the value of z

[atishree]

If z² - 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

[solmon]

z(z-4)>5
A) if z=0, 0>5 thus wrong answer choice
B) if z=0, 0>5 thus wrong answer choice
C) if z=0, 0>5 thus wrong answer choice
D) if z=0, 0>5 thus wrong answer choice
E) if z=-2, 12>5 CORRECT

[torpedo]

IMO the answer is (E).

[chix475ntu]

z² - 4z > 5
z² - 4z -5 > 0
(z-5) * (z+1) > 0 .. either both expressions are greater than 0 or both expressions are less than 0
so z-5 > 0 & z+1 > 0 OR z-5 < 0 & z+1 < 0
z>5 & z>-1 OR z<5 & z< -1
z> 5 OR z<-1

E fits the criteria

[ashua12]

IfIf z² - 4z > 5 then which of the following is always true

z²-4z-5>0
(z-5)(z+1)>0 or ab>0
there are two cases either a>0 and b>0 or a<0 and b<0
Now question does not end here we have to take into consideration the resulting values with our equation
we get z>-1and z>5 or z<-1 and z<5
here z>5 and z<-1 fits the criteria
hence the solution

[naso]

There is no correct answer.

z² - 4z > 5
z² - 4z - 5 > 0
(z - 5)(z + 1) > 0

Two possibilities: the two factors (z - 5) and (z + 1) are either both positive or both negative. In other words, either z > 5 or z < -1. Plug any number that is greater than 5 or any number that is less than -1 into z² - 4z and you will get a value greater than 5. For example, if z = 6, then z² - 4z = 12, which is greater than 5. Or, if z = -6, then z² - 4z = 60, which is greater than 5.

Now, the question asks "which of the following is always true?"
That z could be -6 proves than neither (A) nor (C) is necessarily true.
That z could be 6 proves that neither (B) nor (D) nor (E) is necessarily true.