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# The range of the heights of the female students in a certain class is

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Math Expert
Joined: 02 Sep 2009
Posts: 60647
The range of the heights of the female students in a certain class is  [#permalink]

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10 Dec 2019, 05:40
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Difficulty:

65% (hard)

Question Stats:

47% (01:39) correct 53% (01:26) wrong based on 32 sessions

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The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches. What is the range of the heights of all the students in the class?

(1) The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
(2) The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.

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The range of the heights of the female students in a certain class is  [#permalink]

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15 Dec 2019, 02:47
Given:

Tallest girl - Shortest girl = 13.2
Tallest boy - Shortest boy = 15.4

To find:

Range of heights of all students

This could be

Tallest boy - Shortest boy, or
Tallest boy - Shortest girl, or
Tallest girl - Shortest boy, or
Tallest girl - Shortest girl

(1) The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.

This tells us that the Tallest boy is the tallest overall. So the overall range could be

Tallest boy - Shortest boy or Tallest boy - Shortest girl, whichever is greater

Tallest boy - Tallest girl = 5.8

So, Tallest boy - 5.8 - Shortest girl = 13.2

Tallest boy - Shortest girl = 19

And so the overall range is 19

1 is sufficient

(2) The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.

This gives us no idea about the tallest/shortest

2 is insufficient

The range of the heights of the female students in a certain class is   [#permalink] 15 Dec 2019, 02:47
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