Dillesh4096 wrote:
The sum of the page numbers after a page is removed from a book is 1000. Find the 2 page numbers on the removed page of this book.
A. 7 and 8
B. 10 and 11
C. 17 and 18
D. 21 and 22
E. 5 and 6
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Looking at the answer choices, we notice that the sum of page numbers removed from the book could be as small as 5 + 6 = 11 or as large as 21 + 22 = 43. Therefore, the actual sum of the pages before any pages were removed should be between 1000 + 11 = 1011 and 1000 + 43 = 1043.
Let’s test some numbers for the pages of books until we find a number between 1011 and 1043. As the formula for the sum of consecutive integers from 1 to n is n(n + 1)/2 and the square root of 1000 is around 30, a good place to start is:
(30 * 31)/2 = 465 - too low
(50 * 51)/2 = 1275 - too high
(40 * 41)/2 = 820 - too low
(45 * 46)/2 = 1035 - success
Since n = 45 results in a number between 1011 and 1043, the book can have a total of 45 pages. All we have to do now is to find an answer choice which adds up to 1035 - 1000 = 35.
A) 7 + 8 = 15
B) 10 + 11 = 21
C) 17 + 18 = 35
So, we know that the book had 45 pages and the sum of the page numbers was 1035 before any page was removed. After the page with page numbers 17 and 18 was removed, the sum of the remaining numbers was 1035 - (17 + 18) = 1000. The answer is C.
Answer: C
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