inequality problem

[AsadA969]

Hi Ron, I can’t make decision that how the answer will be ‘C’ from my explanation in this bellowing question.
Is (x-2) (x-3)>0 ?
(1) x>2
(2) x<3
to make true the question stem, (x-2) (x-3) both must be either positive or negative simultaneously. here, I've solved this math like this way:
Statement 1:
x>2
--->x-2>0, so x-2 is positive. But, I still don’t know (x-3) is positive or not.
Here, x-3= (x-2)-1
=positive -1
=+1-1
=0 positive? (I don’t know is it positive or not)---------(1)

Again, x-3= (x-2)-1
=positive-1
=2-1
=1 positive? ----->yes-----------(2)
So, statement 1 is insufficient…

Statement 2:
x<3
-->x-3<0, so x-3 is negative. But i have no idea about x-2. Is x-2 is negative or not?
Here, x-2=(x-3)+1
=negative+1
=-1+1
=0 negative? (I don’t know is it negative or not)----------(3)

Again, x-2=(x-3)+1
=negative+1
=-2+1
=-1 negative? -----Yes.-----------(4)

So, statement 2 is insufficient…
Now, how can I make a decision from my equations (# 1, 2, 3, 4) after combining statement 1 and statement 2? I’ll be very glad if I’ve your explanation? Thanks…

N.B.: from statement 1: (x-2) is positive and from statement 2 (x-3) is negative. So, positive*negative>0 ?
The answer is NO. But, I can’t make any decision from my equation how it is “C”?

Source: NOVA’S GMAT Math Bible (new edition 2014)…question no. 66. Page no. 432.

[RonPurewal]

ok, so, this is just an issue of understanding the very basics of data sufficiency.

remember—
"sufficient" means that there's only one answer to the question.
"not sufficient" means there are 2 or more answers to the question.

if you have a yes/no question, then think about what these mean:

• if the answer to the question is DEFINITELY "YES", then that's JUST ONE ANSWER... so that's sufficient.

• if the answer to the question is DEFINITELY "NO", then that's JUST ONE ANSWER... so that's sufficient.

• if it's possible for the answer to be "yes" AND possible for the answer to be "no", then that's TWO answers ... so that's not sufficient.

here, you are dealing with the purple thing.

the purple thing -- a SUFFICIENT answer that is definitely "NO" -- is surprisingly rare on this exam. (i think i've only seen it once or twice, among about a thousand official problems.) but... it's still a thing that could happen, so you have to know how to interpret it correctly.

[AsadA969]

ok, so, this is just an issue of understanding the very basics of data sufficiency.

remember—
"sufficient" means that there's only one answer to the question.
"not sufficient" means there are 2 or more answers to the question.

if you have a yes/no question, then think about what these mean:

• if the answer to the question is DEFINITELY "YES", then that's JUST ONE ANSWER... so that's sufficient.

• if the answer to the question is DEFINITELY "NO", then that's JUST ONE ANSWER... so that's sufficient.

• if it's possible for the answer to be "yes" AND possible for the answer to be "no", then that's TWO answers ... so that's not sufficient.

here, you are dealing with the purple thing.

the purple thing -- a SUFFICIENT answer that is definitely "NO" -- is surprisingly rare on this exam. (i think i've only seen it once or twice, among about a thousand official problems.) but... it's still a thing that could happen, so you have to know how to interpret it correctly.

Hi Ron, Thank you for your response. I've an idea about above, but I can't make decision HOW it is definitely NO.
My first equation says: I don’t know is it positive or not
second equation says: YES
third equation says: I don’t know is it negative or not
fourth equation says: YES.
here, there are 2 YES and 2 I don’t know. if I consider the first and third equation simultaneously, they say just ''I don’t know''. which indicates the correct answer is ''E''. again, if I consider the second and fourth equation simultaneously, they say just YES, which indicates the correct answer is ''C". But, how can i combine YES and I don't know?
Thanks...

