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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....

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

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

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

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." _________________

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.

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....

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

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....

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

When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), 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.
_________________

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
_________________

Clipper Ledgard GMAT Coach

Last edited by cledgard on 31 Aug 2017, 09:11, edited 1 time in total.

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.

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

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