A grid of light bulbs measures x bulbs by x bulbs, where x 2. If 4

Question

A grid of light bulbs measures x bulbs by x bulbs, where x > 2. If 4 light bulbs are illuminated at random, what is the probability, in terms of x, that the 4 bulbs form a 2 bulb by 2 square?

A.  \frac{4(x - 1)}{x^2}

B.  \frac{24(x - 1)}{x^2(x^2 - 2)(x^2 - 3)(x + 1)}

C.  \frac{24(x + 1)}{x^2(x^2 - 2)(x - 1)}

D.  \frac{4(x + 1)}{x^2(x^2 - 2)(x - 1)}

E.  \frac{4x - 1}{x^2(x^2 - 2)}

Lampard42 · Answer

Total Ways of selecting 4 bulbs from a grid of x*x bulbs = x^2C4 = x^2(x^2-1)(x^2-2)(x^2-3)/24 Now ways of selecting 4 continuous bulbs can be done in (x-1)^2 . SO probability = (x-1)(x-1)*24/(x^2(x-1)(x+1)(x^2-2)(x^2-3)) =24(x-1)/(x^2(x+1)(x^2-2)(x^2-3) IMO Option B

Archit3110 · Answer

GMATinsight  ; sir could you please help in providing solution to this probability question ..

GMATinsight · Answer

Let, we have a grid of 3x3 i.e. x = 3 (where a, b, c... etc are the bulbs)

a . b . c

d . e . f

g . h . i

Now, 2x2 grids that are available in 3x3 grid = 4
Grid 1: abde
Grid 2: degh
Grid 3: bcef
Grid 4: efhi

So the probability = 4 / 9C4 = 4/126 = 2/63

Check options

Answer: Option B

Alternatively

The 2x2 grids in x*x grid = ((x-1)*(x-1)

Total ways of picking 4 bulbs out of  x^2  =  x^2 C4

Required probability =  (x-1)^2  /  x^2 C4

Answer: Option B

Archit3110

Saransh123 · Answer

I am having a headache just by reading this question

Posted from my mobile device

GMATinsight · Answer

Saransh123 You read the question is the first step towards improvement.

So headache or no headache, now you should read the explanation as well. I have given two explanations here and first one is soooo simple. check it out. Two MUST join YouTube channels for GMAT aspirant GMATinsight (1000+ FREE Videos) and GMATclub

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Contropositive · Answer

Hi  GMATinsight  , Why haven't you considered ''DBFH'' combination? That too is a possibility, right?

Regor60 · Answer

Yes.

And if you consider a 4×4 set of lights the additional squares are at least 4 beyond that implied by the answer.

This question is faulty.

Posted from my mobile device

Regor60 · Answer

This forum is going to lose its legitimacy if moderators continue to delete without explanation or correction reports on faulty posts.

Posted from my mobile device

rmahe11 · Answer

Is this really even a GMAT question ?

A grid of light bulbs measures x bulbs by x bulbs, where x > 2. If 4

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