Is M + Z > 0? 1) M - 3Z > 0

[Guest]

From GMAT Prep Test:

Is M + Z > 0

1) M - 3Z > 0
2) 4Z - M > 0

The answer is c but I am not sure how you could glean much information from either of the statements.

[Jeff]

You can plug in numbers (think both positive and negative) to convince your self that 1) and 2) are not sufficient by themselves and rule out answers a,b, and d.

Then consider both together: 3z<M<4z. If 3z<4z, then z must be positive since this would not hold for negative value of z. If z is positive, then 3z is also positive and if M is greater then 3z, then M is also positive. If M and z are positive, then m+z >0 must always be true and the answer is C.

Jeff

[Guest]

Thanks, Jeff. Your explanation is extremely helpful.

[dbernst]

Thanks Jeff. You are making our job extremely easy!

[harjai.sharad]

M + Z > 0

1) M - 3Z > 0
2) 4Z - M > 0
My ans is E but OA is C.

Here is my method.

M-3Z > 0 M>3Z
4Z-M> 0 4Z>M
I REWROTE IT AS 4 > M/Z > 3

THEREFORE M and Z are either positive or negative.
therefore m+z>0 can be positive or negative.
my ans is therefore E.

Please tell where i am going wrong.

[camille.lambert]

Equations :

M - 3Z > 0
-M + 4Z > 0

What I did is I simply noticed that if you add the two equations, M cancels off and you are left with only one Z which is practical :

M-M -3Z +4Z > 0
gives :
Z>0

NOTE : obviously you can do this only if the two inequality signs face in the same direction!

So we now Z is positive. Now consider "M - 3Z > 0". We can conclude M is positive

so M + Z ===> positive + positive so is positive

Thus C.

[camille.lambert]

Hello Harjai

Basically you rewrote

M-3Z>0 to M>3Z
4Z-M>0 to 4Z>M

So far no mistake. But to get to 4 > M/Z > 3 means that you divided both sides by Z like so :

M-3Z>0 to M>3Z TO M/Z>3
4Z-M>0 to 4Z>M TO 4>M/Z

This forbidden as you don't know if Z is positive or negative. Remember if you multiply both sides of an inequality by a negative number you need to switch the inequal sign. Look :

-3 < -1 multiply both sides by -2 : 6 > 2

Hope its clearer now

Cheers and good luck for your exam
Camille

[harjai.sharad]

Thank you camille for your expedite help.

[RonPurewal]

Hello Harjai

Basically you rewrote

M-3Z>0 to M>3Z
4Z-M>0 to 4Z>M

So far no mistake. But to get to 4 > M/Z > 3 means that you divided both sides by Z like so :

M-3Z>0 to M>3Z TO M/Z>3
4Z-M>0 to 4Z>M TO 4>M/Z

This forbidden as you don't know if Z is positive or negative. Remember if you multiply both sides of an inequality by a negative number you need to switch the inequal sign. Look :

-3 < -1 multiply both sides by -2 : 6 > 2

Hope its clearer now

Cheers and good luck for your exam
Camille

yes, good.

you can't divide an inequality by an unknown, unless you know the sign of that unknown.

[sudaif]

can someone please explain...how did they quickly rule out that statements 1 and statements 2 were insufficient?
when i encounter such a question, i tend to plug numbers which takes up quite a bit of time. is there a way to think about such inequality questions?
thanks.

[talk2pyus]

Thanks Jeff!! I thought answer was incorrect. I was so sure about that but then when i saw your explanation it opened my eyes. I must say this was the trickiest question I have ever encountered in my GMAT preparation till now and you explained it so well! Thanks!

[RonPurewal]

can someone please explain...how did they quickly rule out that statements 1 and statements 2 were insufficient?
when i encounter such a question, i tend to plug numbers which takes up quite a bit of time. is there a way to think about such inequality questions?
thanks.

when you see "< 0" or "> 0", you should consider the NUMBER PROPERTIES of POSITIVE/NEGATIVE/ZERO.

notice that these sign properties can give quick answers to the statement in the problem -- if both m and z are positive, then the answer will be "yes"; if both are negative, then the answer will be "no".

the first statement reduces to m > 3z, which can definitely be satisfied by two positive numbers, and can definitely be satisfied by two negative numbers. therefore, this statement is insufficient.

the second statement reduces to 4z > m, which can definitely be satisfied by two positive numbers, and can definitely be satisfied by two negative numbers. therefore, this statement is insufficient.

