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CAT 2008 — QA Question 18

Miscellaneous ProgressionsEasy
Passage / Data

Directions for next 2 questions:

The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

Find the sum 1+112+122+1+122+132+.....+1+120072+120082

Answer & solution

  • 2008-12008

  • B

    2007-12007

  • C

    2007-12008

  • D

    2008-12007

  • E

    2008-12009

Solution

Consider only first term,

1+112+122 = 1+1+14 = 94 = 32 = 2-12

Now consider fisrt two terms,

1+112+122 + 1+122+132 = 32 + 1+14+19 = 32 + 4936 = 32+76 = 83 = 3-13

Similarly,

1+112+122 + 1+122+132 + ... + 1+120072+120082 = 2008-12008

Hence, option (a).

CAT 2008 QA Q18: Find the sum 1 + 1 1 2 + 1 2 2 + 1 + 1 2 2 + 1 3 2 + . . . . . + 1 + 1 2007 2 + 1 2008 2 — Solution | TheCATExam