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

 It is currently 19 Jan 2020, 03:56

### 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

# If x, y, and z are positive integers, then what is the value of the mo

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60484
If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

### Show Tags

12 Dec 2019, 00:06
00:00

Difficulty:

75% (hard)

Question Stats:

43% (01:53) correct 57% (01:55) wrong based on 35 sessions

### HideShow timer Statistics

Competition Mode Question

Data set A is {x, 2x+y, 2y, y+z, x+z}.
If x, y, and z are positive integers, then what is the value of the mode of Data set A?

(1) x is equal to one half of y and twice of z

(2) The median of Data set A is equal to 125.

Are You Up For the Challenge: 700 Level Questions

_________________
Director
Joined: 07 Mar 2019
Posts: 573
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

### Show Tags

12 Dec 2019, 03:15
1
Data set A is {x, 2x+y, 2y, y+z, x+z}.
If x, y, and z are positive integers, then what is the value of the mode of Data set A?
Mode = element appearing most number of times in Data Set A = ?

(1) x is equal to one half of y and twice of z
x = y/2 and x = 2z
y = 4z
So, Data Set A = {2z, 8z, 8z, 5z, 3z}
Since z is not known.

INSUFFICIENT.

(2) The median of Data set A is equal to 125.
Nothing is known about any element. No relationship.

INSUFFICIENT.

Together 1 and 2.
Data Set A = {2z, 3z, 5z, 8z, 8z}
Median = 5z
5z = 125
z = 25
Mode = 8z = 200

SUFFICIENT.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5693
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

### Show Tags

12 Dec 2019, 03:44
1
#1
x is equal to one half of y and twice of z
x=y/2
x=2z
we can have set A= (4,16,16,12,8 ) and ( 5,20,20,15,10)
y=8 , x =4 z=4 and y=10 x=5 z=5
insufficient
#2
The median of Data set A is equal to 125
4x+4y+z=625
insufficient
from 1&2
we know
x=y/2
x=2z
so
13x=625
x= 48 ,y = 96 z = 24
mode = ( 48,192,192,120,72) ; 192

sufficient

IMO C

Data set A is {x, 2x+y, 2y, y+z, x+z}.
If x, y, and z are positive integers, then what is the value of the mode of Data set A?

(1) x is equal to one half of y and twice of z

(2) The median of Data set A is equal to 125
VP
Joined: 24 Nov 2016
Posts: 1069
Location: United States
If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

### Show Tags

Updated on: 13 Dec 2019, 04:21
Quote:
Data set A is {x, 2x+y, 2y, y+z, x+z}.
If x, y, and z are positive integers, then what is the value of the mode of Data set A?

(1) x is equal to one half of y and twice of z

(2) The median of Data set A is equal to 125.

The mode is the most frequent VALUE in a set. If there is none more frequent, then there is no mode.

(1) x is equal to one half of y and twice of z insufic

x=y/2=2z: {x, 2x+y, 2y, y+z, x+z} = {2z, 8z, 8z, 5z, 3z} = 8z mode;
but what is the value of z?

(2) The median of Data set A is equal to 125. insufic

(1 and 2) sufic

median {2z, 8z, 8z, 5z, 3z} = 5z = 125, z = 25;
mode = 8z = 8(25) = 200.

Ans (C)

Originally posted by exc4libur on 12 Dec 2019, 04:16.
Last edited by exc4libur on 13 Dec 2019, 04:21, edited 2 times in total.
Director
Joined: 18 May 2019
Posts: 646
Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

### Show Tags

12 Dec 2019, 09:57
1
We are given the data set A to be {x, 2x+y, 2y, y+z, x+z}, whereby x,y, and z are positive integers.
we are to determine the mode.

Statement 1: x is equal to one half of y and twice of z
From statement 1, x=y*1/2 meaning y=2x, and x=2z meaning z=x/2. Substituting these values into the set yields
A = {x, 2x+2x, 2(2x), 2x+0.5x, x+0.5x} = {x, 4x, 4x, 2.5x, 1.5x}
From the data, we know that the mode is 4x.
But what is the value of x? We don't know, hence there are infinite possibilities. All that we can infer from the given information is that x is even. Statement 1 is insufficient.

Statement 2: The median of Data set A is equal to 125.
Clearly, statement 2 is insufficient. We don't know whether the elements of set A are ordered. The fact that 2y cannot be 125 means that the elements in set A are not ordered.

1+2:
From one we have set A = {x, 4x, 4x, 2.5x, 1.5x} reordered A = {x, 1.5x, 2.5x, 4x, 4x}.
from this set, the midian is 2.5x and the mode is 4x.
Statement 2 states that the median is 125.
Hence 2.5x=125
x=125/2.5 = 1250/25 = 50.
The mode is, therefore, =4*50 = 200.

Senior Manager
Joined: 25 Jul 2018
Posts: 467
Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

### Show Tags

12 Dec 2019, 19:11
1
Data set A is {x, 2x+y, 2y, y+z, x+z}.
If x, y, and z are positive integers, then what is the value of the mode of Data set A?

(Statement1): x is equal to one half of y and twice of z
—> x =( 1/2)y, —> y = 2x
—> x = 2z, —> z= (1/2)x

Set A = {x, 4x, 4x, 2.5x, 1.5x }
—> SetA= {x, 1.5x, 2.5x, 4x, 4x}
No info about what the value of x is.
Insufficient

(Statement2): The median of Data set A is equal to 125.
x,y,z — any positive integers. We can’t find the median of the set.
Insufficient

Taken together 1&2,
—> 2.5x = 125
x = 50
—> Set A = { 50. 75, 125, 200, 200}
The mode is 400.
Sufficient

Posted from my mobile device
Re: If x, y, and z are positive integers, then what is the value of the mo   [#permalink] 12 Dec 2019, 19:11
Display posts from previous: Sort by