The average of three numbers is -4. If a fourth number is added, the a

Question

The average of three numbers is -4. If a fourth number is added, the arithmetic mean of all four numbers is -1. What is the fourth number?

(A) 210
(B) 2
(C) 8
(D) 10
(E) 16

100mitra · Answer

Correct Option C = 8 
a+b+c = (-4*3) = -12 ----(1)
a+b+c+d = (-1*4) = -4 ---(2)
From (1) and (2)
a+b+c+d = -4
-12 + d = -4
d = 12-4
d = 8
 Option C

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supriya3196 · Answer

Correct Option C = 8 
average of 3 numbers is -4 so total value = -4*3 = -12
Average of 4 numbers is -1 so total value = -1*4 = -4

sum of 3 numbers + 4th number = -4
4th number = -4 +12 = 8.

CrackverbalGMAT · Answer

#First Approach:

The number added has two parts that consists of,

(a) Contribution to the average of the group

(b)Contribution made as an increase/decrease in the group

For (a),the new average once the 4th value enters the list = -1 and hence  contribution to the average of the group is -1

For (b),the new number increased the average from -4 to -1 and hence contributed+3 to each of the 3 terms.

Total contribution of increase = 3 * 3 =9 and hence total contribution made as an increase in the group

The number thus is sum of both these contributions

=-1 + 9 =8

Alternately, 
#SecondApproach
Given average of 3 numbers is -4

Sum of these 3 numbers = Average * Number of Numbers

=-4*3 = -12

Given average of 4 numbers is -1

Sum of these numbers = Average * Number of Numbers

= -1*4 = -4

Sum of 3 numbers + 4th number =Sum of all 4 numbers = -4

Thus, the 4th number = -4 -Sum of 3 numbers

= -4 +12

= 8
 (option c)
 
  D.S
GMAT SME

Sunoonazeez · Answer

average of 3 numbers is -4
ie. (A+B+C)/3 = -4
=>A+B+C=-12

Now adding a number x makes the average -1
ie. (A+B+C+X)/4=-1
=>A+B+C+X=-4
As A+B+C=-12 , X=-4-(-12) =8
 
So IMO answer is 8 (option c)

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