Is x + 2y - 3z 0 ?

Question

Is  x + 2y - 3z > 0  ?

(1)  4x - 3y - z > 0

(2)  3x + 2z - 5y > 0

Project DS Butler Data Sufficiency (DS3) 
 For DS butler Questions  Click Here

chetan2u · Answer

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

HoneyLemon · Answer

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 .

alwaysHP · Answer

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

GCMEMBER · Answer

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

Posted from my mobile device

itsarudolf · Answer

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

itsarudolf · Answer

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

chetan2u · Answer

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.

itsarudolf · Answer

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

chetan2u · Answer

Hi

Even if you have to subtract, you never subtract the same side, because we don’t know how much equation is greater than other side.

For example 
7>6
5>1
7-5>6-1......NO
But 7+5>6+1

Another example 
3>0 and 5>0
3-5>0-0....-2>0......NO

GMATGuruNY · Answer

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

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.

E

swim2109 · Answer

Can someone expain this.  Bunuel

BrentGMATPrepNow · Answer

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.

More here:
 https://www.youtube.com/watch?v=S_fjYmCtvy0

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is x + 2y - 3z > 0 ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Is x + 2y -­ 3z > 0 ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Is x + 2y - 3z > 0 ?