The figure above represents a rectangular tile. The 8 hexago

Question

hexagon.jpg The figure above represents a rectangular tile. The 8 hexagons in the design are equilateral and equiangular. what is the area of the tile? (1) w = 5 inch (2) l = 3*(root 3) inch

arpanpatnaik · Answer

A wonderful graphical question!

Great job summer101!

The answer is . To find the area of the hexagonal region, clearly, one has to find the area of the individual hexagonal space. Now, for that one can divide the hexagon into a square and 2 isosclenes traingles. We know that the hexagon has an internal angle of 120 degrees. Hence the isosclenes traingle would have 30 degrees as its other angles. Hence, the total lenght and width can be expressed in terms of the hieght and the width/length of the smaller sqaure in such a way. Let x be the length and width of the inner square. l and w be the lenght of the bigger rectangle. h be the altitude of the isosclenes traingle. l = 3x and w = 4h + 3x. Now from angles of a traingle property, h = x*sine 30 = x/2 hence w = 2x + 3x= 5x. Hence, as per Statement 1 , w = 5 = 5x, x = 1. and Statement 2 , l = 3*(root 3 ) = 3x , x = root 3. Area of the hexagon = Area of the rectangle + 2*Area of the isosclenes traingle = x*x + x*x/2 = 3x*x/2 Hence from either of the statements the value of the area can be obtained! Hence, . Regards, A

fozzzy · Answer

Can someone provide an alternate explanation...

What would be the difficulty level of this question? Do we need to know sine 30 etc

jellybean23 · Answer

Ya...Can someone please provide an alternate explanation to this question??????? :roll:

KarishmaB · Answer

No, you don't need to know anything. It's a ten second question. All you need to know is that a regular hexagon is a symmetrical figure. All sides are equal and the internal angle is 120 degrees. So if you give me the length of any side of the hexagon, I can find any other related length of that hexagon. Ques3.jpg Given the length of AB, I can tell you the length of AC and BE. How is not important. Important is that AC and BE will have a fixed length once the length of AB is fixed. We know the angles and we can easily use trigonometry to get the other lengths. I first look at statement 2 because it feels easier to incorporate due to the symmetry. The length 'l' is made up of three AC kind of lengths. Look at the green line in bold. Knowing AC, I can get AB and BE. We can represent AB and BE in terms of AC. w is made up of BE + AB + BE (look at the bold red line in the fig below) hexagon.jpg So knowing the value of l, I can easily get w. Since we will have both l and w, we will easily get the area of the tile. Similarly, if we know w, we can get l. We will represent w as BE + AB + BE where both BE and AB can be written in terms of AC. So we will get AC. Hence each statement alone is sufficient. Remember, you need to understand that you CAN find l and w given one of them. You don't actually need to find them. This is a DS question.

fozzzy · Answer

Great Explanation but I don't think its a ten second question. The Stats for this question seem to say otherwise.

mau5 · Answer

I agree it should not take more than 10-15 secs,only if one understands that one has to find out if the given data is SUFFICIENT or NOT, and not actually calculate for anything.

Once this fact sinks in, this problem is more like a thought-experiment. It is like giving a convoluted question where the actual calculation is very cumbersome, but the hunt for finding whether the given data is Sufficient or not is easier.

For eg, there is this unique question from GMATPrep :

If p is a prime number greater than 2, what is the value of p ?

(1) There are a total of 100 prime numbers between 1 and p+1

(2) There are a total of p prime numbers between 1 and 3912

Give yourself some time and find out how much time you will actually take to  Solve  as compared to how much time you will take to find out whether the given  data is Sufficient.

KarishmaB · Answer

That's the fun of being thorough with your concepts fozzzy - where others would take 2 mins or more, you could get done in 10 secs because you really do understand. It doesn't take any time at all to figure out that the data is sufficient. Though the language of the question was a little suspect but I assumed they meant to say that the hexagons are regular and identical. Then it was only about seeing that one side is available which would mean that everything else can be figured out. Getting the actual value of area would obviously take more time.

Also, the time people take on average to solve a particular question will often be more than the time one might take if one is very clear in one's head. Yet another thing, the time taken to solve the question is usually related but not proportional to the difficulty level of the question. A 700+ level question could be solved in a few seconds if it is conceptual and doesn't involve much work. It could still be hard for most people because of the concept involved.

Bluefalkon · Answer

it is a simple question..using equilateral hexagon property, if given any one side of rectangle, we would b able to find the shaded area

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The figure above represents a rectangular tile. The 8 hexagons in the design are equilateral and equiangular. what is the area of the tile?

(1) w = 5 inch
(2) l = 3*(root 3) inch
 
In a regular n-polygon, there is one variable, and 2 equations are given by the conditions, so there is high chance (D) will be the answer.
For condition 1, if we let one side of the regular hexagon by 2a, 10a=5, and a=1/2. The condition is sufficient.
For condition 2, 6root(3)a=3root3, a=1/2, and is sufficient for the same reason.
The answer therefore becomes (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

BillyZ · Answer

Height, h = (\sqrt{3})s 
 Diagonal, d = 2s 
 Area, a = (1.5\sqrt{3}) s^{2} 
 Perimeter, p = 6s

fozzzy  &  jellybean23  Therefore, if it is given any side of the hexagon, it is able to solve the area of tile.

Answer : D

The figure above represents a rectangular tile. The 8 hexago

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GMAT Data Sufficiency (DS) Questions

The figure above represents a rectangular tile. The 8 hexago

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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