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HI rahulkashyap, OA given is A, maximum students would miss out on a crucial point and ans C but the answer should be E.

xz < 0 MEANS " Is x and z of OPPOSITE sign?"

1) |x+y| = |x| + |y| This tells us that x and y are of SAME sign.. But what about z? Insuff

2) |y+z| = |y| + |z| This tells us that z and y are of SAME sign.. But what about x? Insuff

combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient..

BUT what if y is 0 1) |x+y| = |x| + |y|..... y = 0...... x can be POSITIVE or NEGATIVE 2) |y+z| = |y| + |z|..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign Insuff

HI rahulkashyap, OA given is A, max would miss out on a ccrucial point and ans C but the answer should be E.

xz < 0 MEANS " Is x and z of OPPOSITE sign?"

1) |x+y| = |x| + |y| This tells us that x and y are of SAME sign.. But what about z? Insuff

2) |y+z| = |y| + |z| This tells us that z and y are of SAME sign.. But what about x? Insuff

combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient..

BUT what if y is 0 1) |x+y| = |x| + |y|..... y = 0...... x can be POSITIVE or NEGATIVE 2) |y+z| = |y| + |z|..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign Insuff

E

Amazing skill displayed by pointing out 'y=0' case. +1. Thanks chetan2u _________________

------------------------------ "Trust the timing of your life" Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

I got this wrong. I need to remember these problems can always be zero.
_________________

I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

=> Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 3 variables and 0 equation, E is most likely to be the answer.

Conditions 1) & 2)

From the condition 1) and 2), |x+y| = |x| + |y| is equivalent to xy ≥ 0 and |y+z| = |y| + |z| is equivalent to yz ≥ 0. Then we have xy^2z ≥ 0 or xz ≥ 0.

x = 1, y = 0, z = 1 implies xz = 1 > 0. x = -1, y = 0, z = 1 implies xz = -1 < 0.

Both conditions together are not sufficient.

The answer is E.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Thus, E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously, there may be cases where the answer is A, B, C or D.
_________________

HI rahulkashyap, OA given is A, maximum students would miss out on a crucial point and ans C but the answer should be E.

xz < 0 MEANS " Is x and z of OPPOSITE sign?"

1) |x+y| = |x| + |y| This tells us that x and y are of SAME sign.. But what about z? Insuff

2) |y+z| = |y| + |z| This tells us that z and y are of SAME sign.. But what about x? Insuff

combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient..

BUT what if y is 0 1) |x+y| = |x| + |y|..... y = 0...... x can be POSITIVE or NEGATIVE 2) |y+z| = |y| + |z|..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign Insuff

E

For the answer to be E, even if x or z=0, that would work, correct?

RHS is the summation of two positive numbers i.e |x|+|y|, so LHS must be equal to this. this is only possible when both are of equal sign i.e {+,+} or {-, -} or x=y=0. If either of the two numbers have different sign i.e{+,-}, then |x+y| will yield a less value and hence will not be equal to RHS

I got this wrong. I need to remember these problems can always be zero.

Hey,

Would you please share your knowledge about "these" problems? What pattern in questions are you referring to? I have got the idea but want to get extra sure from you. Thank you
_________________

------------------------------ "Trust the timing of your life" Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

I got this wrong. I need to remember these problems can always be zero.

Hey,

Would you please share your knowledge about "these" problems? What pattern in questions are you referring to? I have got the idea but want to get extra sure from you. Thank you

The point of this question is the following property.

\(|x+y| = |x| + |y|\) is equivalent to \(xy ≥ 0\).
_________________

RHS is the summation of two positive numbers i.e |x|+|y|, so LHS must be equal to this. this is only possible when both are of equal sign i.e {+,+} or {-, -} or x=y=0. If either of the two numbers have different sign i.e{+,-}, then |x+y| will yield a less value and hence will not be equal to RHS