Average of a set of 75 different integers is 50.If 0,45,55,100,50 are

Question

Average of a set of 75 different integers is 50.If 0,45,55,100,50 are removed from the set,what will be average of the remaining integers in the set?

A)50
B)75
C)100
D)125
E)150

broall · Answer

It remains the same.

Assume that set X has 75 diffirent integers. Average of X is 50 so the Sum of X is $50 \times 75$.

5 elements {0, 45, 55, 100, 50} are removed. The sum of these 5 elements is 
$0+45+55+100+50=(0+100)+(45+55)+50=100+100+50=250=50\times 5$

Hence, the new average of X' is $\frac{50 \times 75 -50 \times 5}{75-5}=\frac{50 \times 70}{70}=50$

The answer is A.

MathRevolution · Answer

Sum: 75 * 50 = 3750
Total numbers = 75

Removal of total sum: 0 + 45 + 55 + 100 + 50 = 250  
Removal of total numbers: 5

New Average =  \frac{3500 }{ 70} = 50

Answer A

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