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What is the value of x^3 2x^2 + 7?

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Bunuel
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What is the value of x^3 2x^2 + 7? [#permalink] New post   31 Jan 2016, 07:38
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A
B
C
D
E

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75% (hard)

Question Stats:

38% (01:55) correct 63% (01:43) wrong based on 16 sessions
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What is the value of x^3 − 2x^2 + 7?

(1) 3x^3 − x = 2
(2) x^5 = 1



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B
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   01 Feb 2016, 05:37
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of x^3 − 2x^2 + 7?

(1) 3x^3 − x = 2
(2) x^5 = 1


In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), 3x^3-x-2=0, (x-1)(3x^2+3x+2)=0 and 3x^2+3x+2>0 is always valid(discriminant=3^2-4*3*2<0). Thus, x=1 and the answer is unique and sufficient.
For 2), x=1, which is unique and sufficient.
Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   13 Feb 2016, 04:17
What is the value of x^3 − 2x^2 + 7?

(1) 3x^3 − x = 2
(2) x^5 = 1

Statement 1 : 3x^3 − x = 2
on simplifying this, we get (x-1)(3x^2+3x+2)=0 which gives either x=1 or some negative fractional value of x
if we put both values in given equation, we will get two different values, i.e., one is an integer and one is fraction => insuff

Statement 2 : x^5=1
this gives x=1 => sufficient
hence, answer is B.
PS : we can't assume ANYTHING in GMAT DS. That's the catch in statement 1.
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   19 Feb 2016, 12:35
Hi Bunuel, Kindly provide the solution.

BR//
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   20 Feb 2016, 21:24
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gandhigauravz wrote:
Hi Bunuel, Kindly provide the solution.

BR//


Hi,
I am sure Bunuel will put in his bit, but let me try to find a solution for it..

lets see the Q

Quote:
What is the value of x^3 − 2x^2 + 7?

(1) 3x^3 − x = 2
(2) x^5 = 1


What are we asked?


Value of x^3 − 2x^2 + 7..
this requires any of the two values as mentioned below..
1) A unique value of x..
2) value of x^3 − 2x^2 in form of another equation

Lets see if teh eq provide the info


(1) 3x^3 − x = 2
lets check this for the two requirements above:-
A) It is a polynomial of degree 3, so will have 3 values of x.
All three can be same if we have it in form (x-some numeric value)^3, but it is not the case here..
so NO UNIQUE VALUE OF x..
B) We cannot change 3x^3 − x to x^3 − 2x^2, by any mathematical operation..

So Insuff

(2) x^5 = 1
this gives us a unique value of x, x=1, so Suff

ans B
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   20 Feb 2016, 21:30
chetan2u wrote:
gandhigauravz wrote:
Hi Bunuel, Kindly provide the solution.

BR//


Hi,
I am sure Bunuel will put in his bit, but let me try to find a solution for it..

lets see the Q

Quote:
What is the value of x^3 − 2x^2 + 7?

(1) 3x^3 − x = 2
(2) x^5 = 1


What are we asked?


Value of x^3 − 2x^2 + 7..
this requires any of the two values as mentioned below..
1) A unique value of x..
2) value of x^3 − 2x^2 in form of another equation

Lets see if teh eq provide the info


(1) 3x^3 − x = 2
lets check this for the two requirements above:-
A) It is a polynomial of degree 3, so will have 3 values of x.
All three can be same if we have it in form (x-some numeric value)^3, but it is not the case here..
so NO UNIQUE VALUE OF x..
B) We cannot change 3x^3 − x to x^3 − 2x^2, by any mathematical operation..

So Insuff

(2) x^5 = 1
this gives us a unique value of x, x=1, so Suff

ans B


Question for you. Statement 1 polynomial gives you 1 real and 2 complex (imaginary) solutions. Dont you think as GMAT deals with only REAL solutions, you can consider that there is only 1 'usable' value of x in this question, making this statement sufficient? IMO, it is not as straightforward or simple as just mentioning that there will be 3 solutions for x without checking how many will be real.

Again, GMAC is never going to give such an ambiguous question.
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   20 Feb 2016, 21:41
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Engr2012 wrote:

Question for you. Statement 1 polynomial gives you 1 real and 2 complex (imaginary) solutions. Dont you think as GMAT deals with only REAL solutions, you can consider that there is only 1 'usable' value of x in this question, making this statement sufficient? IMO, it is not as straightforward or simple as just mentioning that there will be 3 solutions for x without checking how many will be real.

Again, GMAC is never going to give such an ambiguous question.


Hi,
you are absolutely correct on the part that we have 1 real and 2 unreal solution for the statement ONE..
So, you will be correct when you say that the probability of seeing a Q with unreal numbers is very low..
But you can always see these type of Qs with real solutions..



Also the purpose of the Q is to tell you " how to tackle these kind of problems?"..
A + sign turned to -ive or one odd term added would have been enough to make it a totally valid and good Q..
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   21 Feb 2016, 08:22
Dear Sir

I agree with you and the your way of solving the problem. However, the D is being showed as incorrect i.e. answer what we have found and the ans that system has generated are not the same.

Regards
kaustav
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   21 Feb 2016, 08:27
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KAUSTAV89 wrote:
Dear Sir

I agree with you and the your way of solving the problem. However, the D is being showed as incorrect i.e. answer what we have found and the ans that system has generated are not the same.

Regards
kaustav


Hi kaustav
are you saying D should have been the answer..
B is shown as answer..
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   21 Feb 2016, 08:30
Yeah, you got me right.

Option A is also sufficient. It is generating only one unique real value.
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Re: What is the value of x^3 2x^2 + 7? [#permalink] New post   21 Feb 2016, 09:07
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KAUSTAV89 wrote:
Yeah, you got me right.

Option A is also sufficient. It is generating only one unique real value.


Hi,
You are correct as Engr2012 too has observed...
As I have said taht the actual GMAT is not likely to test us on imaginary numbers...
you may have a part of equation factored as x^2+ 7=0 in real GMAT..
this will have imaginary solutions and can be set aside..
But in these terms is very rare

The intent of Q is to test you in knowing that 3x^3 − x = 2 is of order 3 and will have 3 roots..
and since this Q is unlikely from OG, the source may not have gone deep into what roots can be..

The Qs are made for average/above average guys, but to expect someone to spend >2 minutes on just one statement will not be the motive of GMAC.
If I may ask, how much time did you spend on finding roots of Eq in statement 1..



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Re: What is the value of x^3 2x^2 + 7? [#permalink]
21 Feb 2016, 09:07
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