[harika.apu]

can someone please explain...how did they quickly rule out that statements 1 and statements 2 were insufficient?
when i encounter such a question, i tend to plug numbers which takes up quite a bit of time. is there a way to think about such inequality questions?
thanks.

when you see "< 0" or "> 0", you should consider the NUMBER PROPERTIES of POSITIVE/NEGATIVE/ZERO.

notice that these sign properties can give quick answers to the statement in the problem -- if both m and z are positive, then the answer will be "yes"; if both are negative, then the answer will be "no".

the first statement reduces to m > 3z, which can definitely be satisfied by two positive numbers, and can definitely be satisfied by two negative numbers. therefore, this statement is insufficient.

the second statement reduces to 4z > m, which can definitely be satisfied by two positive numbers, and can definitely be satisfied by two negative numbers. therefore, this statement is insufficient.

Hello Ron ,
i do understand what you have told in second paragraph ("notice that these...)
before starting with evaluating statements knowing this information was enough , but should i not consider m+z can be 0 also ?
what if one positive and other is negative ?
what if both of them are zeroes(although after going to statements this condition can't be true)


Thanks in advance for all help

[sahilk47]

can someone please explain...how did they quickly rule out that statements 1 and statements 2 were insufficient?
when i encounter such a question, i tend to plug numbers which takes up quite a bit of time. is there a way to think about such inequality questions?
thanks.

when you see "< 0" or "> 0", you should consider the NUMBER PROPERTIES of POSITIVE/NEGATIVE/ZERO.

notice that these sign properties can give quick answers to the statement in the problem -- if both m and z are positive, then the answer will be "yes"; if both are negative, then the answer will be "no".

the first statement reduces to m > 3z, which can definitely be satisfied by two positive numbers, and can definitely be satisfied by two negative numbers. therefore, this statement is insufficient.

the second statement reduces to 4z > m, which can definitely be satisfied by two positive numbers, and can definitely be satisfied by two negative numbers. therefore, this statement is insufficient.

Hello Ron ,
i do understand what you have told in second paragraph ("notice that these...)
before starting with evaluating statements knowing this information was enough , but should i not consider m+z can be 0 also ?
what if one positive and other is negative ?
what if both of them are zeroes(although after going to statements this condition can't be true)


Thanks in advance for all help

Hi Harika

If I may, in Data Sufficiency ("DS") questions, our objective is to determine the sufficiency/ insufficiency of the "Statement 1" and "Statement 2" for the purpose of solving the given question. As you have rightly mentioned we must also consider M+z = 0, however, as I put above, the objective of DS questions is to determine the sufficiency/ insufficiency of the given statements. Thus, if with the given statements (individually or combined) you are able to come up with (M+Z) not greater than 0 ( why? because question asks is M+Z > 0 ) then we can safely say that the respective statement or the combined statements (as the case may be) are insufficient to determine whether (M+Z) is greater than 0.

Thank you

[harika.apu]

Hi Harika

If I may, in Data Sufficiency ("DS") questions, our objective is to determine the sufficiency/ insufficiency of the "Statement 1" and "Statement 2" for the purpose of solving the given question. As you have rightly mentioned we must also consider M+z = 0, however, as I put above, the objective of DS questions is to determine the sufficiency/ insufficiency of the given statements. Thus, if with the given statements (individually or combined) you are able to come up with (M+Z) not greater than 0 ( why? because question asks is M+Z > 0 ) then we can safely say that the respective statement or the combined statements (as the case may be) are insufficient to determine whether (M+Z) is greater than 0.

Thank you[/quote]

Thank you sahil , i just was looking for more negative cases when one is actually enough to prove.