If x

Question

If  x\leq{2} , Which of the following is equal to  \sqrt{28x^2 - 112x + 112}

A.  2(x+2) \sqrt{7}

B.  -2\sqrt{7}(x-2)

C.  7(x-2)

D.  14(x-2)

E.  -2 \sqrt{(7x^2 + 28x+28)}

mysterymanrog · Answer

We can factor the equation as follows:
root(28x^2-112x+112)
root(28(x^2-4x+4x))
root(28(x-2)^2))
Take the root, we get:

2root(7)abs(x-2)

Note that (x-2)^2 does not become x-2, because you take its square - therefore it becomes the absolute value of it. 
Now, because abs(x-2) is not in the answer choice, it is required to figure out if the negative or positive case is taken. 
The stem states that x<=2. Therefore, we take the negative case (x-2<0 when x<2, and we can ignore 0 because its the same for both positive and negative case)

So it becomes 2root(7)-(x-2), or -2root(7)(x-2), which is the same as answer choice B.

gmatophobia · Answer

Note: The value of this expression will always be non negative as the expression is under root.

-112x + 112 jumps right off the page; at x = 1, the values will get cancelled out.

So we can take x = 1 as it is a valid value i.e. 1 falls within within the permissible boundary of x ( x\leq{2} )

At x = 1 ,  \sqrt{28x^2 - 112x + 112}

\sqrt{28}  = 5.XX (We don't need the exact value, so I will keep it as 5.XX)

Let's try to match the options and find out which options gives us a value of 5.XX

Answer choice elimination

I will start with the obvious eliminations first, notice option C , D and E yields us a negative value.

C.  7(x-2)

7 * -1 = -7 |   Eliminate

D.  14(x-2)

14 * -1 = -14 |   Eliminate

E.  -2 \sqrt{(7x^2 + 28x+28) }

-2 * positive value= negative value |   Eliminate

Let's look at A and B now

A.  2(x+2) \sqrt{7}

2(1+2) \sqrt{7}

6 \sqrt{7}  -- Definitely greater than 6, we need 5.XX |   Eliminate

B.  -2\sqrt{7}(x-2)

The only option left.

Option B

If you're extra curious

-2\sqrt{7}(x-2)

-2\sqrt{7}(1-2)

2\sqrt{7}

2 * 2.6

5.2

SaquibHGMATWhiz · Answer

Solution:

We are given that  x\leq 2  
 And  \sqrt{28x^2 - 112x + 112} 
 ⇒\sqrt{28(x^2-4x+4)} 
 ⇒\sqrt{28(x-2)^2} 
 ⇒2\sqrt{7}\sqrt{(x-2)^2} 
 ⇒\pm 2\sqrt{7}(x-2)  
 Since  x\le 2 ,  x-2\le 0  which means  x-2   has to be either 0 or negative  
 We can ignore  x-2=0  case because none of the options satisfy that
 ⇒-2\sqrt{7}(x-2)

Hence the right answer is    Option B

bumpbot · Answer

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If x <= 2, Which of the following is equal to (28x^2 - 112x + 112)

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