GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Jun 2020, 20:38 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x, y, and z are distinct integers, which integer is the median of t

Author Message
TAGS:

### Hide Tags

Director  B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 516
GPA: 2.81
If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

13 00:00

Difficulty:   95% (hard)

Question Stats: 35% (01:44) correct 65% (01:18) wrong based on 215 sessions

### HideShow timer Statistics

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

Originally posted by AbdurRakib on 01 Sep 2015, 22:30.
Last edited by Bunuel on 15 Nov 2018, 03:08, edited 2 times in total.
Formatted the question.
Intern  Joined: 09 Jun 2015
Posts: 9
Concentration: Statistics, Technology
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

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
Manager  Joined: 13 Jun 2013
Posts: 248
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

2
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).

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9022
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

1
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.
_________________
CEO  G
Joined: 20 Mar 2014
Posts: 2545
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

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.

If you know our own innovative logics to find the answer, you don’t need to

actually solve the problem.
http://www.mathrevolution.com
- The one-and-only World’s First Variable Approach for DS and IVY Approach

for PS that allow anyone to easily solve GMAT math questions.

- The easy-to-use solutions. Math skills are totally irrelevant. Forget

conventional ways of solving math questions.

- The most effective time management for GMAT math to date allowing you to

solve 37 questions with 10 minutes to spare

- Hitting a score of 45 is very easy and points and 49-51 is also doable.

http://www.mathrevolution.com/gmat/lesson

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

Thanks
Intern  B
Joined: 13 Jul 2019
Posts: 2
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

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!!!
Intern  B
Joined: 22 May 2019
Posts: 11
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 64227
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

1
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.
_________________
Manager  S
Joined: 18 Apr 2019
Posts: 78
Location: India
GMAT 1: 720 Q48 V40
GPA: 4
Re: If x, y, and z are distinct integers, which integer is the median of t  [#permalink]

### Show Tags

1
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  Re: If x, y, and z are distinct integers, which integer is the median of t   [#permalink] 11 Aug 2019, 02:32

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