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Data Sufficiency Structure :: length and width of rectangles

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Dear Leah (and other Official GMAC Representatives),

I hope I will have (again) the pleasure to count on GMAC´s authoritative definitive answer, for the benefit of myself, my students, other "GMAT Experts", their students, and the full BeatTheGMAT community!

The problem that "motivates" my question is the one below, presented in the Official Guide.
(I don´t know the year of the publication because it was posted by the BTG moderator. Link at the end of this post.)

------------------------------------------------------------------------------------------------------------
The perimeter of a rectangular garden is 360 ft. What is the length of the garden?

1) the length of the garden is twice the width
2) the difference between the length and width of the garden is 60 ft

Official Answer: D
------------------------------------------------------------------------------------------------------------


The issue is related to statement (2) ALONE, therefore let us focus on it, exclusively.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ARGUMENT 1:

Statement (2) is sufficient, because we may ALWAYS consider this statement as "equivalent" (meaning: exactly the same information contained) to the one below:

2b) the difference IN THAT ORDER between the length and width of the garden is 60 ft

Hence we MUST have L-W = 60, and using L+W = 180 (from the question stem pre-statements), we find a unique numerical value for L (the length of the garden).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ARGUMENT 2:

Statement (2) is sufficient, because we must ALWAYS consider the length of the rectangle as the greater dimension of the rectangle. (When we have a square, we understand "greater" as any of the two equal dimensions, of course.)

Hence we MUST have L-W = 60 (because W-L = 60 would imply W>L and this is ALWAYS impossible), and using L+W = 180 (from the question stem pre-statements) we find a unique numerical value for L (the length of the garden).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

To be absolutely sure that you (psychometricians inlcuded) are able to give us a definitive answer, I would like to propose a problem in which those two arguments DIVERGE, so that the official answer to this problem will close the case without any doubt...

Question:
The perimeter of a rectangular garden is 360 ft. What is the length of the garden?
1) the length of the garden is twice the width
2) the length and the width of the garden differ by 60 ft

If ARGUMENT 1 is correct, the answer is (A) , because statement (2) would translate to |L-W| = 60 and, consequently, two different possibilities are viable:
> Length = 120 and Width = 60 , answering 120 (feet)
> Length = 60 and Width = 120 , answering 60 (feet)

If ARGUMENT 2 is correct, the answer is (D), because statement (2) would translate to L-W = 60 (because W-L = 60 would imply W>L , impossible) and, consequently,
> Length = 120 and Width = 60 , answering 120 (feet)

The link for the original question and for many different points-of-view is the following:
https://www.beatthegmat.com/the-perimet ... 04164.html


Thank you very much for your support!

Regards,
Fabio Skilnik (GMATH).
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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fskilnik@GMATH wrote:
Sun Sep 16, 2018 11:16 am
Dear Leah (and other Official GMAC Representatives),

I hope I will have (again) the pleasure to count on GMAC´s authoritative definitive answer, for the benefit of myself, my students, other "GMAT Experts", their students, and the full BeatTheGMAT community!

The problem that "motivates" my question is the one below, presented in the Official Guide.
(I don´t know the year of the publication because it was posted site by the BTG moderator. Link at the end of this post.)

------------------------------------------------------------------------------------------------------------
The perimeter of a rectangular garden is 360 ft. What is the length of the garden?

1) the length of the garden is twice the width
2) the difference between the length and width of the garden is 60 ft

Official Answer: D
------------------------------------------------------------------------------------------------------------


The issue is related to statement (2) ALONE, therefore let us focus on it, exclusively.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ARGUMENT 1:

Statement (2) is sufficient, because we may ALWAYS consider this statement as "equivalent" (meaning: exactly the same information contained) to the one below:

2b) the difference IN THAT ORDER between the length and width of the garden is 60 ft

Hence we MUST have L-W = 60, and using L+W = 180 (from the question stem pre-statements), we find a unique numerical value for L (the length of the garden).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -


- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ARGUMENT 2:

Statement (2) is sufficient, because we must ALWAYS consider the length of the rectangle as the greater dimension of the rectangle. (When we have a square, we understand "greater" as any of the two equal dimensions, of course.)

Hence we MUST have L-W = 60 (because W-L = 60 would imply W>L and this is ALWAYS impossible), and using L+W = 180 (from the question stem pre-statements) we find a unique numerical value for L (the length of the garden).
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

To be absolutely sure that you (psychometricians inlcuded) are able to give us a definitive answer, I would like to propose a problem in which those two arguments DIVERGE, so that the official answer to this problem will close the case without any doubt...

Question:
The perimeter of a rectangular garden is 360 ft. What is the length of the garden?
1) the length of the garden is twice the width
2) the length and the width of the garden differ by 60 ft

If ARGUMENT 1 is correct, the answer is (A) , because statement (2) would translate to |L-W| = 60 and, consequently, two different possibilities are viable:
> Length = 120 and Width = 60 , answering 120 (feet)
> Length = 60 and Width = 120 , answering 60 (feet)

If ARGUMENT 2 is correct, the answer is (D), because statement (2) would translate to L-W = 60 (because W-L = 60 would imply W>L , impossible) and, consequently,
> Length = 120 and Width = 60 , answering 120 (feet)

The link for the original question and for many different points-of-view is the following:
the-perimeter-of-a-rectangular-garden-i ... 04164.html


Thank you very much for your support!

Regards,
Fabio Skilnik (GMATH).

Oh, that is exactly waht I was looking for, thank you!