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Either both z-5>0 and z+1>0 (positive times positive > 0) => z>5 and z>-1 => z>5 Or both z-5<0 and z+1<0 (negative times negative > 0) => z<5 and z<-1 => z<-1
If z^2 - 4z > 5 then which of the following is always true
A) z > -5
B) z < 5
C) z > -1
D) z < 1
E) z < -1
It's a REALLY BAD question. (z-5)*(z+1) > 0 -> either z > 5 or z < -1
There is a problem with logic. If z < -1 -> (z-5)*(z+1) > 0 but not the other way. for example, z = 6 satisfies (z-5)*(z+1) > 0. Does that mean that it satisfies z < -1 -> NO.
Inequalitys are usually one of my weak spots. Dealing with it algebraically that is.
My approach was to just use 0 for Z, which can be done for each except E.
Thus E it is.
And you would be correct if the question was right. But it is not. Answer is definitely not A, B, C or D, you are right with that. But nor is it E.
Answer is z>5 OR z<-1.
Hence z<-1 is not enough: it doesn't answer the question, since we cannot say "if z^2 - 4z > 5 then z is always less than -1" (try z=6 if you are not convinced).
So either this is not a GMAT question, or there is a mistake in it (in fact either way there is a mistake in it).
If z^2 - 4z > 5 then which of the following is always true
A) z > -5
B) z < 5
C) z > -1
D) z < 1
E) z < -1
z^2 - 4z -5>0 (z+1) (z-5) > 0
z-5>0 or z+1 <0 Soln: z> 5 or z<-1 Since we don't see z > 5, z<-1 is the solution. This is quadratic inequalities question, we can also solve it using graphs, the possible solution will be either z>5 or z<-1.
If z^2 - 4z > 5 then which of the following is always true
A) z > -5
B) z < 5
C) z > -1
D) z < 1
E) z < -1
It's a REALLY BAD question. (z-5)*(z+1) > 0 -> either z > 5 or z < -1
There is a problem with logic. If z < -1 -> (z-5)*(z+1) > 0 but not the other way. for example, z = 6 satisfies (z-5)*(z+1) > 0. Does that mean that it satisfies z < -1 -> NO.
You can't deal with inequalities the same way you deal with equalities (in which you set the equation equal to zero and solve for the parts that make one or the other equal to zero). This is because, the value of the variable affects the other component of the inequality. A graphical representation might help:
Attachments
inequality.gif [ 9.73 KiB | Viewed 841 times ]
_________________
Factorials were someone's attempt to make math look exciting!!!
brokerbevo, you are wrong. Try z = 6. It satisfies the first inequality z^2-4z > 5 but doesn't satisfy option E : z < -1.
Ahhh. I see what you are saying now. Yes, question is worded badly-- probably won't see this on GMAT. I spent all that time making that graph for nothing. _________________
Factorials were someone's attempt to make math look exciting!!!