If x, y, and z are positive integers, is x - y - z positive ?

Question

(1) x > y

(2) y > z

Bunuel · Accepted Answer

It's straight E. When we combine the statements we get that x > y > z but this does not mean that x is greater than the sum of y and z:

If x = 100, y = 2 and z = 1, then x - y - z is positive.
If x = 3, y = 2 and z = 1, then x - y - z is NOT positive.

Answer: E.

MulanQ · Answer

hahaha.. nice trap!!!

Cadaver · Answer

E.....3,2,1 not possible

dontquixote · Answer

Algebraic approach

In order for X - Y - Z to happen you need the following condition to be met.

X - (Y + Z). You factor out the negative in Y and Z to make -(Y + Z)

The statement does not give you anything related to this.

It does give you X > Y > Z however this still has nothing to do with the above requirement.

Temurkhon · Answer

Is x-y-z>0?

means, Is x>y+z OR x-y>z OR x-z>y?

St1 Or St2 not suff.

St1 And St2 means x>y>z. None of above. INSUFF

E

hvelas93 · Answer

x-y-z positive? y/n translates into

x>y-z? y/n

1) x>y
insufficient, we don't know anything about z

2) y>z
insufficient, we don't know anything about x

1+2) 
combine the inequalities
x+y>y+z
x>z 
Insufficient, we don't know anything about y

Choice E

CrackverbalGMAT · Answer

An effective approach in solving this question is to analyse till a particular stage and then use simple values to prove the statements/combination insufficient. 
x, y and z are positive integers. To find out if x-y-z is positive, we have to find out if x-y-z>0. To do this, it’s sufficient to find out if x>y+z.

From statement I alone, x>y. This is insufficient to find out if x>y+z since we do not have any information about z. 
For example, if x = 2, y = 1 and z = 1, x>y BUT x = y+z. On the other hand, if x = 5, y = 1 and z = 1, x>y AND x>y+z.
Statement I alone is insufficient to determine if x>y+z. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, y>z. This is insufficient to find out if x>y+z since we do not have any information about x. 
For example, if x = 3, y = 2 and z = 1, y>z BUT x = y+z. On the other hand, if x = 5, y = 2 and z = 1, y>z AND x>y+z.
Statement II alone is insufficient to determine if x>y+z. Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, we have the following:
From statement I, we have x>y; from statement II we have y>z. Therefore, x>y>z. This is insufficient to determine if x>y+z.
If x = 3, y = 2 and z = 1, x = y+z. But, if x = 5, y = 2 and z = 1, x>y+z. The combination of statements is insufficient to determine a unique YES or NO. Answer option C can be eliminated.

The correct answer option is E .

Hope that helps!

AnkithaSrinivas · Answer

takeaway: if x is greater than y and z does not mean x is greater than the sum.

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.

If x, y, and z are positive integers, is x - y - z positive ?

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

GMAT Data Sufficiency (DS) Questions

If x, y, and z are positive integers, is x - y - z positive ?

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