Is m+z>0?
m>3z
put m = 1, z= 0
1+0 >0.. YES
put m = -1, z = -2
-1-2<0.. NO
INSUFF
m<4z
put m = 0, z=1
0+1>0.. YES
put m= -10, z = -1
-10-1 <0.. NO
INSUFF
Combining:
m>3z
m<4z
3z<m<4z
4z<m+z<5z
4z<5z implies that z>0
m>3z
implies that m>0
Hence m+z>0
SUFF
pick C
DS-Prob 1
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Source: Beat The GMAT — Data Sufficiency |
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selango
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m+z>0?
stmt1,
m>3z
No info abt m and z signs.
Insuff
stmt2,
m<4z
No info abt m and z signs.
Insuff
Combining 1 and 2,
m>3z --A
m<4z or -m>4z--B
A+B-->7z>0 or Z>0
3z<m<4z
Since Z>,m must surely positive and m>0
Hence m+z>0
stmt1,
m>3z
No info abt m and z signs.
Insuff
stmt2,
m<4z
No info abt m and z signs.
Insuff
Combining 1 and 2,
m>3z --A
m<4z or -m>4z--B
A+B-->7z>0 or Z>0
3z<m<4z
Since Z>,m must surely positive and m>0
Hence m+z>0
--Anand--
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lunarpower
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to the original poster:
your error is here --
if this is not obvious, the obfuscation comes from the fact that the numbers are negative -- many people don't really have the proper intuition regarding negative numbers. however, the statement -15 < m < -20 is a lot like the statement 10 < m < 5; both are contradictory to themselves.
in fact, the statement 3z < m < 4z, by itself, proves that m and z are both positive, since "3z < 4z" is a false statement unless z is positive (and once you've established that z this positive, it follows that m must also be positive, since it's sandwiched between two positive values).
your error is here --
"-15 < m < -20" is impossible; a number can't be both greater than -15 and less than -20 at once.er.twi.fb wrote:let z=-5, then -15<m<-20 and suppose m=-16,so m+z=-5-16<0
if this is not obvious, the obfuscation comes from the fact that the numbers are negative -- many people don't really have the proper intuition regarding negative numbers. however, the statement -15 < m < -20 is a lot like the statement 10 < m < 5; both are contradictory to themselves.
in fact, the statement 3z < m < 4z, by itself, proves that m and z are both positive, since "3z < 4z" is a false statement unless z is positive (and once you've established that z this positive, it follows that m must also be positive, since it's sandwiched between two positive values).
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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On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
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Yves Saint-Laurent
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lunarpower
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by the way, this problem is from GMATPREP, and it has not been reproduced faithfully.
the original of the problem is:
Is m + z > 0 ?
(1) m - 3z > 0
(2) 4z - m > 0
note that this original form makes it much easier to combine the statements: just add them together!
once you've figured out that the two individual statements are insufficient, add them together:
m - 3z > 0
4z - m > 0
--------------
z > 0
once you figure out that z > 0, then realize that m > 3z, so m is also positive.
therefore m and z are also positive, so m + z > 0.
the original of the problem is:
Is m + z > 0 ?
(1) m - 3z > 0
(2) 4z - m > 0
note that this original form makes it much easier to combine the statements: just add them together!
once you've figured out that the two individual statements are insufficient, add them together:
m - 3z > 0
4z - m > 0
--------------
z > 0
once you figure out that z > 0, then realize that m > 3z, so m is also positive.
therefore m and z are also positive, so m + z > 0.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
GMAT/MBA Expert
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lunarpower
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just for fun, here's an awesome (but useless, in terms of takeaways/studying) solution!lunarpower wrote:the original of the problem is:
Is m + z > 0 ?
(1) m - 3z > 0
(2) 4z - m > 0
* first, eliminate statements 1 and 2 individually
* then, some magic:
multiply statement (1) by 5, and multiply statement (2) by 4
then add them!
you get:
5m - 15z > 0
16z - 4m > 0
-----------------
m + z > 0
i will now return to providing solutions that are actually useful :)
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
