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

Question

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.

Lampard42 · Answer

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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Archit3110 · Answer

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

rishabhshreyas14 · Answer

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

LeoN88 · Answer

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.
 rishabhshreyas14

Lampard42 · Answer

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.

rishabhshreyas14 · Answer

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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adroid015 · Answer

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.

Shishou · Answer

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

exc4libur · Answer

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)

Cuttlefish · Answer

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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Vivek1707 · Answer

Some key points to remember when dealing such range questions

When you are given the range of a data set, then by adding values i.e by increasing the size of the set you cannot reduce the range. You can only increase the range.

Eg if you have a set of values say  , now if you have to add another value say x to this set, there will be only 3 possibilties :

x will be a number which falls in between the highest and lowest values in the set. In that case the range wont change.
x will be equal to the highest or the lowest value in the set. In that case again the range wont change.
x will either be less than lowest value or higher than highest values. In this case the value of range will  INCREASE .

Now here when you know the distance between the highest value of a set of with a lower range and the highest value of the set with the higher range, it means that the overall distance between the highest value and the lowest value of both sets combined is fixed.

Example

1 _____________ 14.2__________20
 Lower range set ^^^^ ---> this distance is fixed i.e given as 5.8

Hence the range of the combined set would be 19. Hence A is sufficient

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

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

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