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Math Expert V
Joined: 02 Sep 2009
Posts: 56277
What is the value of x^3?  [#permalink]

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5 00:00

Difficulty:   5% (low)

Question Stats: 91% (00:30) correct 9% (00:29) wrong based on 381 sessions

### HideShow timer Statistics What is the value of x^3?

(1) |x|=2
(2) 5x+6=16

Kudos for correct solution.

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Director  D
Joined: 05 Mar 2015
Posts: 992
Re: What is the value of x^3?  [#permalink]

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4
Bunuel wrote:
What is the value of x^3?

(1) |x|=2
(2) 5x+6=16

Kudos for correct solution.

(1) IXI=2
x=2,-2
so X^3=8,-8
not sufff..
(2) 5X+6=16

x=2
so X^3=8 suff.
Ans B
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7599
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the value of x^3?  [#permalink]

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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?

(1) |x|=2
(2) 5x+6=16

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), x^3=-8,8 is derived from x=-2,2, which is not unique and not sufficient.
For 2), 5x=10, x=3, x^3=8 is derived, which is unique and sufficient.

 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?  [#permalink]

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1
Here the concept tested is one property of even and odd powers
Even powers will result in a +ve sign always
ODD powers will have the same sign of the variable. So for ODD powers it is must to know the sign of variable
S1 : +2 or -2 ( sign not fixed)
S2 = sign and value both are confirmed
So B
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Joined: 26 Mar 2013
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Re: What is the value of x^3?  [#permalink]

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(1) |x|=2..........> X=2, X^3=8 or X=-2, X^3=-8 Ins

(2) 5x+6=16.....> X=2, X^3=8 Suf

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Re: What is the value of x^3?  [#permalink]

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2
(1) IXI=2
x=2,-2
so X^3=8,-8
not sufff..
(2) 5X+6=16

x=2
so X^3=8 suff.
Ans B . WE KNOW THAT MODS CAN BE POSITIVE OR NEGATIVE , SO WE CANT GET UNIQUE VALUES.
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Thanks Senior Manager  G
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Posts: 496
Location: United States (LA)
Re: What is the value of x^3?  [#permalink]

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1
Statement 1 states |x|=2 which means that x can be either +2 or -2 so clearly insufficient as we would get 2 values of $$x^3$$
Statement 2 states 5x+6=16 which can simplified as 5x = 10 which gives x = 2 so we get a definite value of $$x^3$$ which is $$2^3$$ = $$8$$
so sufficient
Senior Manager  Joined: 18 Jan 2010
Posts: 251
Re: What is the value of x^3?  [#permalink]

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1
Bunuel wrote:
What is the value of x^3?

(1) |x|=2
(2) 5x+6=16

Kudos for correct solution.

Statement 1

x = 2 or x = -2. Value of $$x^3$$ will be different in both cases. Not sufficient.

Statement 2

5x+6=16; 5x = 10; x = 2. We can get a unique value of $$x^3$$ from this. Sufficient.

Current Student S
Joined: 26 Jun 2014
Posts: 78
Re: What is the value of x^3?  [#permalink]

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MathRevolution wrote:
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?

(1) |x|=2
(2) 5x+6=16

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), x^3=-8,8 is derived from x=-2,2, which is not unique and not sufficient.
For 2), 5x=10, x=3, x^3=8 is derived, which is unique and sufficient.

 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.

Thanks for sharing. But how is ti different from the conventional method?
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Re: What is the value of x^3?  [#permalink]

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Bunuel wrote:
What is the value of x^3?

(1) |x|=2
(2) 5x+6=16

Kudos for correct solution.

Statement 1. |x|=2 , x can be either -2 or 2.
Therefore x^3 can have two values, 8 or -8.
Hence insufficient.

Statement 2.
Solving 5x +6 =16 will yield only one value of X
Therefore statement two is sufficient.

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Re: What is the value of x^3?  [#permalink]

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Bunuel wrote:
What is the value of x^3?

(1) |x|=2
(2) 5x+6=16

Kudos for correct solution.

Question: x^3 = ?

St 1: |x|=2

means x = 2 or -2, then x^3 will be 8 or -3. Insufficient

Even power always results in positive

Odd power holds the original sign of the variable.

St 2: 5x+6=16

x = 2

X^3 = 8

Sufficient

(B)
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Intern  B
Joined: 21 Nov 2016
Posts: 39
Re: What is the value of x^3?  [#permalink]

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We need to find the value of x^3
We are given as per statement 1 lxl = 2
Which means that x = +2 or -2 , then x^3 would be equal to either -8 or 8.
So insufficient.
As per statement which is a linear equation in one variable...
5x+6 = 16
5x = 10
x = 2 .
So, since we get an unique value, Statement 2 is sufficient. Answer B. Re: What is the value of x^3?   [#permalink] 17 Mar 2019, 20:23
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