What is the value of x?

Question

(1)  (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0

(2)  x^2 + x -2 = 0

Kudos for a correct  solution .

mehrdadtaheri92 · Answer

Answer is A ....

DATA # 1) : ( x^2 + 3 ) ^2 - 11 ( x^2 +3 ) ^2 + 28=0

For making the equation simple, lets consider the whole term ( x^2 +3 ) ^2 to be T .

So plug -in this letter in the equation and we will have : T -11 T +28=0 Or 10 T =28 and then T = 28/10 = 14/5

so we have ( x ^2 + 3 ) ^2 = T = 14/5 and we have : x^2 + 3 = (14/5 ) ^(1/2) then : x^2 = (14/5) ^ (1/2 ) -3 and then : x = ( (14/5)^(1/2) - 3 ) ^ (1/2 ) !!!!! so this info

Gives us Only one valid value for x and is Sufficient .... NOTICE : IN GMAT ONLY positive ROOT of EVEN ROOT is accepted and negative root is not. so, this info is sufficient ...

DATA #2 ) : x ^2 + x -2 =0 or : ( x+2 ) (x-1 ) =0 OR X =-2 Or X=1 this data Gives us TWO possible value for X and is not Sufficient

1 sufficient , 2 NOT sufficient , so answer is A....

GauravSolanky · Answer

Have a doubt, in GMAT can we consider imaginary values for X ?

After solving like we did above we will have, x^2 + 3 = (14/5 ) ^(1/2). This will give you x^2 <0

14/5=2.8 and if we take root of this then it should give us value <1.7

so, x^2 +3 = 1.7 (taking approx. value)

This implies ,x^2 less than zero ?

Anyone, any thoughts over this ?

Thanks,
Gaurav

ENGRTOMBA2018 · Answer

GMAT always deals with Real numbers as written on the first page of the PS section in the official guide.

GauravSolanky · Answer

Thanks. Then, if we solve above we will get imaginary values for x. How come we can go for answer as A. Can you please explain that as well ? Thanks, Gaurav :-D

ENGRTOMBA2018 · Answer

The OA is E as statement 1 DOES NOT give you any real values and statement 1 gives you x=1 and x=-2. Thus even after combining you will get 2 values of x and hence E is the correct answer.

Here is the excerpt from Official Guide 2013 page 272 (this is the same note for both PS and DS) :  "Numbers: All numbers used are real numbers."

GauravSolanky · Answer

Oops..sorry, I overlooked it. Somehow, I had in mind that A is official answer. I was also expecting E as an answer. Thanks. :-D

Cheers, Gaurav

snowygari · Answer

Just wanted to check..
statement 1 gives x=+-2,+-1. right?

ENGRTOMBA2018 · Answer

No, statement 1 gives you no real solutions while statement 2 gives you x = 1 or -2.

samusa · Answer

On the GMAT all numbers are real numbers.

A gives us unreal solutions and B gives us two real solutions.

So, E .

However, I mistakenly chose A even though I noticed the tricky presentation in statement 1.

snowygari · Answer

oops.. got it.. calucation mistake

chesstitans · Answer

after realizing that each st1 cannot conclude the value of x, take values of x from st2 and put in equations in st1 => E

devanshu92 · Answer

1 ---> Taking (x^2+3)^2 common, we get the equation as : (x^2+3)^2 = 28/10. We cannot get value of x. Hence not sufficient.
2 ---> Solving, we get x=1 or x=-2. Hence, not sufficient.

(1) + (2) ---> Values from statement 2 does not satisfy 1. Hence, we cannot find value of x. Hence E.

shettytarun · Answer

Hi, Can you please clarify why you mention root cannot be negative - x^2 = (14/5) ^ (1/2 ) -3
root of 14/5 - this itself can be -ve or +ve right? I mean if 14/5 would have been 9 instead, when we take root of 9, we do consider +/- 3 as options
then we have to take the second root and again the same thing follows

Bunuel · Answer

When the GMAT provides the square root sign for an even root, such as  \sqrt{x}  or  \sqrt {x} , then the only accepted answer is the positive root.  Even roots have only a positive value on the GMAT.  That is,  \sqrt{25}=5 , NOT +5 or -5.

In contrast, the equation  x^2=25  has TWO solutions, +5 and -5.

OFFICIAL GUIDE:  
 \sqrt{n}  denotes  the positive number  whose square is n.

cledgard · Answer

This is  not  a valid GMAT DS question.

Statements 1 and 2  must be true , not contradictory.

It is clear that statement 2 gives us  x = 1  or   x = -2 , so it is not sufficient.
But the answer in 1 is neither of these answers, so the  problem is wrong as it is .

Choice E will tell us that using both statements together is insufficient; however, in this instance,   using both statements together is not that is insufficient, it is impossible.

Definitely, not a valid GMAT question.

However, This might be a misprint. I suppose that  (x^2 + 3)^2 - 11(x^2 + 3)^2 + 28 = 0  is wrong
-  11(x^2 + 3)^2  should be   11(x^2 + 3)  without squaring it.

In that case statement 1 would give us x = 1, x = -1, x = 2, and x = -2

Then the answer would be E

Bunuel · Answer

Yes, you are right. Edited the typo. (1) reads:  (x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0

thank you for noticing it.

Pi8 · Answer

Post the edit in the question,

Statement i suggests x = 2 or 1
Statement ii suggests x = -2 or 1

Shouldn't the answer be  C ? with x=1 being confirmed by both statements.

Bunuel · Answer

(x^2 + 3)^2 - 11(x^2 + 3) + 28 = 0 --> x = -2, -1, 1, or 2.
x^2 + x -2 = 0 --> x = -2, or 1.

So, when taken together x can be -2 or 1.

eswarchethu135 · Answer

(1)  (x^2+3)^2 − 11(x^2+3) + 28=0

Let  (x^2+3) = a

Now statement 1 can be written as  a^2 - 11a + 28 = 0

a^2 - 4a - 7a + 28 = 0 
 a(a-4) - 7(a-4) = 0 
 (a-7)(a-4) = 0 
a = 7 or 4

x^2+3  = 7 or 4
 x^2  = 4 or 1
x = 2, -2 or 1, -1

Clearly INSUFFICIENT

(2)  x^2 + x − 2 = 0

x^2 + 2x - x - 2 = 0 
 x(x+2) -1(x+2) = 0 
 (x-1)(x+2) = 0 
x = 1 or -2

Clearly INSUFFICIENT

Combining 1) + 2) Still x can be either of 1 and -2. So combining didn't work.

OPTION:  E

What is the value of x?

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