Xavier Aptitude Test 2011 Paper

Question : 35 of 101

Marks: +1, -0

In a list of 7 integers, one integer, denoted as x is unknown. The other six integers are 20, 4, 10, 4, 8 and 4. If the mean, median , and mode of these seven integers are arranged in increasing order, they form an arithmetic progression. The sum of all possible ways of x is

Validate

Solution:

(e) The given integers are

4,4,4,8,10,20

and

x

Let

x<4

Let

x<4

Mean

=\ {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=6

Consider $(\ {c}) 8\ {58}/{7}$
Median

=8

Mode

=4

As 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.

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