If it is true that z < 8 and 2z > -4, which of the following : GMAT Problem Solving (PS)
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# If it is true that z < 8 and 2z > -4, which of the following

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If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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03 Dec 2010, 01:13
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If it is true that z < 8 and 2z > -4, which of the following must be true?

(A) -8 < z < 4
(B) z > 2
(C) z > -8
(D) z < 4
(E) None of the above
[Reveal] Spoiler: OA
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03 Dec 2010, 01:21
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surendar26 wrote:
If it is true that z < 8 and 2z > -4, which of the following must be true?
(A) -8 < z < 4
(B) z > 2
(C) z > -8
(D) z < 4
(E) None of the above

Note that we are asked which of the following MUST be true.

Given: $$z<8$$ and $$2z>-4$$, or dividing by 2 $$z>-2$$. So we have: $$-2<z<8$$.

Now, no matter what $$z$$ actually is, since it's in the range $$-2<z<8$$ then it'll definitely be more than -8, so C. $$z>-8$$ must be true.

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03 Dec 2010, 01:41
If Z>-8,Z may be any value b/t -7 to infinity then -2<Z<8 condition will fail.
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03 Dec 2010, 01:50
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surendar26 wrote:
If Z>-8,Z may be any value b/t -7 to infinity then -2<Z<8 condition will fail.

We are told that $$-2<z<8$$, so this statement is GIVEN to be true. For example z might be -1, 0, 1.5, 5, ... ANY value of z from this (true) range $$-2<z<8$$ will be more than -8.

So when you say that z might for example be -7 it's not true as $$-2<z<8$$.

To elaborate more. Question uses the same logic as in the examples below:

If $$x=5$$, then which of the following must be true about $$x$$:
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x>-10

Answer is E (x>-10), because as x=5 then it's more than -10.

Or:
If $$-1<x<10$$, then which of the following must be true about $$x$$:
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x<120

Again answer is E, because ANY $$x$$ from $$-1<x<10$$ will be less than 120 so it's always true about the number from this range to say that it's less than 120.

Or:
If $$-1<x<0$$ or $$x>1$$, then which of the following must be true about $$x$$:
A. x>1
B. x>-1
C. |x|<1
D. |x|=1
E. |x|^2>1

As $$-1<x<0$$ or $$x>1$$ then ANY $$x$$ from these ranges would satisfy $$x>-1$$. So B is always true.

Hope it's clear.
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03 Dec 2010, 18:27
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To understand this, take a real life example.

Her weight is more than 120 pounds but less than 130 pounds. Then which of the following is definitely true about her weight?
A. Her weight is 125 pounds.
B. Her weight is more than 110 pounds.

Isn't statement B definitely true about her weight? Since I know her weight is between 120 and 130 pounds, it is more than 110 pounds.
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If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 08:26
If it is true that z < 8 and 2z > -4, which of the following must be true?
(A) $$-8 < z < 4$$
(B) $$z > 2$$
(C) $$z > -8$$
(D) $$z < 4$$
(E) None of the above

It's a relatively easy question. However, the answer and explanation provided by Sackmann are totally confusing. Curious to know what you guys will come up with.

Edit: Something went wrong with the >< and (-), updated the question.
Source: Total GMAT
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Last edited by megafan on 11 Jan 2013, 09:27, edited 3 times in total.
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 08:36
Are you sure the OA is correct? I am getting B.
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 09:08
OA is incorrect. Choice(B) should be the answer.
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 09:15
Solving, 2<z<8

However, I just noticed that the thread title has z<8 and 2z> -4, but the problem states 2z>4 and z<8.
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 09:23
bteller wrote:
Solving, 2<z<8

However, I just noticed that the thread title has z<8 and 2z> -4, but the problem states 2z>4 and z<8.

My Bad, updated the question. The OA is pretty confusing to me as well. But the OA I have is correct.
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 09:28
PraPon wrote:
OA is incorrect. Choice(B) should be the answer.

Sorry, something went wrong with the copy-paste from pdf. Updated the question, please try again.
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 11:09
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megafan wrote:
If it is true that z < 8 and 2z > -4, which of the following must be true?
(A) $$-8 < z < 4$$
(B) $$z > 2$$
(C) $$z > -8$$
(D) $$z < 4$$
(E) None of the above

It's a relatively easy question. However, the answer and explanation provided by Sackmann are totally confusing. Curious to know what you guys will come up with.

Edit: Something went wrong with the >< and (-), updated the question.
Source: Total GMAT

Merging similar topics. Please refer to the solutions above.
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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11 Jan 2013, 15:30
Awesome! thanks for merging with this post. Your examples above—http://gmatclub.com/forum/if-it-is-true-that-z-8-and-2z-4-which-of-the-following-105709.html#p826787 cleared up my confusion. I was thinking in a completely different way. Now it makes sense that you want to pick a solution that covers all the possible values of X—and that's pretty much all this is, it's so simple when you realize it!
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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15 Apr 2015, 10:12
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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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19 Aug 2015, 01:54
surendar26 wrote:
If it is true that z < 8 and 2z > -4, which of the following must be true?

(A) -8 < z < 4
(B) z > 2
(C) z > -8
(D) z < 4
(E) None of the above

Another way to solve this is adding the inequalities:

8>z
2z>-4

8+2z>z-4, subtract z
6+z>0, subtract 6
z>-6

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Re: If it is true that z < 8 and 2z > -4, which of the following [#permalink]

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08 Feb 2017, 17:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If it is true that z < 8 and 2z > -4, which of the following   [#permalink] 08 Feb 2017, 17:10
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