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UPSC Prelims

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

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CSAT 2020

Q14 2020, CSAT 2020

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?

1. एक पुस्तिका, जिसके पन्ने सामान्य रूप से हैं, पहले पन्ने की संख्या 1 से प्रारम्भ करते हुए अंकित हैं। इस पुस्तिका से एक पन्ना फाड़ लिया जाता है। बचे हुए पन्नों पर अंकित पृष्ठ संख्याओं का योग 195 है। फटे हुए पन्ने पर निम्न में से कौन-सी संख्याएँ है?

Explanation Please wait..

After tearing away the page, we get a sum of 195 from remaining page numbers. Since, numbers are in sequence, we use arithmetic progression.

Sum of consecutive numbers from 1 to n = n(n+1)/2 = 195 or n(n+1)= 390 with one page torn.

If we add the digits on torn page, we will get a number more than 390.

For n to be an integer, the minimum possible value of n(n+1) over 390 is received when we put n = 20

So, n(n+1) = 20 × 21 = 420

So, sum of 20 pages = n(n+1)/2 = (20 × 21)/2 = 210

Hence, sum of the two numbers on the torn page = 210 – 195 = 15

Only option b gives 15 as sum.

Hence, 7,8 is the answer.

व्याख्या Please wait..

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