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# Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1201
Location: India
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Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0  [#permalink]

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03 May 2018, 22:47
Bunuel wrote:
Is m+z > 0

(1) m - 3z > 0. Insufficient on its own.

(2) 4z - m > 0. Insufficient on its own.

$$(m-3z)+(4z-m)>0$$;

$$z>0$$, so $$z$$ is positive.

From (1) $$m>(3z=positive)$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive). Therefore, $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: http://gmatclub.com/forum/is-m-z-0-1-m- ... 75657.html

For these types of questions, is there a rule of thumb or a easy way to tell whether the statements alone will be sufficient? I always waste a lot of time on these types of questions.

Note that we have two variables here m & z but each statement offers you only ONE equation. Hence it is not possible to solve. For solving two variables you need at least another equation or a relationship between the two variables (which will be your other equation).

So you can negate the statements simply by looking at it. this will save your time.
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Joined: 19 Aug 2016
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Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0  [#permalink]

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22 Jul 2018, 17:38
Bunuel wrote:
Is m+z > 0

(1) m - 3z > 0. Insufficient on its own.

(2) 4z - m > 0. Insufficient on its own.

$$(m-3z)+(4z-m)>0$$;

$$z>0$$, so $$z$$ is positive.

From (1) $$m>(3z=positive)$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive). Therefore, $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: http://gmatclub.com/forum/is-m-z-0-1-m- ... 75657.html

Hi Bunuel...

From statement 2 we know that 4z>m in which case lets say.. 4(1)>1 the statement is suff that m+z>0

But 4(1)>-2 in which case M+z>0 is not true

Thanks For ur help in advance
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0  [#permalink]

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22 Jul 2018, 20:27
zanaik89 wrote:
Bunuel wrote:
Is m+z > 0

(1) m - 3z > 0. Insufficient on its own.

(2) 4z - m > 0. Insufficient on its own.

$$(m-3z)+(4z-m)>0$$;

$$z>0$$, so $$z$$ is positive.

From (1) $$m>(3z=positive)$$, so $$m$$ is positive too ($$m$$ is more than some positive number $$3z$$, so it's positive). Therefore, $$m+z=positive+positive>0$$. Sufficient.

For graphic approach refer to: http://gmatclub.com/forum/is-m-z-0-1-m- ... 75657.html

Hi Bunuel...

From statement 2 we know that 4z>m in which case lets say.. 4(1)>1 the statement is suff that m+z>0

But 4(1)>-2 in which case M+z>0 is not true

Thanks For ur help in advance

Yes, (2) is not sufficient because it gives an YES and a NO answers to the question whether m + z > 0 but what is your doubt?
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Re: Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 &nbs [#permalink] 22 Jul 2018, 20:27

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