If z^2 – 4z 5, which of the following is always true?

Question

If z^2 – 4z > 5, which of the following is always true? (A) z > 5 (B) z < 5 (C) z > -1 (D) z < 1 (E) none of above

chetan2u · Accepted Answer

Yes, the answer would be A if the Q asked  CAN be true ..
But Question  is ALWAYS true. 
So the equation is true when x<-1..
This means z can be -2, so z need not ALWAYS be >5

Hope it helps

JeffTargetTestPrep · Answer

We’ll treat it as an equation first: z^2 – 4z = 5 z^2 – 4z – 5 = 0 (z - 5)(z + 1) = 0 z = 5 or z = -1 The two solutions above divide the number line into three intervals: 1) z < -1 2) -1 < z < 5 3) z > 5 For each of these intervals, if one number from the interval satisfies the inequality, then the whole interval will satisfy the inequality. 1) z < -1 Let’s pick z = -2: (-2)^2 - 4(-2) > 5? 4 + 8 > 5? (Yes) 2) -1 < z < 5 Let’s pick z = 0: 0^2 - 4(0) > 5? 0 - 0 > 5? (No) 3) z > 5 Let’s pick z = 6: 6^2 - 4(6) > 5? 36 - 24 > 5? (Yes) We see that the solution to the inequality is z < -1 or z > 5. Note that the question is asking for a statement that is ALWAYS true; for any of the given answer choices, we can always find a value of z that does not satisfy the given inequality. Thus, none of the provided answer choices are always true. Answer: E

chetan2u · Answer

lets solve the equation.. z^2-4z>5........z^2-4z-5>0.....(z-5)(z+1)>0 so two options .. 1) BOTH z-5 and z+1 are positive.. when z>5 both are positive 2) both are negative z-5 and z+1.. z<-1, both are negative so z<-1 and or z>5 two ranges possible Insufficient.. E

hellosanthosh2k2 · Answer

Hi, answer must be E.

As z^2 - 4z > 5
=> z^2 - 4z - 5 > 0
(z - 5)(z + 1) > 0

when -1 < z < 5, (z-5)(z+1) < 0 always
when z = -1 or 5, (z-5)(z+1) = 0
when z < -1 or z > 5, then (z-5)(z+1) > 0 always

since none of the options match z < -1 or z > 5, answer must be E

vitorpteixeira · Answer

My doubt is, since any value Z>5 satisfy the inequality, why A is wrong?

shanks2020 · Answer

I think the answer should be A. It looks same as the Question which asks "must be true". There is in value of z>5 which would not satisfy the given question condition.
Please let me know where i am wrong.

AnirudhaS · Answer

Hi, the answer is actually E. The question asks which MUST BE TRUE.

if you solve the equation, it looks like (z+1)(z-5)>0. 
This signifies that either (a) z<-1 or (b) z>5
Therefore it z>5 is NOT A MUST because z can be less than -1. Does this make sense? let me know if you need further explanation.

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If z^2 – 4z > 5, which of the following is always true?

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