Data Sufficiency

Hi all,

Is 2<x<4?

1) x"2-5x+6<0
2)5x"2-25x>0

The answer is D which means both are sufficient...I don't understand why 2 is enough.

Thank you.

Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D

[email protected] wrote:Hi all,

Is 2<x<4?

1) x"2-5x+6<0
2)5x"2-25x>0

The answer is D which means both are sufficient...I don't understand why 2 is enough.

Thank you.

What is the source? Findings from the two statements would never contradict on real GMAT.

liferocks wrote:Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D

i do not get your answer, correct me if i am wrong please but:

statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!

from the statements above it's hard to tell if x is between 2 and 4 (i.e. 2<x<4).

i think the asnwer is (E)

[email protected] wrote: statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!

these two inferences are in correct.
(x-3)(x-2) < 0 range of values of x is 2<x<3 for any other value the inequality will not satisfy.You can pickup any value and check

Similarly if 5x(x-5) > 0 range of values of x is x<0 and x>5..any value from 0 to 5 will not satisfy the inequality.you can pickup any value and verify this.

[email protected] wrote:

liferocks wrote:Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D

i do not get your answer, correct me if i am wrong please but:

statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!

from the statements above it's hard to tell if x is between 2 and 4 (i.e. 2<x<4).

i think the asnwer is (E)

(x-3)(x-2) < 0===> if x-3<0 then x-2>0 or if x-2<0 then x-3>0 an invalid condition===> 2<x<3 the only condition will satisfy the inequality

thephoenix wrote:

[email protected] wrote:

liferocks wrote:Here we are looking for a yes/no for question Is 2<x<4
From 1
(x-2)(x-3)<0
so 2<x<3...

hence ans for Is 2<x<4--yes

From 2

5x(x-5)>0
or x(x-5)>0

so x and x-5 should have same sign .Hence the values of x which will satisfy this are x<0 and x>5

so x cannot have a value between 2 and 4

hence ans for Is 2<x<4--no

since we can definitely give an answer for 'Is 2<x<4? ' from both statements independently

Ans is option D

i do not get your answer, correct me if i am wrong please but:

statement 1: x^2-5x+6 < 0 => (x-3)(x-2) < 0 => x<3 or x<2 ... this is insuffient, isn't it?

statement 2: 5X^2-25X > 0 => 5x(x-5) > 0 => x>0 or x>5 ... this is insufficient!

from the statements above it's hard to tell if x is between 2 and 4 (i.e. 2<x<4).

i think the asnwer is (E)

(x-3)(x-2) < 0===> if x-3<0 then x-2>0 or if x-2<0 then x-3>0 an invalid condition===> 2<x<3 the only condition will satisfy the inequality

:

i still do not get it but it's fine. thanks.

Thank you everyone

I guess what Mogorosi is questioning is,

Given that (x-2)(x-3)< 0 , then why not say ( just as you would for an equation) , either (x-2)< 0 or (x-3)< 0 but rather (x-2)>0 and (x-3)<0 ...and ultimately 2<x<3. I know this creating a mental graph but that not going to be possible here. Is there a general rule?

Hey Haress, mogorosi

Technically you are correct to think that if a product of two factors is positive, either factor could be positive and the other negative. However in this case we don't need to worry about the possibility that (x-2) is negative and (x-3) is positive.

(x-2)(x-3) is negative, so one factor must be positive and the other negative. Because (x-2) is greater than (x-3) for any value of x*, (x-2) must be the positive factor and (x-3) must be the negative factor.

x-2>0 --> x > 2
x-3<0 ---> x < 3

Merge the two to get 2<x<3


Does that make sense?
-Patrick

*To compare x-2 to x-3, subtract x from both sides and you get -2 vs. -3. The left is greater than the right.