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Question

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x, y are 10 and 25 respectively, then which of the following is false (x>y)

A
x2+y2=148
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B
xy=54
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C
xy=210
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D
x,y are rational numbers
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Solution

The correct option is D x,y are rational numbers
Given, 64+x+y8=10
x+y=16 (1)
x2in(¯x)2=25
x2+y2=148 (2)
(x+y)22xy=148
xy=54 (3)
Using equations (1),(2) and (3), we get
x=8+10 and y=810 (x>y)
xy=210
Clearly x,y are irrational numbers

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