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# If 5 z – 3 < 3 z + 4, which of the following cannot be a value of

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Joined: 06 Apr 2010
Posts: 17
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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Updated on: 17 Jul 2018, 18:15
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:22) correct 19% (01:32) wrong based on 83 sessions

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If 5 z – 3 < 3 z + 4, which of the following cannot be a value of $$z^{3}$$ ?

A) 0

B) 1

C) 8

D) 27

E) 64

Originally posted by ninayeyen on 09 Mar 2016, 10:02.
Last edited by chetan2u on 17 Jul 2018, 18:15, edited 2 times in total.
Edited the question
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Joined: 02 Sep 2009
Posts: 50619
Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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09 Mar 2016, 10:06
ninayeyen wrote:
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of z3?

A) 0

B) 1

C) 8

D) 27

E) 6

Please check the highlighted parts and edit.
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Math Expert
Joined: 02 Sep 2009
Posts: 50619
Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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09 Mar 2016, 10:43
ninayeyen wrote:
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of $$z^{3}$$ ?

A) 0

B) 1

C) 8

D) 27

E) 6

5 z – 3 < 3 z + 4 gives z < 3.5. I think E should be 64, which is 4^4, in this case the answer would indeed be E.
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Joined: 06 Apr 2010
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Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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09 Mar 2016, 12:07
Bunuel wrote:
ninayeyen wrote:
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of $$z^{3}$$ ?

A) 0

B) 1

C) 8

D) 27

E) 6

5 z – 3 < 3 z + 4 gives z < 3.5. I think E should be 64, which is 4^4, in this case the answer would indeed be E.

Oh you are most likely right! pls can you break it down to how you got z? and why did you round up 3.5 to 4?
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Joined: 02 Sep 2009
Posts: 50619
Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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09 Mar 2016, 12:16
ninayeyen wrote:
Bunuel wrote:
ninayeyen wrote:
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of $$z^{3}$$ ?

A) 0

B) 1

C) 8

D) 27

E) 6

5 z – 3 < 3 z + 4 gives z < 3.5. I think E should be 64, which is 4^4, in this case the answer would indeed be E.

Oh you are most likely right! pls can you break it down to how you got z? and why did you round up 3.5 to 4?

5z – 3 < 3z + 4
5z - 3z < 4 + 3
2z < 7
z < 3.5

z must be 4 for z^3 to be 64. On the other hand z an be 0, 1, 2, or 3 thus z^3 can be 0, 1, 8, or 27.
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Joined: 27 May 2012
Posts: 609
Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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11 Jul 2018, 04:22
Bunuel wrote:
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of $$z^{3}$$ ?

A) 0

B) 1

C) 8

D) 27

E) 6

5z – 3 < 3z + 4
5z - 3z < 4 + 3
2z < 7
z < 3.5

z must be 4 for z^3 to be 64. On the other hand z an be 0, 1, 2, or 3 thus z^3 can be 0, 1, 8, or 27.

Hi Bunuel ,
I was wondering the same thing, I was thinking no answer choice satisfies . Choose E because A to D at least gave Z as an integer and E did not . Then I scrolled down and understood everything . Wouldn't it better to change E from 6 to 64?
Thank you.
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- Stne

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Affiliations: Target Test Prep
Joined: 04 Mar 2011
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Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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17 Jul 2018, 15:26
ninayeyen wrote:
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of $$z^{3}$$ ?

A) 0

B) 1

C) 8

D) 27

E) 6

(Note: All the answer choices are perfect cubes except E, so we think it’s a typo. Choice E should be 64 instead of 6.)

5z - 3 < 3z + 4

2z < 7

z < 3.5

z^3 < 3.5^3

Since 64 = 4^3, it can’t be the value of z^3.

Alternate Solution:

If z^3 = 0, then z = 0. If z^3 = 1, then z = 1. If z^3 = 8, then z = 2. If z^3 = 27, then z = 3. The values z = 0, 1, 2 and 3 all satisfy the given inequality; therefore the answer must be E.

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Joined: 02 Aug 2009
Posts: 7035
Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of  [#permalink]

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17 Jul 2018, 18:20
ninayeyen wrote:
If 5 z – 3 < 3 z + 4, which of the following cannot be a value of $$z^{3}$$ ?

A) 0

B) 1

C) 8

D) 27

E) 64

Hi..

The question has nothing to do with a perfect cube..
5z-3<3z+4........2z<7.......z<7/2
Therefore $$z^3<(\frac{7}{2})^3..........z^3<\frac{343}{8}...z<42.9$$

So z^3 can be anything LESS than 42.9. it can be even 41, need not be perfect cube.
It is not given that z is an integer

E
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Re: If 5 z – 3 < 3 z + 4, which of the following cannot be a value of &nbs [#permalink] 17 Jul 2018, 18:20
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