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What is the value of x?

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What is the value of x? [#permalink] New post   05 Mar 2015, 09:31
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What is the value of x?


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

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



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Re: What is the value of x? [#permalink] New post   05 Mar 2015, 12:57
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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....
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Re: What is the value of x? [#permalink] New post   13 Aug 2015, 09:24
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
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Re: What is the value of x? [#permalink] New post   13 Aug 2015, 09:55
GauravSolanky wrote:
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.
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Re: What is the value of x? [#permalink] New post   13 Aug 2015, 19:43
Engr2012 wrote:
GauravSolanky wrote:
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 :-D
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Re: What is the value of x? [#permalink] New post   13 Aug 2015, 23:22
GauravSolanky wrote:
Engr2012 wrote:
GauravSolanky wrote:
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 :-D


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."
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Re: What is the value of x? [#permalink] New post   13 Aug 2015, 23:33
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
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Re: What is the value of x? [#permalink] New post   15 Aug 2015, 05:50
GauravSolanky wrote:
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





Just wanted to check..
statement 1 gives x=+-2,+-1. right?
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Re: What is the value of x? [#permalink] New post   Updated on: 16 Aug 2015, 06:55
snowygari wrote:

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


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

Originally posted by ENGRTOMBA2018 on 15 Aug 2015, 09:57.
Last edited by ENGRTOMBA2018 on 16 Aug 2015, 06:55, edited 1 time in total.
Edited the solution
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Re: What is the value of x? [#permalink] New post   16 Aug 2015, 06:38
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. :(
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Re: What is the value of x? [#permalink] New post   11 Dec 2015, 16:27
Engr2012 wrote:
snowygari wrote:

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


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



oops.. got it.. calucation mistake :(
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Re: What is the value of x? [#permalink] New post   22 Aug 2017, 17:34
after realizing that each st1 cannot conclude the value of x, take values of x from st2 and put in equations in st1 => E
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Re: What is the value of x? [#permalink] New post   23 Aug 2017, 06:15
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.
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Re: What is the value of x? [#permalink] New post   23 Aug 2017, 19:06
mehrdadtaheri92 wrote:
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....


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
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Re: What is the value of x? [#permalink] New post   23 Aug 2017, 23:42
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shettytarun wrote:
mehrdadtaheri92 wrote:
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....


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.
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What is the value of x? [#permalink] New post   Updated on: 31 Aug 2017, 09:11
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Bunuel wrote:
What is the value of x?

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



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

Originally posted by cledgard on 31 Aug 2017, 09:00.
Last edited by cledgard on 31 Aug 2017, 09:11, edited 1 time in total.
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Re: What is the value of x? [#permalink] New post   31 Aug 2017, 09:08
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cledgard wrote:
Bunuel wrote:
What is the value of x?

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



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.


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

thank you for noticing it.
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Re: What is the value of x? [#permalink] New post   01 Jan 2019, 03:32
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.
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Re: What is the value of x? [#permalink] New post   01 Jan 2019, 03:35
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Pi8 wrote:
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.


(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.
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Re: What is the value of x? [#permalink] New post   01 Jan 2019, 04:37
(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
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Re: What is the value of x? [#permalink]
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