(e) The given integers are 4,4,4,8,10,20 and xLet x<4 Let x<4Mean =
50+x
7
, Median =4, Mode =4 If mean, median and mode are in AP then Here mean =4
50+x
7
=4⇒x=−22 Consider $( {b}) \ 4Mean =
50+x
7
,
54
7
<Mean<
58
7
Mean =x Mode =4 As these are in AP Mean =8∴x=6Consider $(\ {c}) 8\ {58}/{7}$ Median =8 Mode =4As these are in AP, Mean =12 i.e., x=34 ∴x can be −22,6 or 34 The sum of these is 18, which is not given in the options. If negative value of −22 is ignored then mean = median =mode=4. ∴ We have to select 40 answer in the given choices.