posted by Archit3110 on 31 May 2019, 03:39.
Last edited by Archit3110 on 31 May 2019, 03:56, edited 1 time in total.
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Bunuel
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.What is the range of the heights of all the penguins on the island?

(1) The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
(2) 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.

to find range of height of all penguins we need to find total population and avg height of each type
#1 The tallest Gentoo penguin on the island is 5.8 cm 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.
#2median height wont give total height of each type since we do not know total penguins which are living on island
IMO A
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The penguins currently living on an island are of two types, Chinstrap 31 May 2019, 03:51
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Can't we infer from the first statement? Suppose height of tallest CP- x
Height of smallest CP -> x-13.2.

Height of tallest GP - x+ 5.8
height of smallest gp - x+5.8 - 15.4

We can get the whole range from here ? Am i doing something wrong ? Statement A looks sufficient. Bunuel
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The penguins currently living on an island are of two types, Chinstrap Updated on: 31 May 2019, 04:01
Originally posted by LeoN88 on 31 May 2019, 03:59.
Last edited by LeoN88 on 31 May 2019, 04:01, edited 1 time in total.
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Bunuel
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.What is the range of the heights of all the penguins on the island?

(1) The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
(2) 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.

Cmax - Cmin= 13.2 & Gmax - Gmin=15.4

Let's start with easy statement 2. Median heights are definitely insufficient.
Statement 1.

Gmax - Cmax = 5.8

Now two possibilities of range: Gmax - Gmin= 15.4

& Gmax - Cmin = 5.8 + 13.2= 19 So A is sufficient to find the range.
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The penguins currently living on an island are of two types, Chinstrap 31 May 2019, 04:01
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rishabhshreyas14
Can't we infer from the first statement? Suppose height of tallest CP- x
Height of smallest CP -> x-13.2.

Height of tallest GP - x+ 5.8
height of smallest gp - x+5.8 - 15.4

We can get the whole range from here ? Am i doing something wrong ? Statement A looks sufficient. Bunuel

You have considered the same variable X for range of both GP and CP. The height of tallest GP as per your equation would be y+5.8 and thus you cannot arrive at the combined range.
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The penguins currently living on an island are of two types, Chinstrap 31 May 2019, 04:09
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The height of the tallest GP is 5. Something more than the height of tallest CP. That is the statement 1. So if height of the tallest CP is X , we can just add the difference to the tallest gp

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The penguins currently living on an island are of two types, Chinstrap 01 Jun 2019, 18:00
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Required is combined tallest - smallest penguin of both varieties.

Statement 1 says gentoo variety has the taller penguin of the two. If gentoo also has the smaller one then combined range is still 15.4 if not it can be higher. Inconclusive.

Statement 2 provides information on the median. It doesn’t provide information on tallest nor smallest penguin required for range.

Combined they are still insufficient to answer the question.

Hence option E

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Gentoo cannot have the smallest value one as Range of Chinstrip + difference in highest value exceeds the Range of Gentoo.

For example, let us suppose the min value of Gentoo is 10 and then the highest value will be 25.4.
The highest value of Chintoo is 5 less than highest at 20.4. Range is 13 and hence it will be 7.
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The penguins currently living on an island are of two types, Chinstrap 29 Jun 2019, 14:52
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Now the chinstrap penguins have a range of 13.2 and that of the Gentoo is 15.4. If the gentoo's tallest has a height 5.8cm greater than the Chinstrap it will be very obvious that the new range will be the range of the chinstrap+the height difference of 5.8 cm. Statement I is easily sufficient.

The median of the two groups has no effect on the range and the range of the entire group will be at least 15.4cm since it CAN NOT be lesser but the upper limit of the range could be anything depending on the heights of the tallest penguins of both groups.Statement II is insufficient
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The penguins currently living on an island are of two types, Chinstrap 15 Oct 2019, 05:12
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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.What is the range of the heights of all the penguins on the island?

(1) The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
(2) 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.

\(range = tn - a ≥ 0\)
\(Gentoo: x - y = 15.4\)
\(Chinstrap: z - w = 13.2\)

(1) The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island: sufic.

\(x=z+5.8…tn=x\)
\((z+5.8)-y=15.4…z=15.4-5.8+y…z=9.6+y\)
\((9.6+y)-w=13.2…y=13.2-9.6+w…y=3.6+w…y>w…a=w\)
\(range = tn - a=x-w=(z+5.8)-w=(z-w)+5.8=(13.2)+5.8=19\)

(2) 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: insufic.

Answer (A)
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The penguins currently living on an island are of two types, Chinstrap 03 Mar 2024, 18:24
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Let Ct be tallest penguin of the Chinstrap variety and Cs be the shortest penguin of the same variety. Let Gt be the tallest penguin of the Gentoo variety and let Gs be the shortest penguin of the same variety.
Ct - Cs =13.2 (given)
Adding 5.8cm to both sides and given Gt = Ct + 5.8
Gt - Cs = 13.2 + 5.8 = 19
Given Gt - Gs = 15.4
Take away 5.8cm from both sides
Ct - Gs = 9.6

Therefore the difference between Ct and Cs is greater and therefore Cs is the smallest penguin overall. Hence we need Gt - Cs which had been found above.

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