Powers and inequalities

Question

Here's one I just made up: Is (4^-x)(y�) > 0? 1) xy < 0 2) y^x < 0 Difficulty-wise, I'd place this one in the 600-650 range Cheers, Brent

kvcpk · Answer

Brent@GMATPrepNow wrote:Here's one I just made up:

Is (4^-x)(y�) > 0?
1) xy < 0
2) y^x < 0
Difficulty-wise, I'd place this one in the 600-650 range

Cheers,
Brent

4^-x is always greater than 0
y^4 is always greater than 0.
Hence the question always remains true.

We dont need to look at the stmts 1 and 2. Am I missing something?

Brent@GMATPrepNow · Answer

kvcpk wrote: Am I missing something? Yes ...

kvcpk · Answer

Brent@GMATPrepNow wrote:kvcpk wrote: Am I missing something? Yes ... I am unable to think of a case when the given stmt would be false. I would have picked D.

Brent@GMATPrepNow · Answer

kvcpk wrote: 4^-x is always greater than 0
y^4 is always greater than 0.
Hence the question always remains true.

We dont need to look at the stmts 1 and 2. Am I missing something?

Hint: the part in blue is not correct.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

kvcpk · Answer

Brent@GMATPrepNow wrote:kvcpk wrote: 4^-x is always greater than 0 y^4 is always greater than 0. Hence the question always remains true. We dont need to look at the stmts 1 and 2. Am I missing something? Hint: the part in blue is not correct. Cheers, Brent My Bad. I completely lost track. Y can be zero. Ok Now here goes my solution: As per the given statement, (4^-x)(y^4)>0 gives us YES and (4^-x)(y^4)<=0 gives us NO. 4^-x is always>0 y^4 is always greater than 0 except when y=0 So we get an YES everytime except when y=0 Hence we will need to be looking at our 2 given statements to see if they pose a case of y=0. stmt 1: xy<0 if xy<0, then either (x<0 and y>0) or (x>0 and y<0) y cannot be equal to 0. Hence SUFFICIENT. Stmt 2: y^x <0 Even here, y cannot be 0, since 0^anything is 0. Hence SUFFICIENT. Pick D. Did i get it right this time Brent?

Brent@GMATPrepNow · Answer

kvcpk wrote:Brent@GMATPrepNow wrote:kvcpk wrote: 4^-x is always greater than 0 y^4 is always greater than 0. Hence the question always remains true. We dont need to look at the stmts 1 and 2. Am I missing something? Hint: the part in blue is not correct. Cheers, Brent My Bad. I completely lost track. Y can be zero. Ok Now here goes my solution: As per the given statement, (4^-x)(y^4)>0 gives us YES and (4^-x)(y^4)<=0 gives us NO. 4^-x is always>0 y^4 is always greater than 0 except when y=0 So we get an YES everytime except when y=0 Hence we will need to be looking at our 2 given statements to see if they pose a case of y=0. stmt 1: xy<0 if xy<0, then either (x<0 and y>0) or (x>0 and y<0) y cannot be equal to 0. Hence SUFFICIENT. Stmt 2: y^x <0 Even here, y cannot be 0, since 0^anything is 0. Hence SUFFICIENT. Pick D. Did i get it right this time Brent? Perfect! Cheers, Brent

Brent@GMATPrepNow · Answer

Is (4^-x)(y�) > 0?
1) xy < 0
2) y^x < 0

Here's my solution:

Target question: Is (4^-x)(y�) > 0?

This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

First recognize that (4^-x) IS POSITIVE for ANY value of x. So, (4^-x) = some positive number.
In other words, (4^-x)(y�) = (some positive number)(y�)

What can we conclude about y�? Well, y� is always greater than or equal to zero.
In fact, the ONLY time y� is NOT greater than zero is when y = 0.
So, the ONLY time that (4^-x)(y�) is NOT greater than zero, is when y = 0.
In other words, if y has a non-zero value, (4^-x)(y�) > 0.
We can now REPHRASE the target question as follows....
REPHRASED target question: Does y have a non-zero value?

At this point, it's relatively easy to check the statements.

Statement 1: xy < 0
This means that xy ≠ 0, which means that y ≠ 0.
In other words, we can be certain that y has a non-zero value.
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: y^x < 0
If y^x < 0, then we know that y ≠ 0.
In other words, we can be certain that y has a non-zero value.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Rich.C@EMPOWERgmat.com · Answer

Hi kvcpk,

GMAT DS questions are remarkably good at measuring Test Takers on areas that are not exclusive to "math": organization, accuracy, attention to detail, thoroughness, etc.

Brent's question had a design element to it that was built to test your thoroughness. It's important to consider MULTIPLE possibilities when dealing with a DS question. Yes, there are POSITIVE INTEGERS, but WHAT ELSE is there?

To score well on this Test (and by extension, impress Business Schools), you have to show them that you can see more than just the obvious. Keep that in mind as you continue to work on DS questions. You'll be amazed how often there are more possibilities than just the first one that you come up with.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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