Inequalities - please help

[sachin_yadav]

Is M + Z > 0
(1) M - 3Z > 0
(2) 4Z - M > 0

OA is C

I did this question in 1 min 37 secs and i thought it to be correct (selected E)
However,it is C
I am confused when i combine the two statements. I get Z > 0. When i plug in the value of Z in statement (2) i get m < 4. This gives E as the answer.

When i plug in the value of Z in statement (1) i get m > 3. This gives C as the answer.

Please help me identifying my mistake.

Please reply

Thanks & Regards
Sachin

[Brent@GMATPrepNow]

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

Target question: m + z > 0

Statement 1: m - 3z > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 4 and z = 1, in which case m + z is greater than 0
Case a: m = 4 and z = -10, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 4z - m > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 1 and z = 4, in which case m + z is greater than 0
Case a: m = -10 and z = 1, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Rearrange statement 1 to get: -3z + m > 0
Statement 2: 4z - m > 0
Since both inequality signs are facing the same direction, we can add the two given inequalities to get: z > 0
In other words, z is positive.

If z is positive, then 3z is positive, and if 3z is positive then m must be positive (since we know that 3z < m)

If z and m are both positive, then m + z must be greater than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

[Brent@GMATPrepNow]

Is m+z>0

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

Here's another way to handle the two statements combined....

Target question: Is m + z > 0?

Statement 1: m - 3z > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 4 and z = 1, in which case m + z is greater than 0
Case a: m = 4 and z = -10, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 4z - m > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 1 and z = 4, in which case m + z is greater than 0
Case a: m = -10 and z = 1, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Rearrange statement 1 to get: -3z + m > 0
Statement 2: 4z - m > 0

Multiply both sides of -3z + m > 0 by 5 to get: -15z + 5m > 0
Multiply both sides of 4z - m > 0 by 4 to get: 16z - 4m > 0

Since both inequality signs are facing the same direction, we can ADD the two green inequalities to get: z + m > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

[Brent@GMATPrepNow]

Is M + Z > 0
(1) M - 3Z > 0
(2) 4Z - M > 0


I am confused when i combine the two statements. I get Z > 0. When i plug in the value of Z in statement (2) i get m < 4. This gives E as the answer.

Not sure what you mean by plugging in the value of z.
If z is positive, then statement 2 says: 4(some positive number) - m > 0
Add m to both sides to get: 4(some positive number) > m
This doesn't suggest that the answer is E

Cheers,
Brent

[GMATinsight]

Is M + Z > 0
(1) M - 3Z > 0
(2) 4Z - M > 0

Hi Sachin,

You can also get the answer by plugging in the values

Question: Is M + Z > 0

The answer has to be in the form of YES or NO

Statement 1) M - 3Z > 0

@M= 1 and Z=1 the result is Negative therefore answer is NO
@M= 10 and Z=1 the result is Positive therefore answer is YES
Inconsistent answer therefore INSUFFICIENT

Statement 2) 4Z - M > 0
@M= 10 and Z=1 the result is Negative therefore answer is NO
@M= 1 and Z=1 the result is Positive therefore answer is YES
Inconsistent answer therefore INSUFFICIENT

Combining the two statements

M - 3Z > 0 and 4Z - M > 0
M > 3Z and M < 4Z
Therefore
3Z < M < 4Z

Also if you add the two equation the we get
M - 3Z + 4Z - M > 0
Z > 0

Combining both inferences we can conclude that both Z and M must be positive.

Therefore M + Z must be positive and greater than 0

SUFFICIENT

Answer : Option C

[sachin_yadav]

Is M + Z > 0
(1) M - 3Z > 0
(2) 4Z - M > 0


I am confused when i combine the two statements. I get Z > 0. When i plug in the value of Z in statement (2) i get m < 4. This gives E as the answer.

Not sure what you mean by plugging in the value of z.
If z is positive, then statement 2 says: 4(some positive number) - m > 0
Add m to both sides to get: 4(some positive number) > m
This doesn't suggest that the answer is E

Cheers,
Brent

Brent,

Thank you so much for your reply.
As you said 4(some positive number) > m and z > 0
Suppose if z = 1, then we get 4 > m or m < 4
Now here we can take negative values of m such as m = -4
Now, m + z > 0
m = -4
z = 1
-4 + 1 > 0
-3 > 0 (that is not possible)

Now if i say m = 3 and z = 1
3 + 1 > 0 (true)

This is the only reason why i am selecting E

Regards
Sachin

[Brent@GMATPrepNow]

In your example, you are ignoring statement 1, which says that 4Z - M > 0. So, you are basically demonstrating that statement 2 ALONE is not sufficient. In other words, if we take statement 2 ALONE, then we can't any conclusions about whether or not m + z > 0.

Likewise, statement 1 ALONE is not sufficient.

However, if we consider statements 1 AND 2, we have sufficient information.

Cheers,
Brent

[sachin_yadav]

I think i am not getting you.

I combined both (1) and (2) and got z > 0. Now i am confused where to put this z > 0 to get m.
Should i put in statement (1) or statement (2)
This is the same thing that we do in algebra such as 2x + 3y > 5 and 3x + 4y > 10. Adding them and plugging the value in one of the equations to get another value.

I think this is what we are supposed to do here. I am plugging z > 0 in both the equations, but i am getting different values.

Regards
Sachin

[GMATinsight]

I think i am not getting you.

I combined both (1) and (2) and got z > 0. Now i am confused where to put this z > 0 to get m.
Should i put in statement (1) or statement (2)
This is the same thing that we do in algebra such as 2x + 3y > 5 and 3x + 4y > 10. Adding them and plugging the value in one of the equations to get another value.

I think this is what we are supposed to do here. I am plugging z > 0 in both the equations, but i am getting different values.

Regards
Sachin

Hi Sachin,

You are missing on one thing

Combining the two statements

M - 3Z > 0 and 4Z - M > 0
M > 3Z and M < 4Z
Therefore
3Z < M < 4Z

Also if you add the two equation the we get
M - 3Z + 4Z - M > 0
Z > 0 [You got this already]

If you take any value of Z>0 then you may get different values of M but all values have to be within the range 3Z and 4Z

But more importantly you should also understand that since Z is positive therefore M will also be positive finally rendering the value of M + Z as positive and greater than 0

Therefore SUFFICIENT

Answer : Option C

[sachin_yadav]

I got it. I missed on this one and was going for E. Thanks and really appreciate it.

Hi Sachin,

You are missing on one thing

Combining the two statements

M - 3Z > 0 and 4Z - M > 0
M > 3Z and M < 4Z
Therefore
3Z < M < 4Z

Also if you add the two equation the we get
M - 3Z + 4Z - M > 0
Z > 0 [You got this already]

If you take any value of Z>0 then you may get different values of M but all values have to be within the range 3Z and 4Z

But more importantly you should also understand that since Z is positive therefore M will also be positive finally rendering the value of M + Z as positive and greater than 0

Therefore SUFFICIENT

Answer : Option C