DisciplinedPrep wrote:
Adam tears off a page from his textbook. The sum of the remaining page numbers is 10000. What are the two page-numbers on the torn-off pages of his textbook?
A. 8 and 9 or 76 and 77
B. 33 and 34 or 5 and 6
C. 77 and 78 or 8 and 9
D. 97 and 98 or 77 and 78
E. 76 and 77 or 5 and 6
Let the numbers be a and b, and total pages be n, so sum of n pages = \(\frac{n(n+1)}{2}=10000+a+b....n(n+1)=20000+2(a+b)\)
Thus 20000+2(a+b) should be the product of two consecutive numbers n and n+1..
You can check from choices or look for the squareroot of 20000, which is closer to 140..
So if 140 pages are there..14*141=19740<20000, so take next value of n as 141
141*142=20022, so look for 2(a+b) = 22...a+b=11...From choices 5 and 6 fit in
Answer is B or E
Take next value of n as 142, so 142*143=20306...look for 2(a+b)=306...a+b=153...Only 76+77=153 fits in
E
Hi, I did not get your explanation like how you solved it and what approach you used. Can you explain me a different approach?