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

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Difficulty:   75% (hard)

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

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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.

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Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

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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.

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Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

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

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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.
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Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

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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.

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Re: If x, y, and z are positive integers, then what is the value of the mo  [#permalink]

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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
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