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# Is z>2?

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Intern
Joined: 16 Apr 2017
Posts: 45

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17 Jul 2017, 09:01
2
1
00:00

Difficulty:

(N/A)

Question Stats:

25% (00:24) correct 75% (02:47) wrong based on 4 sessions

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Is z > 2?

1) |(z-2)^2| > 4
2) |8x – 4k| = z, where x , k are variables

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Math Expert
Joined: 02 Aug 2009
Posts: 7688
Re: Is z > 2?  [#permalink]

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17 Jul 2017, 09:31
2
1
Supermaverick wrote:
Is z > 2?

1) |(z-2)^2| > 4
2) |8x – 4k| = z, where x , k are variables

hi,

lets see the statements..

1) $$|(z-2)^2| > 4$$
z could be -3 or anything less than 0.... ans NO
z could be anything >2... ans YES
insuff

2) $$|8x – 4k| = z$$, where x , k are variables
4|2x-k|=z
if 2x=k, z=0....ans NO
or z>0... ans can be YES or NO
insuff..

combined..
I tells us z<0 or z>2
II tells us z=0 or z>0

ONLY common region in BOTH statements is z>2
thus Sufficient

C
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Joined: 02 Aug 2009
Posts: 7688
Re: Is z > 2?  [#permalink]

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20 Jul 2017, 07:22
chetan2u wrote:
Supermaverick wrote:
Is z > 2?

1) |(z-2)^2| > 4
2) |8x – 4k| = z, where x , k are variables

hi,

lets see the statements..

1) $$|(z-2)^2| > 4$$
z could be -3 or anything less than 0.... ans NO
z could be anything >2... ans YES
insuff

2) $$|8x – 4k| = z$$, where x , k are variables
4|2x-k|=z
if 2x=k, z=0....ans NO
or z>0... ans can be YES or NO
insuff..

combined..
I tells us z<0 or z>2
II tells us z=0 or z>0

ONLY common region in BOTH statements is z>2
thus Sufficient

C

Responding to a PM
1) x and k are variables means these do not have a CERTAIN value and can take ANY value unless specified.
2) statement II
2) $$|8x – 4k| = z$$, where x , k are variables..
4|2x-k|=z....
As x and k are variables, we have to cater for all values so if 2k=x, 4|2k-x|=4|2k-2k|=4*0=0=z..
But if 2k is NOT equal to x, |2k-x| will be some POSITIVE value as Modulus, values in |..| are always positive or 0
so z becomes 4* some positive value or z>0..
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Re: Is z > 2?  [#permalink]

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21 Jul 2017, 04:55
1
Supermaverick wrote:
Is z > 2?

1) |(z-2)^2| > 4
2) |8x – 4k| = z, where x , k are variables

1) |$$(z-2)^2$$| > 4
=> z > 4, or z = 0
x = 1, k = 1 => z = 4
x = 1, k = 2 => z = 0
Insufficient.

1+2)
S1 - z > 4 or z = 0
=> z cannot be less that 0, and is greater than 4

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19 Apr 2019, 04:12
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Re: Is z>2?   [#permalink] 19 Apr 2019, 04:12
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