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

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zanaik89

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Bunuel

Is m+z > 0

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

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

(1)+(2) Remember we can add inequalities with the sign in the same direction:

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

\(z>0\), 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.

Answer: C.

For graphic approach refer to: https://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

Bunuel

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22 Jul 2018, 20:27

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zanaik89

Bunuel

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?

ProfChaos

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21 Sep 2020, 02:15

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kman

Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

Hi Bunuel

Help me with what is wrong in my approach

Q.Stem : is m+z>0
Since we dont know anything about m and z we cannot do anything with the stem.
m/z can be 0/+ve/-ve

Statement 1: m-3z>0 ==> m>3z
Let z=0 ==> 3z=0 ==> m>0, let m=1 ==> m+z = 1+0 = 1 > 0 (YES)
Let z=1 ==> 3z=3 ==> m>3, let m=4 ==> m+z = 4+1 = 5 > 0 (YES)
Let z=-1 ==> 3z=-3 ==> m>-3. let m=-2 ==> m+z = (-2)+(-1) = -3 < 0 (NO)
INSUFFICIENT

Statement 2: 4z - m > 0 ==> 4z>m ==> m<4z
Let z=0 ==> 4z=0 ==> m<0, let m=-1 ==> m+z = -1+0 = -1 < 0 (NO)
Let z=1 ==> 4z=4 ==> m<4, let m=3 ==> m+z = 3+1 = 4 > 0 (YES)
Let z=-1 ==> 4z=-4 ==> m<-4. let m=-5 ==> m+z = (-5)+(-1) = -6 < 0 (NO)
INSUFFICIENT

Combining 1 and 2
We get, m>3z and m<4z, let m=3.5z ==> m+z = 3.5z+z = 4.5z
Let z=0 ==> 4.5z = 0 ==> 0 = 0 (NO)
Let z=1 ==> 4.5z = 4.5 ==> 4.5 > 0 (YES)
Let z=-1 ==> 4.5z = -4.5 ==> -4.5 < 0 (NO)
INSUFFICIENT

Hence (E)

Bunuel

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21 Sep 2020, 02:28

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kman

Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

Notice that 3z < m < 4z implies that z is positive (3z < 4z --> 0 < z), so you should not use negative numbers for z. Positive z on the other hand implies that m is positive too. So, m + z = positive + positive = positive.

Hope it helps.

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Bunuel

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kman

Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

Thank you so much for replying this quickly!

I understood. Thanks a lot Bunuel. You are a saviour!

MathRevolution

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Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 2 variables: Let the original condition in a DS question contain 2 variables . In other words, there are two fewer equations than variables. Now, we know that each condition (1) and (2) would usually give us an equation, however, since we need 2 equations to match the numbers of variables and equations in the original condition, the unequal number of equations and variables should logically give us an answer C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find whether m + z > 0 .

Second and the third step of Variable Approach: From the original condition, we have 2 variables (m and z).To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Let’s take a look at both conditions together .

Condition(1) tells us that m - 3z > 0 or m > 3z .

Condition(2) tells us that 4z - m > 0.

=> 4z - m > 0 or m < 4z

Adding both inequalities: m - 3z + 4z - m > 0 => z > 0 [Hence, z is positive]

Combining both: 3z < m < 4z

When z > 0 then m + z will also be greater than '0' - is m +z > 0 - YES

Since the answer is unique YES , both conditions together are sufficient by CMT 1.

So, C is the correct answer.

Answer: C

CrackverbalGMAT

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The question pertains to the sign of an addition of terms. This should give us a clue that if we have to combine the inequalities, we need to add the inequalities.

From statement I alone, m – 3z > 0.
Therefore, m > 3z

If z = -1 and m = 1, m > 3z but m + z = 0. The main question can be answered with a NO.
If z = -1 and m = 2, m > 3z but m + z > 0. The main question can be answered with a YES.
Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, 4z – m > 0.
Therefore, 4z > m or m < 4z.

If z = 0, m = -1, m <4z but m + z < 0. The main question can be answered with a NO
If z = 1, m = 1, m < 4z but m + z > 0. The main question can be answered with a YES.
Statement II alone is insufficient. Answer option B can be eliminated.

Combining statements I and II, we have the following:
From statement I alone, m > 3z; from statement II alone, m < 4z. Therefore, 3z < m < 4z.

Adding the two inequalities given, m – 3z + 4z – m > 0, we can see that z > 0. Therefore, m has to be positive.
Since both m and z are positive, m + z > 0.
The combination of statements is sufficient. Answer option E can be eliminated.

The correct answer option is C.

Hope that helps!
Aravind B T

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kman

Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

Statement 1: m>3z
m=1; z=-1;
m-3z>0; sure
m+z = 0; So, no

m=8, z=1;
m>3z? yes
m+z>0? yes

So, Statement 1 is insufficient

Statement 2: 4z>m
z=1; m=2
4z>m? Yes
m+z>0? Yes

z=1, m=-2
4z>m? Yes
m+z>0? No

So, Statement 2 is insufficient

Combining both:
(1) m>3z
(2)m<4z

Multiply (1) with -1: -m<-3z
Add (1) to (2)
0<z
i.e. z>0
Put this in original (1)
m>0
Therefore, m+z> 0

Therefore, (C)

We are going to Tahiti

RastogiSarthak99

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My 2 cents on this:

For me, the best way to solve this was to realize that both statements alone were not giving any answer. Goal is to find whether m + z > 0

Jumping ahead to St 1 and 2 together, By adding both statements:

m - 3z> 0
-m + 4z> 0
-------------
z>0

Therefore, if m - 3z >0

m>3z

m> 3 (z, which is some positive number)

hence m is positive and m+z > 0

C

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Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

To answer whether m+z is positive, we need at least some information about the signs of m and z.
Let's dive deep in each of the given information statements.

(1) m - 3z > 0
In inequalities, we can add and subtract without knowing the sign of the variables but to multiply and divide one has to be cautious about the sign of the variables.
Thus, m - 3z > 0 can also be written as m > 3z.
m+z will be greater than 3z+z i.e. 4z. (Only calculation for this statement)
If z is positive then 4z will be greater than 0.
If z is negative then 4z will be less than 0.
Because we are yet to get a confirmation on the sign of z, the statement I is insufficient.

(2) 4z - m > 0
Using the same logic as used in statement I, 4z - m > 0 can be written as 4z > m.
It can be further divided by 4, z>m/4. (Only calculation for this statement)
Because we are yet to get a confirmation on signs of m and z, the statement II is insufficient.

(Both)
m - 3z > 0
4z - m > 0
4z - m > 0 can be re-written as -m + 4z >0

m - 3z > 0
-m + 4z >0
----------------
Adding the 2 equations, we get z > 0.
Wallah, this is what we were looking for; the sign of z is now known to us.

We can proceed further to fill the gap of statement 1 but we will not as we have the answer that data is sufficient.
Hence C is the correct option for this question.

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