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

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)

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.

The answer is therefore 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?

(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

The answer is C

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