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Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #15


The range of the heights of the female

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. Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the students in the class? Indicate all such statements. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class., 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.,The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.

4 Explanations



My interpretation of the answer was as follows,

At the onset, we can eliminate options B & C because they are talking about measures of central tendency. They don't give us concrete information on the absolute values of the data (which we need here).

Now, on to option A. It doesn't really matter whether the Shortest Male (Sm) has been drawn by Chris to be taller than the Shortest Female (Sf). Consider all 3 cases,

Case1 (Sf = Sm)
Sf .______.Tf

Case2 (Sf > Sm)

Case3 (Sf < Sm)
[The one drawn by Chris]

In any of those cases, we can see that the range for all the students can be calculated by incorporating information from option A.

Hope this helps! It is a tricky question!

Aug 22, 2019 • Comment

David Recine

Great additional breakdown, Saptarshi!

Aug 26, 2019 • Reply


Erfan Chowdhury

Why can't I see the video?

Sep 16, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Erfran,

I'm sorry to hear that you're having issues viewing the video explanation! Your browser might be forcing https, which prevents our embedded YouTube videos from properly loading. To get around this, just make sure your URL starts with "http" rather than "https". If that doesn't work, you may want to go to YouTube directly to watch the explanations :)

Hope this helps!

Sep 18, 2016 • Reply



Emphasizing on answer A. - I would use proportional lines here. Using L1 and L2 to represent the ranges of females and males.

Assuming, for starters,shortest female is equal in height to the shortest mail.
L1 |=============| -> Females
L2 |========|==== |===| -> Males
....|-----9.6---- |--3.6--|-2.2|

Considering option A.

Since Tallest Male - Tallest Female = 5.8 and the length 13.2 is same for Females and males, shifting the line for males such that the line is 5.8 ahead of line for females, following is the only possible position.

L1 |=============| -> Females
L2............|========|==== |===| -> Males
Thus A gives sufficient information to ascertain the range of both the sets combined.

Aug 10, 2013 • Comment

David Recine

That's a great visual to go with the lines in Chris's video. Thanks for sharing! :D

Aug 26, 2019 • Reply


Chris Lele

Oct 8, 2012 • Comment

bhavini jain

In option A, what if shortest person was male instead of female, the the range would be different as in equal to 15.4 only? so does getting 2 answers make an option correct?

May 29, 2017 • Reply

Cydney Seigerman, Magoosh Tutor

Hi Bhavini! Happy to help :) Initially, we're not told anything about the relationship between the shortest male and female. However, based on the information in (A), we see that the shortest person would be female in this case. There is only one way for the tallest male to be 5.8" taller than the tallest female, while the tallest female is 13.2" taller than the shortest female.

If we let f represents the shortest female, then

shortest male = f + 13.2 + 5.8 - 15.4 = f + 3.6
tallest female = f + 13.2
tallest male = f + 13.2 + 5.8 = f + 19

So, the range of heights of the entire class is 19.

I hope this helps :)

Jun 7, 2017 • Reply

Meera Gandhi

How does option A explain to us that the shortest girl is shorter than the shortest boy? I'm still not catching that...I understand what you did above, but I'm not understanding how you can tell from option A!

Feb 21, 2018 • Reply

Sam Kinsman

Hi Meera,

A good way to see how this works is to plug in some numbers. Let's say that the tallest woman in the class is 70 inches tall. (To keep things simple, we'll just use feet, and no inches).

A says that "the tallest male student in the class is 5.8 inches taller than the tallest female student in the class." This means that the tallest male student would be 70 + 5.8 = 75.8 inches tall.

We know that the range of the heights of the male students in the class is 15.4 inches, so the shortest male student is 75.8 - 15.4 = 60.4 inches tall.

Now let's think about the women again. The tallest female is 70 inches tall, and the range of the heights of the female students is 13.2 inches. So the shortest female is 70 - 13.2 = 56.8 inches tall.

So we can see that the shortest woman (56.8 in) is shorter than the shortest man (60.4 in).

You can try this with your own numbers - the result will always be that the shortest woman is shorter than the shortest man.

Mar 1, 2018 • Reply

Harshit Singh

If the shortest boy was shorter than the shortest girl then the range of height for boys would be something greater than (13.2+5.8 = 19),where as the range is clearly mentioned as 15.4

Jul 24, 2018 • Reply

David Recine

That's a good point, Tammy. Although it's arguably an unsupported assumption (and arguably sexist!), the GRE OG itself relies on the shortest female being shorter than the shortest male. This assumption is clearly used in ETS's own answer explanation on page 200 of the book.

Because that is ETS's assumption, we've made our own answer explanation accordingly.

But you're right-- in reality-- outside of the imaginary world of this problem-- it's distinctly possible that the shortest male would be smaller than the shortest female. Without an assumption to the contrary, (A) is actually insufficient.

Jul 25, 2018 • Reply

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