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.
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Source: Beat The GMAT — Data Sufficiency |
1) (x-2) (x-3) < 01) 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
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
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!!!)
(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!!!)
200 or 800. It don't matter no more.
Sorry, I should have provided my answer with more detail
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
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
so,(x-2)(x-3) has be negative and only way to get negative number is combinations of -number*+number,-number*+number not -*-,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 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
same thing applies, except that answer now has to be positive.2) 5x² - 25x > 0
(5x-25)(x)>0 meaning x<0 and x>5 sufficient,
provides 2<x<4 to be false
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
