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inequility questions

by Thephu » Mon Jan 21, 2008 9:35 pm
Can someone please help to clarify?
I have explanation but I don't understand in bold....

Is 2 < x < 4?
1) x² - 5x + 6 <0> 0

OA is D

(D) The key to this problem is to factor the expressions. You can factor STATEMENT (1) into (x - 3)(x - 2). If the expression is negative that means x -3 and x -2 must have opposite signs. This can only happen if 2 < x < 3. Thus, (1) alone is sufficient.

STATEMENT (2) alone is sufficient since the expression factors into 5x (x -5). To be positive both 5x and x -5 must have the same sign. This will happen if x <0> 5. This means x does not satisfy 2 <x < 4. So (2) alone is sufficient. Remember answering the question does not only mean answering yes, the question is true. Deciding that a statement is not true also answers the question of whether or not the statements are sufficient.

Thank you very much. ;)
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by simplyjat » Mon Jan 21, 2008 9:41 pm
You are missing the second statement....

Where did you get the question?
AFAIK answer D is only true when both the statements I & II give the same answer, but here both the statements are giving different answers and thus D could not be the correct answer....
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by Thephu » Mon Jan 21, 2008 11:25 pm
sorry i missed statement 2
here it is..


2) 5x^2 - 25x > 0

i got this test from simulated test. I think it called 800 Score test. Not so sure how it called.
Last edited by Thephu on Tue Jan 22, 2008 12:42 am, edited 1 time in total.
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by camitava » Tue Jan 22, 2008 12:42 am
Thephu, I think again u have missed to include the stmt-2. Do u want to mean - 1. x^2 - 5x + 6 <0> 0 - these are two stmts for this Qs? Can u pls clarify?
Correct me If I am wrong


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by Thephu » Tue Jan 22, 2008 2:05 am
Oppss.. sorry again.. here it is the questions.

Is 2<x<4?

1) x^2 - 5x + 6 less than 0
2) 5x^2 - 25x more than 0


OA is D.

Thanks
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by simplyjat » Tue Jan 22, 2008 3:11 am
Where did you get this question ?

GMAT is very clear about the answer option D "both statements should result in the same answer". But here the answer is different on first and second information...
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by camitava » Tue Jan 22, 2008 3:32 am
simplyjat, sorry I don;t know what u have said. But in this forum itself, I faced a DS Qs something like this - I mean - having two different answers at all. But by that u can reach to the conclusion what has been asked in the Qs. So it was D.
And Thephu, from stmt-1
(x - 2)(x - 3) <0> 2 and x < 3 - so SUFF

And from stmt - 2.
x = 0 or x = 5 - so SUFF

So IMO D.
Look simplyjat, the Qs is asking something what we can achieve from both the options. So what's the problem to select both the options.

Ohhho! May be I sound little awkward. But while answering this Qs, always the incidence related to the last post (mentioned above) is coming into my mind. Sorry for that ...
Correct me If I am wrong


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by Stuart@KaplanGMAT » Tue Jan 22, 2008 4:41 am
Thephu wrote:Oppss.. sorry again.. here it is the questions.

Is 2<x<4?

1) x^2 - 5x + 6 less than 0
2) 5x^2 - 25x more than 0


OA is D.

Thanks
For a yes-no question, a statement will be sufficient if it gives us a definite yes or a definite no answer to the question.

(1) x^2 - 5x + 6 < 0

(x-3)(x-2) < 0

if we know that the product of two numbers is negative, then one of them must be + and one -

Therefore, we know that either:

(x-3) < 0 and (x-2) > 0

or

(x-3) > 0 and (x-2) < 0

In the first case, we solve as x < 3 and x > 2

So, we have 3 > x > 2

If x is between 2 and 3, it's definitely between 2 and 4 - this solution gives us a "yes" answer.

In the second case, we get x > 3 and x < 2

However, this makes no sense at all (since there are no values that satisfy 2 > x > 3), so we can discard this solution.

Therefore, statement (1) gives us only a "yes" answer - sufficient.

(2) 5x^2 - 25x > 0

We can start by dividing through by 5 to get:

x^2 - 5x > 0

and then factor out x to get:

x(x-5) > 0

Since the product of these terms is positive, we know that they're both positive or they're both negative, so one solution is:

x > 0 and (x-5) > 0

or

x > 0 and x > 5

When we have two inequalities with the same direction, to satisfy them both we need to satisfy the more extreme one.

Therefore, x > 5 is one solution. If x > 5 then it's never between 2 and 4. So, we an get a "no" answer from statement (2).

The other solution is:

x < 0 and (x-5) < 0

or

x < 0 and x < 5

To satisfy them both, we need x < 0. If x < 0 then it's never between 2 and 4, so we get another "no" answer. Since we can only get "no" answers, it would seem that statement (2) is also sufficient.

Now we get to Simplyjat's objection. On the GMAT, we will NEVER be presented with contradictory statements. On a yes-no question, here's what could happen:

(1) gives you just yes, (2) gives you yes/no... (A)
(1) gives you just no, (2) gives you yes/no.. (A)
(1) gives you yes/no, (2) gives you just yes.. (B)
(1) gives you yes/no, (2) gives you just no... (B)
(1) gives you yes/no, (2) gives you yes/no... but when you put them together, you get just yes... (C)
1) gives you yes/no, (2) gives you yes/no... but when you put them together, you get just no... (C)
(1) gives you just yes, (2) gives you just yes... (D)
(1) gives you just no, (2) gives you just no... (D)
(1) gives you yes/no, (2) gives you yes/no... and when you put them together, you still get yes/no... (E)

It is IMPOSSIBLE for (1) to give you just yes and (2) to give you just no
It is IMPOSSIBLE for (1) to give you just no and (2) to give you just yes

Therefore, this question is invalid and can never appear as it does on the GMAT.
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by camitava » Tue Jan 22, 2008 5:09 am
Sorry Stuart! Sorry for my mistake ...
Correct me If I am wrong


Regards,

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by Thephu » Tue Jan 22, 2008 6:09 am
Thank you very much everyone :) I got it now..
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by humeixia » Thu Apr 10, 2008 2:40 pm
:D
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