Inequalities

[oks]

Is 2 < x < 4?
1) x² - 5x + 6 < 0
2) 5x² - 25x > 0

OA is D.

Thanks.

[zenithexe]

hmm I think its E

1) x² - 5x + 6 < 0
(x-2)(x-3)<0 so x<2, or x<3
insufficient

2) 5x² - 25x > 0
(5x-25)(x)>0 so X>0 or X>5
insufficient?

I have no idea, please someone help ><

Edited:
I just realized, the answer is D,

1) x² - 5x + 6 < 0
(x-2)(x-3)<0 meaning that x>2 and x<3 sufficient
provides 2<x<4 to be true

2) 5x² - 25x > 0
(5x-25)(x)>0 meaning x<0 and x>5 sufficient,
provides 2<x<4 to be false

each clauses are capable of answering the question by itself.

[muna_m]

1) x² - 5x + 6 < 0
(x-2)(x-3)<0 meaning that x>2 and x<3 sufficient
provides 2<x<4 to be true

2) 5x² - 25x > 0
(5x-25)(x)>0 meaning x<0 and x>5 sufficient,
provides 2<x<4 to be false

1) (x-2) (x-3) < 0
How can you conclude x>2 and x<3? Why not x<2 and x>3?

Also, should 2) be x>0 and x>5 or x<0 and x<5 since 5x² - 25x > 0 i.e positive.

Please explain. Thanks

[yogami]

Hmmm..IMO its should be E
(1) Tells is that x < 2 OR x < 3 (because x^2 - 5x + 6 < 0 => (x -3)(x - 2) < 0
=> x is less than 3 or 2 but not both so insufficient
(2) Tells us that 5x^2 - 25 > 0 => x^2 - 5 > 0
=> (x + sqrt(5))(x - sqrt(5)) > 0
=> x < 2. something and x < -2.something
or x > 2.something and x > -2.something
so insufficient

OA explanation please (my math skills have gone awry after I took a two week break from GMAT!!!)

[zenithexe]

Sorry, I should have provided my answer with more detail

1) x² - 5x + 6 < 0
(x-2)(x-3)<0 meaning that x>2 and x<3 sufficient
provides 2<x<4 to be true

so,(x-2)(x-3) has be negative and only way to get negative number is combinations of -number*+number,-number*+number not -*-,

so us to have negative answer, x must be greater than 2,
eg. if x=2.1 ((2.1)-2)((2.1)-3)=(+0.1)(-0.9)=negative number, for any number above 2 but less than 3
ie, x=3.1 does not work ((3.1)-2)((3.1)-3)=positive number

if x=1.9, (1.9-2)(1.9-3)=(negative number)(negative number) an so forth for any number below 2,

so this provides that 2<x<3

2) 5x² - 25x > 0
(5x-25)(x)>0 meaning x<0 and x>5 sufficient,
provides 2<x<4 to be false

same thing applies, except that answer now has to be positive.
if x=-1, (5(-1)-25)(-1)=(negative)(negative)=positive
x=1, (5(1)-25)(1)=(negative)(positive)=negative
x=4, .... well you get he point.

I hope this explains. Thanks

[muna_m]

Ah! Thanks.. got it now