AP ICET 2016 Paper

Question : 16 of 200

Marks: +1, -0

If a is the average of the numbers 1,2, 3 and x, what is the value of x?
I. x is an integer
II.

x=\;\;{1}/{2}(6a-x)

if the statement 1 alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Solution:

Given

a={1+2+3+x}/4

⇒4a=6+x

...(i)
I. It gives no additional information on ‘a’ or its relation with x .
∴ I alone is not sufficient.
Given :

x=1/2(60-x)

....(ii)
There are two unknowns (a and x) and we have two distinct equations (i) and(ii) , Hence these can be solved to find x.
eg.

x=1/2[6/4(6+x)-x]⇒4x=18+3x-x

⇒x=9

∴ II alone is sufficient

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