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

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10 00:00

Difficulty:   95% (hard)

Question Stats: 37% (01:37) correct 63% (01:15) wrong based on 179 sessions

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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

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

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Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

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

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1
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]

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1
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

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]

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1
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.

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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.

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Thanks
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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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1
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]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 57297
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
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]

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1
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  Re: If x, y, and z are distinct integers, which integer is the median of t   [#permalink] 11 Aug 2019, 03:32
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# If x, y, and z are distinct integers, which integer is the median of t

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