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# Is 2 < x < 4? (1) x^2 – 5x + 6 < 0 (2) 3x^2 – 9x < 0

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Math Expert
Joined: 02 Sep 2009
Posts: 60625
Is 2 < x < 4? (1) x^2 – 5x + 6 < 0 (2) 3x^2 – 9x < 0  [#permalink]

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19 Nov 2019, 01:53
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Difficulty:

45% (medium)

Question Stats:

56% (01:36) correct 44% (02:04) wrong based on 27 sessions

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Is $$2 < x < 4$$?

(1) $$x^2 – 5x + 6 < 0$$

(2) $$3x^2 – 9x < 0$$

Are You Up For the Challenge: 700 Level Questions

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Joined: 02 Aug 2009
Posts: 8335
Re: Is 2 < x < 4? (1) x^2 – 5x + 6 < 0 (2) 3x^2 – 9x < 0  [#permalink]

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19 Nov 2019, 03:11
1
Bunuel wrote:
Is $$2 < x < 4$$?

(1) $$x^2 – 5x + 6 < 0$$

(2) $$3x^2 – 9x < 0$$

Are You Up For the Challenge: 700 Level Questions

(1) $$x^2 – 5x + 6 < 0.......x^2-3x-2x+6<0......(x-3)(x-2)<0$$....This means 2<x<3.....YES, 2<x<4.

(2) $$3x^2 – 9x < 0.......3x(x-3)<0$$. This means 0<x<3. x can be 1, then NO or x can be 2.5, then YES.

A
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Re: Is 2 < x < 4? (1) x^2 – 5x + 6 < 0 (2) 3x^2 – 9x < 0  [#permalink]

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19 Nov 2019, 03:40
chetan2u, Sir , I face difficulties in combining range in factorization . Would u pls show effective technique to deal with combination of range , specially in inequality . Thanks .
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Re: Is 2 < x < 4? (1) x^2 – 5x + 6 < 0 (2) 3x^2 – 9x < 0  [#permalink]

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20 Nov 2019, 09:28
1
Bunuel wrote:
Is $$2 < x < 4$$?

(1) $$x^2 – 5x + 6 < 0$$
(2) $$3x^2 – 9x < 0$$

(1) $$x^2 – 5x + 6 < 0$$ sufic

$$x^2 – 5x + 6 < 0…(x-3)(x-2)<0…(less.than=inside.rng)…2<x<3$$

(2) $$3x^2 – 9x < 0$$ insufic

$$3x^2 – 9x < 0…x^2-3x<0…x(x-3)<0…(less.than=inside.rng)…0<x<3$$

Ans (A)
Re: Is 2 < x < 4? (1) x^2 – 5x + 6 < 0 (2) 3x^2 – 9x < 0   [#permalink] 20 Nov 2019, 09:28
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