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Algebra Inequalities

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Source: — Data Sufficiency |
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by cramya » Sun Mar 22, 2009 7:07 pm
Question:

If x+y+z>1 is z > 1

(or)

Is x+y < -1 then we know z > 1

Stmt I

z > x+y+1

z-1 > x+y

Therefore z-1+z > 0 (replace x+y in x+y+z>0 by z-1)

2z>1

z>1/2

INSUFF

Stmt II

x+y < -1

Exactly what we need

SUFF

Choose B
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by cramya » Sun Mar 22, 2009 7:13 pm
Or another approach pick values

Stmt I

x= -.3 y=-.3 z=.9 NO

x=1 y=2 z=1000 YES

INSUFF

Stmt II

x + y < -1

-1+z>0 (since x+y < -1)

z > 1



SUFF

B
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by BlindVision » Sun Mar 22, 2009 7:20 pm
You are right, OA = B.

Thanks Cramya! It makes more sense now :D
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by apple100 » Tue Mar 24, 2009 11:12 pm
cramya wrote:Question:

If x+y+z>1 is z > 1

(or)

Is x+y < -1 then we know z > 1

Stmt I

z > x+y+1

z-1 > x+y

Therefore z-1+z > 0 (replace x+y in x+y+z>0 by z-1)

2z>1

z>1/2

INSUFF

Stmt II

x+y < -1

Exactly what we need

SUFF

Choose B

How did you derive
"If x+y+z>1 is z > 1" from the question?
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by lunarpower » Wed Mar 25, 2009 12:51 am
apple100 wrote:
How did you derive
"If x+y+z>1 is z > 1" from the question?
hi - you must be a newcomer to the gmat scene.

ALL data sufficiency questions can be expressed in this format:

statement 1 can be understood and answered as "if (statement 1), then (question prompt)?"

statement 2 can be understood and answered as "if (statement 2), then (question prompt)?"

if necessary, the combination of the two statements can be understood and answered as "if (both statements together), then (question prompt)?"

in fact, considering these questions as though they literally contained these "if"s and "then"s can be an invaluable problem-solving aid.
Ron has been teaching various standardized tests for 20 years.

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by lunarpower » Wed Mar 25, 2009 12:55 am
the most routine, and possibly most straightforward, way to answer this question is with the following standard fact about inequalities (note that the "alligator" is the "<" or ">" sign):

you can ADD inequalities if the alligators face the same way.

--

in statement (1), you know that
x + y + z > 0
and
z > x + y + 1

you can just add these together, giving x + y + 2z > x + y + 1. then cancel (i.e., subtract) the x and the y, giving 2z > 1, or z > 1/2. this is insufficient to answer the question of whether z is greater than 1.

--

in statement (2), you know that
x + y + z > 0
and
0 > x + y + 1 (i.e., the second statement, just written the other way so that the alligator is the same as the first one)

you can just add these together, giving x + y + z > x + y + 1. then cancel (i.e., subtract) the x and the y, giving z > 1.
sufficient.

ans (b)
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

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by apple100 » Wed Mar 25, 2009 3:28 am
lunarpower wrote:the most routine, and possibly most straightforward, way to answer this question is with the following standard fact about inequalities (note that the "alligator" is the "<" or ">" sign):

you can ADD inequalities if the alligators face the same way.

--

in statement (1), you know that
x + y + z > 0
and
z > x + y + 1

you can just add these together, giving x + y + 2z > x + y + 1. then cancel (i.e., subtract) the x and the y, giving 2z > 1, or z > 1/2. this is insufficient to answer the question of whether z is greater than 1.

--

in statement (2), you know that
x + y + z > 0
and
0 > x + y + 1 (i.e., the second statement, just written the other way so that the alligator is the same as the first one)

you can just add these together, giving x + y + z > x + y + 1. then cancel (i.e., subtract) the x and the y, giving z > 1.
sufficient.

ans (b)
perfect, thanks!
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