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# Is x + 2y -­ 3z > 0 ?

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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
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Imo E.
Is $$x + 2y -­ 3z > 0$$ ?

(1) $$4x ­- 3y ­- z > 0$$

No info about x or y or z.
x , y and z all cannot be zero .
but the exact values not known . So insufficient .

(2) $$3x + 2z -­ 5y > 0$$

No info about x or y or z.
x , y and z all cannot be zero .
but the exact values not known . So insufficient .

Combining 1 and 2 .
Adding the 2 equation also will not give any info on the individual x ,y or z .
Subtracting .. eq 1 - eq 2.
=
x + 2y -­ 3z .. but we cannot be very sure that subtraction will lead a positive value .
So insufficient .

Hence E is the correct ans .
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
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Is x+2y−­3z>0x+2y−­3z>0 ?

(1) 4x­−3y­−z>0
Clearly we cannot decide

(2) 3x+2z−­5y>0
Clearly cannot be decided since we cannot reduce it to the original question

1 and 2 can only be added in this cases since both are greater than 0 hence from the final addition the solution cannot be deducted
Possible ans is E
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
Is x+2y−­3z>0?

(1) 4x­−3y­−z>0
Cannot be determined from (1)
Not sufficient

(2) 3x+2z−­5y>0
Cannot be determined from (2)
Not sufficient

(1) + (2)
7x-8y+z>0

Still cannot determine whether x+2y−­3z>0

Not sufficient
Option E

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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
HoneyLemon wrote:
Imo E.
Is $$x + 2y -­ 3z > 0$$ ?

(1) $$4x ­- 3y ­- z > 0$$

No info about x or y or z.
x , y and z all cannot be zero .
but the exact values not known . So insufficient .

(2) $$3x + 2z -­ 5y > 0$$

No info about x or y or z.
x , y and z all cannot be zero .
but the exact values not known . So insufficient .

Combining 1 and 2 .
Adding the 2 equation also will not give any info on the individual x ,y or z .
Subtracting .. eq 1 - eq 2.
=
x + 2y -­ 3z .. but we cannot be very sure that subtraction will lead a positive value .
So insufficient .

Hence E is the correct ans .

Bunuel can you, please, explain why we can subtract the inequalities, getting a result according to our stem and still have E as the answer? IMO statement 1 - statement 2 results in x + 2y - 3z > 0 or what happens with the part "> 0"?

Cheers
Rudolf
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
chetan2u wrote:
Bunuel wrote:
Is $$x + 2y -­ 3z > 0$$ ?

(1) $$4x ­- 3y ­- z > 0$$

(2) $$3x + 2z -­ 5y > 0$$

THREE variables and that too an INEQUALITY.
The answer should be E in most cases unless one of the statements can be converted to the question inequality or both statements can add up to the question inequality.

(1) $$4x ­- 3y ­- z > 0$$

(2) $$3x + 2z -­ 5y > 0$$

None of the can be modified to read $$x + 2y -­ 3z > 0$$.
Also when we add up the two statements, we get 7x-8y+z>0. Also we can find relations, in terms of inequality, between any two variables.
But we cannot answer the given question.

E

chetan2u you state that either (1) or (2) have to result in the equation in the stem or their sum. Why not their subtraction?

Cheers
Rudolf
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
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rudywip wrote:
chetan2u wrote:
Bunuel wrote:
Is $$x + 2y -­ 3z > 0$$ ?

(1) $$4x ­- 3y ­- z > 0$$

(2) $$3x + 2z -­ 5y > 0$$

THREE variables and that too an INEQUALITY.
The answer should be E in most cases unless one of the statements can be converted to the question inequality or both statements can add up to the question inequality.

(1) $$4x ­- 3y ­- z > 0$$

(2) $$3x + 2z -­ 5y > 0$$

None of the can be modified to read $$x + 2y -­ 3z > 0$$.
Also when we add up the two statements, we get 7x-8y+z>0. Also we can find relations, in terms of inequality, between any two variables.
But we cannot answer the given question.

E

chetan2u you state that either (1) or (2) have to result in the equation in the stem or their sum. Why not their subtraction?

Cheers
Rudolf

Rudolf,

I meant all inclusive in 'the statements add up to ...' . Basically I meant, whatever we do to both of them, may be multiply with some integers and then add/subtract these , or whatever mathematical operations one can do to get to the original equation.
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
chetan2u but if we subtract 1 and 2, will the result not be the inequality mentioned in the stem? If not, kindly explain why.

Cheers
Rudolf
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Is x + 2y -­ 3z > 0 ? [#permalink]
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Bunuel wrote:
Is $$x + 2y -­ 3z > 0$$ ?

(1) $$4x ­- 3y ­- z > 0$$

(2) $$3x + 2z -­ 5y > 0$$

One way to simplify the problem is to let z=0 and test values for x and y.
If z=0, the problem becomes:

Quote:
Is x+2y > 0?

1. 4x-2y > 0
2. 3x-5y > 0

Both statements are satisfied if x=2 and y=1.
In this case, x+2y > 0, so the answer to the rephrased question stem is YES.
Both statements are satisfied if x=2 and y=-1.
In this case, x+2y=0, so the answer to the rephrased question stem is NO.
Since the answer is YES in the first case but NO in the second case, the two statements combined are INSUFFICIENT.

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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
rudywip wrote:
chetan2u but if we subtract 1 and 2, will the result not be the inequality mentioned in the stem? If not, kindly explain why.

Cheers
Rudolf

Can someone expain this. Bunuel
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
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swim2109 wrote:
rudywip wrote:
chetan2u but if we subtract 1 and 2, will the result not be the inequality mentioned in the stem? If not, kindly explain why.

Cheers
Rudolf

Can someone expain this. Bunuel

We can add any qualities but we can't subtract inequalities.

Consider these two inequalities:
2 < 3
1 < 3

If we add the inequalities we get: 3 < 6, which is true.
If we subtract the second inequality from the first inequality, we get: 1 < 0, which is not true.

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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
Bunuel wrote:
Is $$x + 2y -­ 3z > 0$$ ?

(1) $$4x ­- 3y ­- z > 0$$

(2) $$3x + 2z -­ 5y > 0$$

Project DS Butler Data Sufficiency (DS3)

This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
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Re: Is x + 2y -­ 3z > 0 ? [#permalink]
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