M23-24

Official Solution:


If the area of a rectangle is 80, what is the angle between the diagonal of the rectangle and its longer side?

Important piece of information that will help to solve this question:

In a “what is the value?” GMAT DS question, your primary goal is not to calculate the value, but to determine whether you can do so with the information provided. Therefore, obtaining a numerical answer is not always necessary for this type of question.

In a "yes/no” GMAT DS question, your primary goal is not to calculate a value, but to determine whether the information provided is sufficient to answer the question with a "yes" or "no" response. Therefore, obtaining a numerical answer is not always necessary for this type of question.

Let the length and width of the rectangle be \(a\) and \(b\), respectively. We are given that \(ab = 80\) and asked to find the angle between the diagonal of the rectangle and its longer side.

(1) The perimeter of the rectangle is 84.

This statement tells us that \(2(a + b) = 84\), or that \(a + b = 42\). We can solve the system of equations \(ab = 80\) and \(a + b = 42\) to get unique values of \(a\) and \(b\). This means that the rectangle is fixed at a unique configuration, and we can answer any question regarding that rectangle. Therefore, statement (1) is sufficient.

(2) The shorter side of the rectangle is 2.

This statement implies that the longer side is 40. Again, the rectangle is fixed at a unique configuration, and we can answer any question regarding that rectangle. Therefore, statement (2) is also sufficient.


Answer: D
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Hi All,

Must Known for GMAT,

IF YOU CAN DRAW THE FIGURE, IT MEANS THAT YOU KNOW ALL PROPERTIES

From Stem : \(width * length = 80\)

Statement 1 : \(width + length = 42\)

We have two equations, with two variables so we can solve and find the two sides : 40 and 2 ==> SUFFICIENT

Statement 2 : Shorter side is 2

So we have \(2 * length = 80\)
Therefore length = 40 and thus we can draw the figure and know all the angles. ==> SUFFICIENT

Answer D.

I think this is a high-quality question and I don't agree with the explanation. When we solve wstatement-1, we will get 2 values either (l,b) = (40,2) or (2,40), so accordingly angle will also be different. So, not sufficient. Answer must be option B. Kindly correct if I am wrong.

We need to find the angle between the diagonal of the rectangle and its longer side. So, it does not matter whether it's (40,2) or (2,40). In any case we should find the angle between the diagonal and the side of length 40.
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I like this Magoosh explanation in regards to determining the uniqueness of a triangle. In short, if we can determine unique values for SAS, SSS, and etc (see link for full list), then we can determine everything about a triangle since we are essentially breaking the problem down into two triangles.

https://magoosh.com/gmat/2012/gmat-data ... nce-rules/

Hi Bunuel chetan2u GMATinsight ,

I am way too confused with this one . Two doubts :

1. width and length can be some irrational or a rational (nowhere stated that the length or the width has to be an integer) , and can lead to area 80 and perimeter 84. We can't uniquely define the angle between the longer side and diagnol

2. for option B, we can make two diagrams

one--- with length as 2 and width as 40 ,,,, so the diagnol will make some angle with the width
two--- with width as 2 and length as 40 ,,,, so the diagnol will make some angle with the length

and in both the above cases we ll have a different angle to look for unless rectangle is a square, which is not the case here.

Please help
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If the area of a rectangle is 80, what is the angle between the diagonal of the rectangle and its longer side?


(1) The perimeter of the rectangle is 84

(2) The shorter side of the rectangle is 2


Area = l*b = 84

STatement 1: Perimeter, l+b = 84/2 = 42

i.e. We get a quadratic equation to get two values of l

but one of them will be l and other will be b so Unique Solution hence

SUFFICIENT

Statement 2: Shorter side = 2

i.e. b = 2 if l > b

i.e. l = 80/2 = 40

there will be a unique rectangle with sides 2 and 40 hence

SUFFICIENT

Answer: Option D

ShankSouljaBoi please make two figures and post here for statement B which are bothering you.
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I have edited the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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