UPSC Prelims 2021 CSAT Paper II · Q26 of 79 Mental Ability medium

Replace the incorrect term by the correct term in the given sequence 3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40 where odd terms and even terms follow the same pattern.

  1. (a) 0 ✓ UPSC's answer
  2. (b) 1
  3. (c) 3
  4. (d) 6

Why the answer is (a)

• The sequence is divided into two alternating series: odd-positioned terms (3, 7, 13, 21, 31, 43) and even-positioned terms (2, 4, 10, 18, 28, 40).",

"- The odd-positioned series follows the pattern of adding consecutive even numbers: 3+4=7, 7+6=13, 13+8=21, 21+10=31, 31+12=43. This series is correct.",

"- The even-positioned series should follow the same pattern of adding consecutive even numbers starting from the first term.",

"- Starting with 2, the next term should be 2+4=6, but the given term is 4. Thus, 4 is incorrect and should be replaced by 6.",

"- However, the question asks to replace the incorrect term with the correct one from the options. Let's re-evaluate the pattern for the even series: 2, 4, 10, 18, 28, 40. Differences are 2, 6, 8, 10, 12. The first difference is 2, which breaks the pattern of adding 4, 6, 8, 10, 12.",

"- If the first even term was 0, the series would be 0, 4, 10, 18, 28, 40. Differences: 4, 6, 8, 10, 12. This matches the pattern perfectly. Therefore, the first even term (2) is incorrect and should be 0.

Why the other options are wrong

(b) 1
Replacing 2 with 1 results in differences of 3, 6, 8, 10, 12, which does not follow the consistent even-number increment pattern.
(c) 3
Replacing 2 with 3 results in differences of 1, 6, 8, 10, 12, which does not follow the consistent even-number increment pattern.
(d) 6
Replacing 2 with 6 results in differences of -2, 4, 8, 10, 12, which does not follow the consistent even-number increment pattern.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

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