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## Is m+z > 0?

tagged by: Brent@GMATPrepNow

This topic has 6 expert replies and 16 member replies
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Deepthi Subbu Master | Next Rank: 500 Posts
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Sat Jul 27, 2013 4:13 am
Even after we figure out that z>0, to find the if m is also > 0, we may substitute the value of z is each of the 2 equations -

1) m-3z > 0

Since m> 3z, m is greater than 0. Hence m+z>0.
(2) 4z-m > 0

4z>m.

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 ?

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Brent@GMATPrepNow GMAT Instructor
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Sat Jul 27, 2013 5:42 am
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

Cheers,
Brent

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Brent@GMATPrepNow GMAT Instructor
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Sat Jul 27, 2013 5:49 am
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

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lunarpower GMAT Instructor
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Tue Aug 06, 2013 1:31 am
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.)

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faraz_jeddah Master | Next Rank: 500 Posts
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Tue Aug 06, 2013 6:52 am
lunarpower wrote:
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.)
Word!

Nina1987 Senior | Next Rank: 100 Posts
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Wed Dec 23, 2015 6:17 pm
Ron,
Is there a systematic way of coming up with such multiples?
Also what is your recommended way of solving such questions? Thank you

lunarpower wrote:
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.)

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Matt@VeritasPrep GMAT Instructor
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Sun Dec 27, 2015 5:49 pm
Nina1987 wrote:
Is there a systematic way of coming up with such multiples?
Yup, just look for the multiples that will give you coefficients that cancel out upon summation, if such multiples exist.

For instance, here you're looking for two numbers r and s such that

rm - sm = m

4sz - 3rz = z

i.e. r - s = 1 and 4s - 3r = 1. This works for r = 5 and s = 4, so those are our multipliers.

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Scott@TargetTestPrep GMAT Instructor
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Tue Dec 05, 2017 5:17 pm
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.

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