Inequality question

After all of that, I must admit I don't understand the question. Perhaps it was worded differently in its original version, or perhaps it's just a badly framed question. We do find, if we solve the question completely, that 1 < x < 3, but that's still an infinite set of numbers. My answer is the same as Stock's, at least as the question is phrased: No, the solution set is not finite.

After all of that, I must admit I don't understand the question. Perhaps it was worded differently in its original version, or perhaps it's just a badly framed question. We do find, if we solve the question completely, that 1 < x < 3, but that's still an infinite set of numbers. My answer is the same as Stock's, at least as the question is phrased: No, the solution set is not finite.

cramya wrote:

After all of that, I must admit I don't understand the question. Perhaps it was worded differently in its original version, or perhaps it's just a badly framed question. We do find, if we solve the question completely, that 1 < x < 3, but that's still an infinite set of numbers. My answer is the same as Stock's, at least as the question is phrased: No, the solution set is not finite.

1<x<3 leaves us with just 2 which is finite, correct. Am I misunderstanding this?

Ian Stewart wrote:

Stockmoose16 wrote:Does the following statement result in a finite set of numbers for X?

X^2-4X+3<0

My answer is "NO," but the actual answer is "yes."

Here's why I say no:

X^2-4X+3<0
= (X-3)(X-1)<0

For this statement to be true, one of the terms has to be negative, the other has to be positive.

So, either of the following should be correct:

X-3>0 & X-1<0

OR

X-3<0 & X-1>0

(i)By statement #1, X>3 AND X>1

(ii) By statement 2, X<3 AND X>1

(i) is not finite... so the answer should be that a finite result does not occur. I realize when you plug in numbers, (i) does not work out correctly, but can someone please explain the logic?

One of your inequality signs got reversed during your simplifications - highlighted in red above - and that's the error in your solution. You correctly found that

(X-3)(X-1)<0

and analyzed this correctly: one factor must be positive, the other negative. At this stage, though, it is useful to make the following observation: x-3 must *always* be less than x-1. So, if exactly one of these two factors is negative, it must be true that x-3 is negative, and x-1 is positive. So you rule out one case quite quickly that way.

After all of that, I must admit I don't understand the question. Perhaps it was worded differently in its original version, or perhaps it's just a badly framed question. We do find, if we solve the question completely, that 1 < x < 3, but that's still an infinite set of numbers. My answer is the same as Stock's, at least as the question is phrased: No, the solution set is not finite.

Ian Stewart wrote:

cramya wrote:

After all of that, I must admit I don't understand the question. Perhaps it was worded differently in its original version, or perhaps it's just a badly framed question. We do find, if we solve the question completely, that 1 < x < 3, but that's still an infinite set of numbers. My answer is the same as Stock's, at least as the question is phrased: No, the solution set is not finite.

1<x<3 leaves us with just 2 which is finite, correct. Am I misunderstanding this?

It is what is called in mathematics a 'bounded' set, but it doesn't give a finite set of values for x; there is still an infinite number of possible values of x. For example, x could be any of the following:

3/2, 4/3, 5/4, 6/5, 7/6, 8/7, ...

which is an infinite set of different values in the required range. So there's something wrong with the wording of the question; a real GMAT question would never be worded that way. As logitech points out, if we knew x was an integer, then we would only have a finite number of solutions (in fact, we would know x=2).