Is m+z > 0?

Deepthi Subbu wrote:
Is m + z > 0?

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

Here's my complete solution . . .
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
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

Deepthi Subbu wrote: Say z=1, m<4, so if m is negative say -10 , m+z < 0
Say m=3 , m<4, so m+z>0.

Hence shouldnt the OA be E ?

The part in green is not right.

Statement 1 says that m - 3z > 0
So, it cannot be the case that z = 1 and m = -10 (as you suggest above)
If we plug these values into the left side of the inequality, we get:
-10 - (3)(1)
= -13
And it is not the case that -13 > 0

Cheers,
Brent

if anyone is in the mood for a fireworks show --
once you get to the (c) vs. (e) part... try multiplying statement 1 by 5, multiplying statement 2 by 4, and then adding the stuff you get.
sha-boom!
like a boss.

(this is not my recommended way of solving the problem... but it's awesome.)

ksutthi wrote:Got this from practice test 1. Can somebody help?

Is m+z > 0?

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

We must determine whether the sum of m and z is greater than zero.

Statement One Alone:

m – 3z > 0

We can manipulate the inequality in statement one to read: m > 3z

However, we still cannot determine whether the sum of m and z is greater than zero. Statement one alone is insufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

4z – m > 0

We can manipulate the inequality in statement two to read: 4z > m

However, we still cannot determine whether the sum of m and z is greater than zero. Statement two alone is insufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using our statements together, we can add together our two inequalities. Rewriting statement 2 as –m + 4z > 0, we have

m – 3z > 0
+ (-m +4z > 0)
z > 0

Since we know that z > 0 and that m > 3z (from statement one), m must also be greater than zero. Thus, the sum of m and z is greater than zero.

Answer: C