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 ?
Is m+z > 0?
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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
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The part in green is not right.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 ?
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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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.)
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.)
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
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Voit esittää kysymyksiä Ron:lle myös suomeksi
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Word!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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Ron,
Is there a systematic way of coming up with such multiples?
Also what is your recommended way of solving such questions? Thank you
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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Yup, just look for the multiples that will give you coefficients that cancel out upon summation, if such multiples exist.Nina1987 wrote: Is there a systematic way of coming up with such multiples?
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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We must determine whether the sum of m and z is greater than zero.ksutthi wrote:Got this from practice test 1. Can somebody help?
Is m+z > 0?
(1) m-3z > 0
(2) 4z-m > 0
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
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