UPSC Prelims 2008 · General Studies

Question 2: Logical Reasoning and Mental Ability

What is the number of terms in the series 117, 120, 123, 126, ..., 333?

a72

b73

c76

d79

AnswerThe answer is (b).

The terms form an arithmetic progression with first term 117 and common difference 3, so the nth term is 117 + (n - 1) x 3. Setting this equal to 333 gives (n - 1) x 3 = 216, so n - 1 = 72 and n = 73. The count of terms is the gap divided by the step, plus one for the first term.

Why each option is right or wrong

(a) 72 is the number of steps; it forgets to add one for the first term.
(b) (333 - 117) / 3 + 1 = 73, counting both end terms.
(c) 76 does not follow from a step of 3; a gap of 216 gives 72 steps.
(d) 79 is too large; 72 steps plus the first term gives only 73.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2008, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.