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A... from eq xy+z=z , we know xy is 0... for lx-yl>0 x-y ≠ 0... si) x ≠ 0 so y=0 and x-y will be a -ive or +ive no... suff sii) y=0... x can be 0 or any other no ...not suff
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xy + z = z; Cancel z: xy = 0. This implies that either x or y (or both) is 0.

(1) x ≠ 0. Since x is not 0, then y = 0. Thus the question becomes is |x| > 0. The absolute value of a non-zero number (x) is always positive. So, we have a definite YES answer to the question. Sufficient.

(2) y = 0. The question becomes is |x| > 0. If x = 0, then the answer is NO but if x ≠ 0, then the answer is YES. Not sufficient.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

Is xy + z = z, is |x-y| > 0 ?

(1) x ≠ 0 (2) y = 0

in the original condition we have xy+z=z, xy=0 and the question asks for |x-y|>0? Since we have 2 variables and 1 equation, in order to match the number of variables and equations we need 1 more equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), y = 0 thus the answer is always yes. Therefore it is sufficient. In case of 2), x = 2 and y = 0 thus the answer is yes, but if x = 0 and y = 0 the answer is no. Therefore it is not sufficient. The answer is A
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xy + z = z; Cancel z: xy = 0. This implies that either x or y (or both) is 0.

(1) x ≠ 0. Since x is not 0, then y = 0. Thus the question becomes is |x| > 0. The absolute value of a non-zero number (x) is always positive. So, we have a definite YES answer to the question. Sufficient.

(2) y = 0. The question becomes is |x| > 0. If x = 0, then the answer is NO but if x ≠ 0, then the answer is YES. Not sufficient.

Answer: A.

Hope it's clear.

Hi Bunuel..well this analysis is clear and many thanx for it, but i went through a different route.. modulus of any number is always greater than zero...isn't it? so either satement alone could be the answer.

In a recent exapmple this was the approach adopted

the question was something like this (actual number may diifer)Is -7*mod(4x-y)<14?? It was explained that modulus of 4x-y would always be positive and when multiplied by a negative number it will always be negative...and THERE IS NO NEED TO ACTUALLY SOLVE...the inequality...

Hi Bunuel..well this analysis is clear and many thanx for it, but i went through a different route.. modulus of any number is always greater than zero...isn't it? so either satement alone could be the answer.

In a recent exapmple this was the approach adopted

the question was something like this (actual number may diifer)Is -7*mod(4x-y)<14?? It was explained that modulus of 4x-y would always be positive and when multiplied by a negative number it will always be negative...and THERE IS NO NEED TO ACTUALLY SOLVE...the inequality...

Why can't we appply this approach here as well?

Desparately need cl;arification

The absolute value of a number is always greater than or equal to 0. What I mean is that |x| = 0, when x = 0.
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