Civil Services Prep

Prelims 2022 · CSAT / Logical Reasoning · Question 29

In the series AABABCABCDABCDE.., which letter appears at the 100th place?

  1. G
  2. H
  3. I
  4. J

Answer

I

Re-checking the series: it is grouped as A | AB | ABC | ABCD | ABCDE | .... Total letters after n groups = n(n+1)/2.

Now, 13×14/2 = 91 and 14×15/2 = 105. So the 100th letter lies in the 14th group: ABCDEFGHIJKLMN.

Its position within that group is 100 − 91 = 9. The 9th letter is I.

Option check:

  • (a) G: 7th letter of the 14th group. Incorrect.
  • (b) H: 8th letter. Incorrect.
  • (c) I: 9th letter; matches the 100th place. Correct.
  • (d) J: 10th letter. Incorrect.

So the earlier conclusion of (d) was a calculation mistake; the correct answer is (c).

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