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# m22#3

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26 Nov 2008, 18:54
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What is the value of $$x$$ ?

1. $$x^4 = |x|$$
2. $$x^2 \gt x$$

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions
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26 Nov 2008, 20:49
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ventivish wrote:
What is the value of $$x$$ ?

1. $$x^4 = |x|$$
2. $$x^2 \gt x$$

1: x = -1 or 0 or 1.

i. if x is +ve,
x^4 = x
x^4 - x = 0
x (x^3 - 1) = 0
x = 0, and x^3 = 1 or x = 1.

ii: if x is -ve,
x^4 = -x
x^4 + x = 0
x (x^3 + 1) = 0
x = 0, and x^3 = -1 or x = -1.
so not suff...

2: x could be anything other than 0 and a +ve fraction.

x^2 > x
x^2 - x > 0
x (x-1) > 0
if x is a +ve (x-1) is also a +ve.
i: x > 0 .......... not possible.

ii: x - 1 > 0
x >1 ............... possible.
so x > 1.

if x is a -ve (x-1) is also a -ve.
i: x < 0 .............. possible.

ii: x < 1 ............... not possible.
so x <0.

1&2: x has to be -1.
so C.
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10 Jan 2013, 05:03
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ventivish wrote:
What is the value of $$x$$ ?

1. $$x^4 = |x|$$
2. $$x^2 \gt x$$

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

What is the value of $$x$$ ?

(1) $$x^4 = |x|$$. This statement implies that $$x=-1$$, $$x=0$$, or $$x=1$$. Not sufficient.

(2) $$x^2> x$$. Rearrange and factor out $$x$$ to get $$x(x-1)>0$$. The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$. Not sufficient.

(1)+(2) The only value of $$x$$ from (1) which is in the range from (2) is $$x=-1$$. Sufficient.

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13 Mar 2010, 16:12
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When combine both the stmt, we get x = -1, so IMO Ans should be C.
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06 Jan 2011, 09:39
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C

From option A, x can be 0 or 1 or -1.
From option B , x can be any negative integer. And it can be any negative fraction value.

Using both we can deduce x value as -1.

Hence the option is c.
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20 Apr 2014, 02:02
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(1) x can be 0, 1 or -1 -> insufficient
(2) clearly insufficient
Combine 2 stats => x=-1 -> sufficient

Choose C
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30 Dec 2009, 05:56
The graphs of y=x^4 and y=|x| 1ntersect each other at three points (-1,1), (0,0) and (1,1), then A is wrong. Any x<0 or x>1 satisfies the inequality x^2>x, then B is wrong.
Both statements together uniquely determine the value x=-1, so C is the answer.

Last edited by nvgroshar on 31 Dec 2009, 14:21, edited 1 time in total.
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30 Dec 2009, 20:01
ANS:E from both statement we can conclude only x>1 not a single value.
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30 Dec 2009, 21:52
It should be C. I thought it E though
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01 Jan 2010, 06:29
1 is not sufficient - x could be 0 or 1, -1
2 X^2>X which means x(x-1)>0 x>1 or x<0

Combine 1 and 2, x=-1
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19 Mar 2010, 07:13
ventivish wrote:
What is the value of $$x$$ ?

1. $$x^4 = |x|$$
2. $$x^2 \gt x$$

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

stmt1L x^4 = x or x^4 = -x
x(x^3-1)=0 or x(x^3+1) =0
so x = 0, -1,1

stmt2: x^2 > x => x(x-1)>0 insuff
combine both. x <>0 or 1 so x is -1
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06 Jan 2011, 08:39
What is the value of x ?

1. x^4 = |x|

X can equal 1 or -1 or 0 (IS)

2. x^2 > x

x(x-1)>0 (IS)

Both: You can conclude that X is -1 using st.2 to validate it.
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06 Jan 2011, 09:42
x= -1,
excellent explanation were given above.
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18 Feb 2011, 00:24
I concur with the OA.

Stmt 1 tells you it is +1 or -1
Stmt 2 tells you it is an integer

Combining the two stmts you can tell that the only possible fit is -1. Therefore, it is C.
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14 Apr 2011, 17:05
1. Not sufficient
When x is +ve x = 1
When x is -ve x = -1

2. Not sufficient
x<0 or x>1

together we have x = -1. Sufficient.

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14 Apr 2011, 21:49
ventivish wrote:
What is the value of $$x$$ ?

1. $$x^4 = |x|$$
2. $$x^2 \gt x$$

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

This one is interesting as the answer is different if you do not know that its a GMAT question.

From statement 1, on squaring both sides we get $$x^8 = x^2$$
or $$x^2*(x^6-1) = 0$$

so, $$x = 0$$ or $$x^6 = 1$$.

Now $$x^6 = 1$$ has six roots and the six sixth roots of unity are ±1, and (±1 ± i√3)/2.

My confusion arose because i considered the complex roots as well and hence my initial reaction was that answer is E.

I guess on GMAT you can go along with only real roots and in that case, answer is indeed C.
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11 Jan 2013, 00:14
Answer C (by taking option 1+ 2).
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21 Feb 2013, 06:08
Bunuel wrote:
ventivish wrote:
What is the value of $$x$$ ?

1. $$x^4 = |x|$$
2. $$x^2 \gt x$$

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

What is the value of $$x$$ ?

(1) $$x^4 = |x|$$. This statement implies that $$x=-1$$, $$x=0$$, or $$x=1$$. Not sufficient.

(2) $$x^2> x$$. Rearrange and factor out $$x$$ to get $$x(x-1)>0$$. The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$. Not sufficient.

(1)+(2) The only value of $$x$$ from (1) which is in the range from (2) is $$x=-1$$. Sufficient.

Bunuel/Karishma
I dont understand the following:

The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$.

shouldn't $$x(x-1)>0$$ mean that x>0 or (x-1)>0 ?
Please explain why it means x<0 ?
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21 Feb 2013, 06:19
Sachin9 wrote:
Bunuel wrote:
ventivish wrote:
What is the value of $$x$$ ?

1. $$x^4 = |x|$$
2. $$x^2 \gt x$$

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

What is the value of $$x$$ ?

(1) $$x^4 = |x|$$. This statement implies that $$x=-1$$, $$x=0$$, or $$x=1$$. Not sufficient.

(2) $$x^2> x$$. Rearrange and factor out $$x$$ to get $$x(x-1)>0$$. The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$. Not sufficient.

(1)+(2) The only value of $$x$$ from (1) which is in the range from (2) is $$x=-1$$. Sufficient.

Bunuel/Karishma
I dont understand the following:

The roots are $$x=0$$ and $$x=1$$, "$$>$$" sign means that the given inequality holds true for: $$x<0$$ and $$x>1$$.

shouldn't $$x(x-1)>0$$ mean that x>0 or (x-1)>0 ?
Please explain why it means x<0 ?

Check here:
x2-4x-94661.html#p731476,
inequalities-trick-91482.html,
everything-is-less-than-zero-108884.html?hilit=extreme#p868863,
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06 Jan 2014, 05:26
OA-C since neither condition 1 nor 2 satisfies the Q to solve x.

Thanks

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# m22#3

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