[tim]

You really need to be more clear in your posts. Please proofread them before you submit them to make sure they are grammatically correct, all references are clear, and your question is prominent.

For example, I have no idea what you mean by "first equation", "second equation", etc.

[AsadA969]

Hi Ron, I can’t make decision that how the answer will be ‘C’ from my explanation in this bellowing question.
Is (x-2) (x-3)>0 ?
(1) x>2
(2) x<3
to make true the question stem, (x-2) (x-3) both must be either positive or negative simultaneously. here, I've solved this math like this way:
Statement 1:
x>2
--->x-2>0, so x-2 is positive. But, I still don’t know (x-3) is positive or not.
Here, x-3= (x-2)-1
=positive -1
=+1-1
=0 positive? (I don’t know is it positive or not)---------(1)

Again, x-3= (x-2)-1
=positive-1
=2-1
=1 positive? ----->yes-----------(2)
So, statement 1 is insufficient…

Statement 2:
x<3
-->x-3<0, so x-3 is negative. But i have no idea about x-2. Is x-2 is negative or not?
Here, x-2=(x-3)+1
=negative+1
=-1+1
=0 negative? (I don’t know is it negative or not)----------(3)

Again, x-2=(x-3)+1
=negative+1
=-2+1
=-1 negative? -----Yes.-----------(4)

So, statement 2 is insufficient…
Now, how can I make a decision from my equations (# 1, 2, 3, 4) after combining statement 1 and statement 2? I’ll be very glad if I’ve your explanation? Thanks…

N.B.: from statement 1: (x-2) is positive and from statement 2 (x-3) is negative. So, positive*negative>0 ?
The answer is NO. But, I can’t make any decision from my equation how it is “C”?

Source: NOVA’S GMAT Math Bible (new edition 2014)…question no. 66. Page no. 432.

Analogy:
Are all instructors of Manhattan prep male?
(1) Statement 1
(2) Statement 2

After calculation:
Statement 1 makes two responses 1) YES, 2) I don’t know. So, should I say? hey, I got my answer; it is “A”----definitely not. Because there are two situations here: 1) YES & 2) I don’t know.
Statement 2 also makes two responses 1) Yes, 2) I don’t know. So, should I say? hey, I got my answer; it is “B”----nope, I can’t say that it is ‘’B’’, because there are two situations here: 1)YES & 2) I don’t know.
Now, I’ll combine the two statements to have the correct answer either ‘’C’’ or “E”. if two statements say (after combining) YES, then it is “C”. if the two statements say NO, then it is also “C”. but, if two statements says YES or NO simultaneously, then it is E. Again, if the two statements say: Are all instructors of Manhattan prep male?-----YES. Are all instructors of Manhattan prep male?-----I don’t know. So, is the data sufficient? Can you take any decision from the RED color?-----definitely not.

So, what is happening in my calculation, let’s see?

After combining two statements, it says YES & I don’t know. So, from my calculation I have got two responses: Are all instructors of Manhattan prep male?-----YES. Are all instructors of Manhattan prep male?----I don’t know. -----NOT sufficient. So, it is “E”. Simple [/b]
So, what is the problem in my calculation (in original post) or lack of understanding?
In short,
Are all instructors of Manhattan prep male?
1) YES, I don’t know
2) YES, I don’t know
Which is “E”. Lack of anything in my understanding?

[RonPurewal]

i'll be honest with you -- i couldn't follow anything in that last post at all.

however, you are clearly overcomplicating this issue.
when you combine the statements, that means that both of them must be true at the same time.

just think about what it means for x > 2 and x < 3 to be true at the same time: it means that x is between 2 and 3.
if that's true, then, (x – 2)(x – 3) < 0.

end of story.

__

if you think you've found any cases for which (x – 2) and (x – 3) are both positive -- or any cases for which they're both negative -- then, nope. either statement 1 or statement 2 will be false.