CAT Practice : Number System

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Number Theory questions make us go from rigour to trial-and-error alternately. This is one such question.

Sum of first n natural numbers

    Q.2: A page is torn from a novel. The sum of the remaining page numbers is 10000. What is the sum of the two page-numbers on the torn page of this novel?
    1. 77 and 78
    2. 33 and 34
    3. 8 and 9
    4. None of these


  • Correct Answer
    Choice D. None of these

Detailed Solution

n (n + 1) / 2
should be nearby 10,000, so n (n + 1) is somewhere near 20,000. So n should be around about 141.

Try 142
142 * 143 = 10153
141 * 142 = 10011
So, the missing pages are either 76 and 77 or 5 and 6.

Correct Answer: None of these

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More questions from Number System

  1. Product of digits
  2. Sum of first n natural numbers
  3. Perfect Square
  4. Last two digits
  5. Multiples
  6. Greatest integer function
  7. Medians, Number
  8. 44th digit of a number
This idea is so good that it comes with an exclamation mark. N! holds marvels that you might not have noticed before. Enter here to see those.