2020 CSAT, all questions
UPSC Prelims 2020 · CSAT
Question 14: Basic Numeracy
One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers?
a5, 6
b7, 8
c9, 10
d11, 12
AnswerUPSC’s answer is (b).
A torn leaf carries two pages, 2k - 1 and 2k, so the torn pages sum to 4k - 1. The booklet total is N(N + 1)/2 with N even. N = 20 gives 210, and 210 - 195 = 15 = 4k - 1, so k = 4: pages 7 and 8. N = 18 is too small (171), and N = 22 leaves 58, which is not of the form 4k - 1.
Why each option is right or wrong
- (a) 5 + 6 = 11 would leave 199 from 210, not 195.
- (b) Right: 7 + 8 = 15 and 210 - 15 = 195.
- (c) 9 + 10 = 19 would leave 191.
- (d) 11 + 12 = 23 would leave 187.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.