Xavier Aptitude Test 2014 Paper

Question : 59 of 103

Marks: +1, -0

x, 17, 3x – y

^{ 2}

– 2, and 3x + y

^{2}

– 30, are four consecutive terms of an increasing arithmetic sequence. The sum of the four numbers is divisible by:

Solution:

(a) since

x, 17,3 x-y^{2}-2

and

3 x+y^{2}-30

are in A.P.

\∴ 17-x=3 x+y^{2}-30-3 x+y^{2}+2

⇒ x + 2y

^{2}

= 45 ............(i)
Also,

17-x=3 x-y^{2}-2-17

\⇒ 4 x-y^{2}=36

..........(ii)
Solving equations (i) and (ii), we get

x=13 .

Now, x + 17 + 3x – y

^{2}

– 2 + 3x + y

^{2}

– 30
= 7x – 15 = 7 (13) – 15 = 76
Out of the given options, 76 is only divisible by 2.

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