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Comment on Values of w, x and y
Hello, I was wondering why w
The given information tells
The given information tells us that w/x > 0.
For w/x to be positive, EITHER w and y are both positive OR w and y are both negative. In each case, we can conclude that xw > 0.
Hello,
In this question, I see wxy ≠ 0 in the question and an answer where wxy < 0. I was confused by the usage, maybe it's just me. In the first instance, should it be inferred as w, x and y ≠ 0 and in the second, the product of wxy is <0?
Thanks!
That's correct.
That's correct.
Saying that wxy ≠ 0 is just a shorthand way of saying w ≠ 0, x ≠ 0 and y ≠ 0.
If course, if wxy ≠ 0, it could be the case that wxy < 0 or wxy > 0. So, statement 2 provided additional information.
Cheers,
Brent
Hi
Please explain the counter example again. Why if w=1, x=1 and Y=-1, is the target question correct? I am struggling to see that deduction. I stopped the vid at 1:30 to ask this question
Thanks
The target question asks "Is
The target question asks "Is w/x > 0?"
In other words, "Is w/x positive?"
First off, w=1, x=1 and y=-1 satisfies the condition in statement 1: (wx)²/y < 0
When w=1 and x=1, the answer to the target question is "YES, w/x IS positive"
Next, w=1, x=-1 and y=-1 ALSO satisfies the condition in statement 1: (wx)²/y < 0
When w=1 and x=-1, the answer to the target question is "NO, w/x is NOT positive"
Does that help?
Why cant we equate (wx)²/y <
Whenever we multiply or
Whenever we multiply or divide both sides of an inequality by a variable, we should always ask "Do I know the sign of this variable?"
If the variable is POSITIVE, then the direction of the inequality REMAINS THE SAME.
If the variable is NEGATIVE, then the direction of the inequality is REVERSED.
More on this concept here: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...
Notice that, if w = 1, x = 1 and y = -1, then the inequality (wx)²/y < 0 holds true.
That is: [(1)(1)]²/(-1) < 0
Notice that, if we multiply both sides of (wx)²/y < 0 by y, we are multiplying both sides by a NEGATIVE value (since y = -1).
As such, the direction of the inequality must be REVERSED to get: (wx)² > 0
Does that help?
Cheers,
Brent
So here is what I understand
1) If Y is positive say +1, then, wx<0
2) If Y is negative, say -1 then, (WX)^2 / -1 <-0 -------- [-(WX)^2] <-0]------------ [(WX)^2 >0] -------- [WX>0]
Is this correct? hence, there are 2 solutions?
There are a couple of
There are a couple of problems with your conclusions.
GIVEN: Statement 1) (wx)²/y < 0
You write: If y is positive, say +1, then, wx < 0
This isn't true.
If y is positive, say +1, then, (wx)² < 0 (you wrote wx < 0)
However, since it's IMPOSSIBLE for (wx)² < 0, we can conclude that y CANNOT be positive.
You also wrote "2) If Y is negative, say -1, then (WX)² / -1 <-0 -------- [-(WX)²] <-0]------------ [(WX)² >0] -------- [WX>0]"
The last part isn't true.
If (WX)² > 0, we can't conclude that WX>0"
For example, if w = 1 and x = -1, then it's TRUE that (WX)² > 0, but it's NOT true that WX>0
Cheers,
Brent
Thanks so much!
Hi Brent,
Thank you for your explanation.
I could follow the logic for this question.
However, I do find that in an exam-situation, for questions like this, it took me awhile to determine that I need to plug whichever values for x, y, and w.
Anytips on deciding which values to try for x,y,w and the likes?
Thank you.
You're right; choosing
You're right; choosing numbers to test can take a while.
Here's a video on choosing "good" numbers to test: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1102
Cheers,
Brent
Hi, could you explain at 2:17
The main concept here is that
The main concept here is that k² ≥ 0, for all values of k.
For example:
5² = 25 (and 25 ≥ 0)
(-4)² = 16 (and 16 ≥ 0)
(-7)² = 49 (and 49 ≥ 0)
0² = 0 (and 0 ≥ 0)
Notice that, as long as k does NOT equal zero, k² will be POSITIVE
Since we're told that wxy ≠ 0, we know that none of the values (w, x, or y) equal zero.
This means that wx ≠ 0, which means (wx)² must be POSITIVE.
Does that help?
Cheers,
Brent
Hi Brent,
I am not clear about the conclusion. Why the combination of 2 statements leads to statement 2 (wx) y < 0
wx: positive; y: negative
I could say that w:negative (xy): positive ?
Please help,
Sam
From statement 1, we can
From statement 1, we can conclude that y is negative. Here's why:
Statement 1 tells us that (wx)²/y is negative
Since we know for certain that (wx)² is positive, we have: (positive)/y = negative
This means y must be negative.
Statement 2 tells us that wxy is negative.
Since we know that y must is negative, we can write: (w)(x)(negative) = negative
You're correct to say that w COULD be negative.
Let's see what happens when w is negative, and let's see what happens when w is positive.
CASE I: w is negative
We get: (negative)(x)(negative) = negative
This means x must be negative.
If w and x are both negative, the answer to the Target question is "YES, w/x > 0"
CASE II: w is positive
We get: (positive)(x)(negative) = negative
This means x must be positive.
If w and x are both positive, the answer to the Target question is "YES, w/x > 0"
Since both possible cases yield the same answer to the target question, the combined statements are sufficient.
Does that help?
Hi Brent,
What happens if we forget to rephrase the question?
First of all, most Data
First of all, most Data Sufficiency questions have target questions that can't be rephrased in any beneficial ways.
Consider, for example, these target questions:
- What is the value of x?
- What was the population of Country X in 2007?
- Is x positive?
There is no useful way to rephrase any of these target questions.
Even if there is a target question that could be rephrased, we can still solve the question without rephrasing. It's just that rephrasing the target question can often make the questions easier to solve.
OK, for this question I
This is tricky, I really need to avoid common mistake.
That's a super common mistake
That's a super common mistake. It just shows you're human :-)
I was able to bring it down
Be careful. We're not
Be careful. We're not concluding that w and x are both positive; we're concluding that w and x have the same sign (that is, w and x are either both positive or both negative). Here's why:
We know that y is negative.
And we know that (wx)(y) is negative.
So, it must be the case that the product wx is positive.
If wx is positive, then either w and x are both positive, or both negative.
Let's examine each case:
If w and x are both positive, then w/x is positive.
If w and x are both negative, then w/x is positive.
So, in both cases, the answer to the target question is YES, w/x is positive.
Does that help?
I understand. I guess I
That's correct.
That's correct.
Always confused with this
I'm glad you liked it!
I'm glad you liked it!