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

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AbdurRakib
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If x, y, and z are distinct integers, which integer is the median of t [#permalink] New post   Updated on: 15 Nov 2018, 04:08
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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


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Why C is not the correct answer? :? :? Please help me to understand
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E

Originally posted by AbdurRakib on 01 Sep 2015, 23:30.
Last edited by Bunuel on 15 Nov 2018, 04:08, edited 2 times in total.
Formatted the question.
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manpreetsingh86
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink] New post   03 Sep 2015, 11:58
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AbdurRakib wrote:
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


Kudos Please :)

Show Spoiler
Why C is not the correct answer? :? :? Please help me to understand


st. 1) let x = 0, and y= 2 then x+y = 2,hence z>2 and min. value of z = 3. so in this case median is y(= 2). Also, since no relationship is given between x and y, so y can also be equal to 0 and x can also be equal to 2. so in this case median is x(=2).

hence st. 1 is not sufficient.

st. 2)
x>y now clearly this statement doesn't provide any information about z. hence st.2 alone is not sufficient.

st.1 + st. 2

here the important thing to consider is that x,y and z can also be negative. so let's assume that x =0 and y =-2, then x+y = -2 and z>-2

now if z is positive, then median will be x(=0). if z is negative, then our three numbers will be -2,-1,0. (-1>-2). in this case median will be z (=-1).

hence answer should be E.
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink] New post   03 Sep 2015, 10:43
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AbdurRakib wrote:
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


Kudos Please :)



Why C is not the correct answer? :? :? Please help me to understand


In order to determine the median, you need to arrange the elements of the set in ascending order. So,lets try to determine that from the statements we have:-
Statement 1: x+y <z..
This cannot help us determine in any way if x>y or if x> z or if z is the smallest of the 3 numbers. So this statement is not sufficient.

Statement 2: x> y
This helps us know that x>y. But again we have no information about z.. So again, not sufficient

Statement1 + Statment 2: Again we see that despite the fact the x>y, we still cannot establish a relation between y and z or even y and z. So again not sufficent.

Hence option E
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink] New post   04 Sep 2015, 04:32
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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] New post   04 Sep 2015, 04:57
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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Your actual solution is very difficult to find in the quoted post and your advertisement. Can you please reduce the size of your advertisement text? or better put it in your signatures. This way your posts will be useful for people in this forum.

Also, put the quoted post in proper formatting, so that your actual post is clearly visible.

Thanks
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Re: If x, y, and z are distinct integers, which integer is the median of t [#permalink] New post   20 Jul 2019, 00:50
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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] New post   10 Aug 2019, 02:53
x+y>z implies x< z and y<z . statment one not sufficient
x>y alone does not answer
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] New post   10 Aug 2019, 03:13
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saiprasanna wrote:
x+y>z implies x< z and y<z . statment one not sufficient
x>y alone does not answer
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] New post   11 Aug 2019, 03:32
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saiprasanna wrote:
x+y<z implies x< z and y<z . statment one not sufficient
x>y alone does not answer
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] New post   13 Nov 2022, 03:44
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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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