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# If x, y, and z are distinct integers, which integer is the median of t

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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
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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.

If x, y, and z are distinct integers, which integer is the median of the set {x, y, z}?

(1) x+y<z

(2) x>y

In the original condition we have 3 variables (x,y,z) and since we need to match the number of variables and equations we need 3 equations. Since there is 1 each in 1) and 2), E is likely the answer.
Using both 1) & 2) together we have x=1, y=-1, z=2 thus median=x, but if x=1, y=-10, z=-1 then the median=z. therefore the answer is not unique, and the conditions are not sufficient. The answer is E.
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
MathRevolution wrote:
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.

If x, y, and z are distinct integers, which integer is the median of the set {x, y, z}?

(1) x+y<z

(2) x>y

In the original condition we have 3 variables (x,y,z) and since we need to match the number of variables and equations we need 3 equations. Since there is 1 each in 1) and 2), E is likely the answer.
Using both 1) & 2) together we have x=1, y=-1, z=2 thus median=x, but if x=1, y=-10, z=-1 then the median=z. therefore the answer is not unique, and the conditions are not sufficient. The answer is E.

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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
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MathRevolution wrote:
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.

If x, y, and z are distinct integers, which integer is the median of the set {x, y, z}?

(1) x+y<z

(2) x>y

In the original condition we have 3 variables (x,y,z) and since we need to match the number of variables and equations we need 3 equations. Since there is 1 each in 1) and 2), E is likely the answer.

Using both 1) & 2) together we have x=1, y=-1, z=2 thus median=x, but if x=1, y=-10, z=-1 then the median=z. therefore the answer is not unique, and the conditions are not sufficient. The answer is E.

So the big take away from your answer is that if x+y<z then it is not always true that both x & y are smaller than z... may be one of x & y is negative (e.g. y is negative) and making x+y smaller instead of summing up to a bigger number... and third number z is smaller than x.. Good Point!!!
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
x+y>z implies x< z and y<z . statment one not sufficient
now ombining , x>y and y<z gives us the median . In my opinion C is correctBunuel can you help here
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
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saiprasanna wrote:
x+y>z implies x< z and y<z . statment one not sufficient
now ombining , x>y and y<z gives us the median . In my opinion C is correctBunuel can you help here

The answer is E because we cannot get a single numerical value of the median. Just saying that it's y is not enough, you should be able to get the value of y statements to be sufficient.
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
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saiprasanna wrote:
x+y<z implies x< z and y<z . statment one not sufficient
now ombining , x>y and y<z gives us the median . In my opinion C is correctBunuel can you help here

z>x+y DOES NOT imply z>x and z>y. THIS is precisely the trap!
Test this by substituting values. if x=4, y=-2 and z=3. x+y= 2 and so, z>x+y BUT z<x.

Hope this makes things more clear
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink]
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