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# Is x greater than 3?

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Intern
Joined: 21 Jan 2019
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Is x greater than 3?  [#permalink]

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24 Feb 2019, 00:15
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35% (medium)

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63% (01:20) correct 37% (01:22) wrong based on 54 sessions

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Is x > 3?

1) x >0
2) $$\sqrt{x^{3}-9x+4}$$>2
Manager
Joined: 10 Apr 2018
Posts: 223
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 680 Q48 V34
GPA: 3.3
Is x greater than 3?  [#permalink]

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Updated on: 10 Oct 2019, 02:37
1
1
Objective: To find if x>3

From statement 1) we know that x>0, but from this we can't say whether or not x>3. So option A and D can be eliminated.

From statement 2) we get:
x^3-9x+4>2^2
x^3-9x+4>4
=> x^3-9x>0
=> x(x+3)(x-3)>0, so from this we can't say whether x>3 or not as x>3 and -3<x<0 are both valid solutions, so option B and D can be eliminated.

Combining statement 1) and 2), we get:
x>0 and x>3 or -3<x<0
Thus, we can say that x>3, so option C is the correct option.

Originally posted by iamsiddharthkapoor on 24 Feb 2019, 00:43.
Last edited by iamsiddharthkapoor on 10 Oct 2019, 02:37, edited 6 times in total.
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Is x greater than 3?  [#permalink]

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Updated on: 24 Feb 2019, 00:47

1. x> 0 no sufficent
2. if we square both side ,

we get x^3-9x+4 > 4
=> x^3-9x>4
x(x^2 -9)>0
x(x-3)(x+3) >0

Not sufficent .

If we combine both,

we get x>0 , it means , x-3 should be greater than 0 or x >3

So answer is C . Both are sufficient.

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Originally posted by kumarankit01 on 24 Feb 2019, 00:46.
Last edited by kumarankit01 on 24 Feb 2019, 00:47, edited 1 time in total.
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Re: Is x greater than 3?  [#permalink]

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24 Feb 2019, 00:46
statement 1: x >0
x can be 2 or 10 , so clearly insufficient

statement 2: $$\sqrt{x^{3}-9x+4}$$ > $$2$$
$$x^{3}-9x+4$$ > $$4$$
$$x^{3}-9x$$ > $$0$$
$$x(x^{2}-9)$$ > $$0$$
$$x(x-3)(x+3)$$ > $$0$$
so we have two valid intervals: $$x$$ > $$3$$ and $$0$$ > $$x$$ > $$-3$$ . since one of them is $$> 3$$ and the other is $$< 3$$, so insufficient

by combining 1 and 2:
knowing $$x$$ > $$0$$ excludes the interval $$0$$ > $$x$$ > $$-3$$, so left with the other interval $$x$$ > $$3$$, so sufficient
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Re: Is x greater than 3?  [#permalink]

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24 Feb 2019, 01:28
Question for managing time: how did you all get -3<x<0 quickly enough? were you able to test values within the time limit or did you surmise from the shape of a cubic graph?
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Is x greater than 3?  [#permalink]

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24 Feb 2019, 01:53
1
sfoo wrote:
Question for managing time: how did you all get -3<x<0 quickly enough? were you able to test values within the time limit or did you surmise from the shape of a cubic graph?

Hi sfoo . the answer is "by speed drawing"

step 1 : find key points of the equation
in our case, the equation is $$x(x-3)(x+3)$$ > $$0$$
so the points are 0,3,-3

step 2: draw them on a straight light in ascending order
so you will have : -----------------------(-3)------------(0)----------(3)-------------

step 3: draw a parabolic line "like an "S" (wavy line starting with the biggest number, starting from the positive side (because x has positive sign beside it))

step 4: since the inequality is asking for intervals > 0, so we take the intervals above the straight line.

note: beware of the inequalities whether it is > or >=

try plugging in different equations in this plot to get sense of how things work: http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ--
Attachments

Untitled.png [ 3.01 KiB | Viewed 495 times ]

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Is x greater than 3?  [#permalink]

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24 Feb 2019, 02:15
1
sfoo wrote:
Question for managing time: how did you all get -3<x<0 quickly enough? were you able to test values within the time limit or did you surmise from the shape of a cubic graph?

Check out the below link to learn how to quickly find solutions for such inequalities:

https://gmatclub.com/forum/wavy-line-me ... 24319.html
Is x greater than 3?   [#permalink] 24 Feb 2019, 02:15
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