z(z-4) > 5
Lets take each option 1 by 1
a) z = 0 invalidates the above
b) z = 0 invalidates the above
c) z = 0 invalidates the above
d) z = 0 invalidates the above
e) All values of z for z < -1 keeps the above inequality
So,(E)
which is TRUE
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GMATGuruNY
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Try to show that the answers DON'T have to be true.GmatKiss wrote: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
Plug z=10 into z² - 4z > 5:
10² - 40 > 5
60 > 5.
This works.
Since it's possible that z=10, eliminate B, D and E.
Plug z= -10 into z² - 4z > 5:
(-10)² - 4(-10) > 5
100+40 > 5
140 > 5.
This works.
Since it's possible that z=-10, eliminate A and C.
None of the answers must be true.
Algebraically:
z² - 4z - 5 > 0
(z+1)(z-5) > 0.
Thus, z=-1 and z=5 are the critical points: the values where z² - 4z - 5 = 0.
When z is ANY other value, z² - 4z - 5 < 0 or z² - 4z - 5 > 0.
To determine the range of z, test values to the left and right of each critical point.
Case 1: z < -1.
Let z = -2.
(-2)² - 4(-2) - 5 > 0
7>0. This works.
z<-1 is part of the range.
Case 2: -1<z<5.
Let z=0.
(0)² - 4(0) - 5 > 0
-5>0.
Doesn't work.
-1<z<5 is not part of the range.
Case 3: z>5.
Let z=6.
(-6)² - 4(6) - 5 > 0.
7>0.
This works.
z>5 is part of the range.
Thus, z<-1 OR z>5 .
Since it's possible that z<-1 or that z>5, none of the answers MUST be true.
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Hi All,
While this is an old series of posts, does anyone know the source of this question? Mitch has properly proven that there is NO correct answer, so either the question was poorly written or the original poster didn't include some detail from the original source. There are plenty of quality sources for practice questions, so if the original source was/is questionable, then it would be best to avoid it and work with established materials.
GMAT assassins aren't born, they're made,
Rich
While this is an old series of posts, does anyone know the source of this question? Mitch has properly proven that there is NO correct answer, so either the question was poorly written or the original poster didn't include some detail from the original source. There are plenty of quality sources for practice questions, so if the original source was/is questionable, then it would be best to avoid it and work with established materials.
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
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Brent@GMATPrepNow
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Although the original question is flawed, students should know how to solve quadratic inequalities.
Here's a free video on this advanced topic: https://www.gmatprepnow.com/module/gmat- ... ing?id=986
Afterwards, here's a tricky practice question to try: https://www.gmatprepnow.com/module/gmat- ... ing?id=987
Cheers,
Brent
Here's a free video on this advanced topic: https://www.gmatprepnow.com/module/gmat- ... ing?id=986
Afterwards, here's a tricky practice question to try: https://www.gmatprepnow.com/module/gmat- ... ing?id=987
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
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Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Although the original question is flawed, students should know how to solve quadratic inequalities.
Here's a free video on this advanced topic: https://www.gmatprepnow.com/module/gmat- ... ing?id=986
Afterwards, here's a tricky practice question to try: https://www.gmatprepnow.com/module/gmat- ... ing?id=987
Cheers,
Brent
Here's a free video on this advanced topic: https://www.gmatprepnow.com/module/gmat- ... ing?id=986
Afterwards, here's a tricky practice question to try: https://www.gmatprepnow.com/module/gmat- ... ing?id=987
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
