if X,Y, Z are positive distinct non zero integers is x(y-z)

Question

if X,Y, Z are positive distinct non zero integers is x(y-z) greater than y(x-z)

1) y>x
2) x>z

pls show working...

christoph · Answer

is x(y-z) > y(x-z) ? the variables are non-zero-integers and +ve. thats why we can simplify very easy. xy-xz > xy-zy => -xz +zy > 0 => x (y-x) > 0 ? 

1) is sufficient because the number in brackets is always +ve.

2) is insufficient. try z=1 x=3 y=2 (NO) or z=1 x=3 y=20 (YES)

HIMALAYA · Answer

the question is: is x(y-z)>y(x-z)? or, (xy-xz)>(xy-yz)? or yz>xz or y>x (because x, y, and z are positive integers)?

so stateent (i) is sufficient.
statement ii is not sufficient because if x>z, it has nothing to do with the information given in the question.

So A is correct.......................................................

HIMALAYA · Answer

the question is: is x(y-z)>y(x-z)? or, (xy-xz)>(xy-yz)? or yz>xz or y>x (because x, y, and z are positive integers)?

so stateent (i) is sufficient.
statement ii is not sufficient because if x>z, it has nothing to do with the information given in the question.

So A is correct.......................................................

ywilfred · Answer

if X,Y, Z are positive distinct non zero integers is x(y-z) greater than y(x-z)

1) y>x
2) x>z 


We're told x, y and z are positive and they are all distinct (means all three are different numbers).

x(y-z) > y(x-z)
xy-xz > yx-yz
xy-yx > xz-yz
yz>xz
y>x

so the real question is aksing you if y is greater x ?

From 1), we know y is greater than x, so 1) is sufficient.
From 2), we know nothing about y. so 2) is nto suffiient.

A is the answer.

ywilfred · Answer

For DS questions, always try to see if you can simplify the expressions to a point where the question is very simply answered. 

And for yes/no type of questions, you just need to verify if the statements is sufficient for you to answer a yes or a no to judge it's sufficiency.

Antmavel · Answer

A too ywilfred already explained everything very well so no need to repeat it :wink:

AJB77 · Answer

x,y,z are distinct and positive integers. We are asked if: x(y-z) > y(x-z) => xy-xz > yx-yz => -xz > -yz => x < y (Since z >= 1) So we need to find is x < y ? S1 gives us that directly, so is sufficient. S2 x > z tells us nothing about the value of x with respect to y so insufficient. Answer is A

Darth_McDaddy · Answer

Thanks for the tip Ywilfred. I started solving the DS by plugging in values, and found that it was taking me a lot of time. I will simplify the DS from now on... and then check the choices

Arsene_Wenger · Answer

I failed this question because i failed to read the question closely (my usual problem). On arriving at yz>xz, i refused to divide by 'z' because 'z' could have been zero. I forgot the question said 'non zero integers'. 

But guys, please confirm. had we not been told that x,y and z are non-zero integers, then we will not have been able to divide by 'z'.

It's a clear (A).

if X,Y, Z are positive distinct non zero integers is x(y-z)

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