If x^2+200x+9991=0, which of the following is a value of x?

Question

if  x^2+200x+9991=0 , which of the following is a value of x?

A. -87

B. -93

C. -101

D. -103

E. -107

chetan2u · Accepted Answer

The question can be done in following ways..
1) substitution -
substitute the choices and see what fits in
2) solve for x
 x^2+200x+9991=0...........x^2+200x=-9991........x(x+200)=-9991

Now it is all about finding factors.... But a bit of logic can help us solve it WAY faster

9991 is NOT a multiple of 3, so BOTH x and x+200 should not be a multiple of 3..

let us see

A. -87.....Multiple of 3....eliminate

B. -93....Multiple of 3....eliminate

C. -101......200-101=99....Multiple of 3....eliminate

D. -103......200-103=97 and 103 both are not multiple of 3, so OK

E. -107.........200-107=93.......Multiple of 3....eliminate

D

WizakoBaskar · Answer

The crux of solving this question is figuring out how to quickly factorise the equation by splitting the middle term. The numbers are not easy ones such as 5x or 4x.

But there is enough clue in the numbers.

We have to split 200 into two parts, say p and q. p + q = 200 and pq = 9991
The product pq will be maximum when p = q = 100. At that point pq = 10,000 which is more than 9991.
If we add a k to 100 to get p and subtract a k from 100 to get q, the sum will remain 200.

If we do that, we have to find (100 + k)(100 - k) = 9991.
i.e., 10,000 - k^2 = 9991 or k = 3.
So, the value of p and q are 103 and 97. Or the middle term is split as 103 and 97.

Now that we know that 200 splits as 103 and 97, the answer is (x + 103)(x + 97) = 0
So, values of x are -103 and -97

ScottTargetTestPrep · Answer

Notice that 9991 = 10,000 - 9. Because both 10,000 and 9 are perfect squares, we can re-express the difference of squares (10,000 - 9) as (100 - 3)(100 + 3) = (97)(103). So we have:

x^2 + 200x + 9991 = 0

(x + 97)(x + 103) = 0

x = -97 or x = -103

Answer: D

nick1816 · Answer

As all the options are integer, we can infer that both roots of quadratic equations are integers.

Hence, check for the option that is factor of 9991

Eliminate A and B right away, as 87 and 93 are divisible by 3, but 9991 is not.

99-91=8; hence, 9991 is not divisible by 101. Eliminate C

999+1*31=1030 is divisible 103. Hence, 9991 is divisible by 103.

D

Kinshook · Answer

9991 = 103*97
x^2 +103x + 97x + 9991 = 0
(x + 103)(x + 97) = 0
x = -103 or -97

IMO D

Roosh18 · Answer

A much easier way to solve this is

x^2 + 200x + 10,000 - 9 = 0 
x^2 + 100x + 100x + 10,000 - 9 =0 
x ( x+100) +100 ( x + 100) -9 =0
(x+100) ^2 - (3) ^2 = 0
applying A^2 - B ^2 formula,

( x+100+3) (x+100-3) =0
x= -103, -97.

adstudy · Answer

I did it in the following way. Method is a little time consuming but could only think of this while attempting -

x^2 +200x + 9991 = 0 
 x^2 +200x + 10000 - 9 = 0 
 (x^2 +100x + 100x + 10000) - 9 = 0 
   - 9 = 0 
 (x +100)^2 - 9 = 0 
 (x +100)^2 - 3^2 = 0 
 (x + 100 - 3)(x + 100 + 3) = 0  { Applying formula  =>  a^2 - b^2 = (a + b)(a - b) }
 (x + 103)(x + 97) = 0

So x = -97 or -103

Hence D

adityaprateek15 · Answer

Another way to solve this:

Use:  (-b ± √(b2 - 4ac)) / 2a

(-200 ± √40000 - 4*9991) / 2

We can save time on calculation,

9991*4 is (10000-9)*4 (Ignore 10000*4 as it will anyway be subtracted by 40000 above)

(-200 ± √36) / 2

-200±6/2 = -206/2 and -194/2

Roots are -103 and - 97

Option D

If x^2+200x+9991=0, which of the following is a value of x?

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GMAT Problem Solving (PS) Questions

If x^2+200x+9991=0, which of the following is a value of x?

Prep Toolkit

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More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards