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Question

The mean & variance of 7 observations are 8,16 respectively. If 5 of the observations are 2,4,10,12,14, then the LCM of remaining two observations is

A
16
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B
24
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C
20
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D
14
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Solution

The correct option is D 16
Observation :-(2,4,10,12,14,x,y)
mean=2+4+10+12+14+x+y7
8=42+(x+y)
56=42+(x+y)
x+y=14....(1)
Variance =(meanx;)2N
16=[(82)2(14)2+(810)2+(812)2+(814)2(8x)2+(8y)2]7
112=36+16+4+16+36+(8x)2+(8y)2
112=108+(8x)2+(8y)2
(8x)2(8y)2=4
|8x|=0, |8y|=2
(x=10or6andy=8)or(x=8y=10or6)
x+y=14(x,y)=(6,6)or(8,6)
LCM(x,y)= LCM of 6 and 8=24

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