For a certain set of 3 numbers, is the average(arithmetic mean) equal

Question

For a certain set of 3 numbers, is the average(arithmetic mean) equal to the median?

(1) The range of the set is double the difference between the smallest number in the set and the middle number.

(2) The set consist of three numbers 10, 16 and 22.

Bunuel · Answer

For a certain set of 3 numbers, is the average (arithmetic mean) equal to the median?

Assume the numbers in ascending order are: a, b, and c.

The range of a set is the difference between the largest and smallest numbers of a set: Range=Largest-Smallest=c-a
The median of a set with odd # of elements is the middle number (when arranged in ascending or descending order): median=b.

Question: is (a+b+c)/3=b --> is a+c=2b?

(1) The range of the set is double the difference between the smallest number in the set and the middle number --> c-a=2(b-a) --> c+a=2b. Sufficient.

(2) The set consist of three numbers 10, 16 and 22 --> directly gives the numbers of the set so we can get the average as well as the median. Sufficient.

Answer: D.

enigma123 · Answer

For a certain set of 3 numbers, is the average (arithmetic mean) equal to the median?

(1) The range of the set is double the difference between the smallest number in the set and the middle number.
(2) The set consists of the three numbers 10, 16, and 22.

Bunuel · Answer

For a certain set of 3 numbers, is the average (arithmetic mean) equal to the median?

Let the 3 numbers in ascending order be: a, b, and c.

The range of a set is the difference between the largest and the smallest numbers of a set, so Range=Largest-Smallest=c-a;
The median of a set with odd # of numbers is the middle number (when arranged in ascending or descending order):, so median=b.

Question: is (a+b+c)/3=b --> is a+c=2b?

(1) The range of the set is double the difference between the smallest number in the set and the middle number --> c-a=2(b-a) --> c+a=2b. Sufficient.

(2) The set consist of three numbers 10, 16 and 22 --> directly gives the numbers of the set so we can get the average as well as the median. Sufficient.

Answer: D.

Hope it's clear.

manpreetsingh86 · Answer

let three numbers be x,y,z. Also we know that for an evenly spaced numbers mean= median.

suppose x,y,z are evenly spaced i.e. differene between first and second, and second and third is same. thus we have 
y-x=z-y
or 2y=x+z---------------------1)

let's consider st.1: 
z-x=2(y-x)
z-x=2y-2x
2y=z+x
as can be seen from 1, thus these numbers are evenly spaced. hence mean=median. therefore statement 1 alone is sufficient.

st.2 again clearly sufficient. as value of x,y,z are given to us.

hence answer should be D

EMPOWERgmatRichC · Answer

Hi All,

For anyone interested - a slightly tougher variation of this question appears in the new OG2016 (DS #135) - it's one of the *new* questions and it showcases the same logic.

GMAT assassins aren't born, they're made,
Rich

mbaaspirant80 · Answer

Say three numbers are X, Y , z in increasing order. Median = Y, hence range =Z-X ------equation(1)

take statement1:  range =2(Y-X)----------equation(2)
From equation(1) and equation(2)

2(Y-X)= Z-X .... 2Y-2X=Z-X this gives Z=2Y-X ----------equation(3)
average =  \frac{(X+Y+Z)}{3}  .... put the value from equation 3
average = Y = Median

Hence sufficient
 take statement2:  median =16 
 average = \frac{(10+16+22)}{3}  =  \frac{48}{3}  =16
Hence sufficient

Ans: D

For a certain set of 3 numbers, is the average(arithmetic mean) equal

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GMAT Data Sufficiency (DS) Questions

For a certain set of 3 numbers, is the average(arithmetic mean) equal

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