If x, y, and z are positive numbers, is x - y

Question

If x, y, and z are positive numbers, is  x - y < z ?

(1)  x + y < z

(2)  xy < z^2

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zhanbo · Answer

(1) Only
x + y < z
So
x - y = (x + y) - 2y < z -2y
Because y > 0
z - 2y < z
So x - y < z
Sufficient

(2) Only
(i) If x = 8, y = 1, z = 3
xy<z^2
x-y>z
(ii) If x = 1, y = 8, z = 3
x - y < z
Not sufficient.

The answer is thus (A).

$!vakumar.m · Answer

If x, y, and z are positive numbers, is \(x - y < z\)?

(1) \(x + y < z\)

(2) \(xy < z^2\)

This is a Data Sufficiency Butler Question

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Show Answer

Official Answer

A

Fdambro294 · Answer

A Property of Inequalities:
It will always be true that for positive values X and Y, the DIFFERENCE between the two positive values will ALWAYS be LESS THAN the SUM of those two positive values

I.e.,
if X and Y are positive numbers, it will always be true that:

(X - Y) < (X + Y)

We are given that X, Y, and Z are positive
Is (x - y) < z?

Statement 1: (x + y) < z
And
It will always be true for any two positive numbers that: (x - y) < (x + y)

Transitive Property of Inequalities tells us:

(x - y) < (x + y) < z

Always YES; statement 1 is sufficient alone

Statement 2: XY < Z^2

case 1: x = 1 , y = 1 , z = 2 ———> YES

Case 2: x = 8 , y = 1 , z = 3 ——-> NO

Statement 2 is not sufficient alone

*A*

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If x, y, and z are positive numbers, is x - y < z ?

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