Question 1161905
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The two pages have consecutive page numbers.<br>
We can find the page numbers using estimation and logical reasoning.<br>
(1) Looking at the first three digits "715", we can see that they lie between 26^2=676 and 27^2 = 729.  So the two page numbers are in the 260's.<br>
(2) The units digit of the product is 6.  The product of two consecutive integers has units digit 6 if the two units digits are either 2 and 3 or 7 and 8.<br>
(3) Since 715 is closer to 729 than to 676, the two page numbers must be 627 and 628.<br>
The answer is verified by multiplying those two numbers and seeing that the product is indeed 71556.<br>
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Comments added after seeing three responses to your question made after I made mine....<br>
In terms of efficiency, if you have a calculator, the quickest way to find the answer is as shown by tutor @ikleyn: take the square root of 71556 to find that it is about 627.5, making the two page numbers 627 and 628.<br>
If you do not have a calculator, then estimation and logical reasoning will get you to the answer in far less time than the method shown by the other two tutors.<br>
Finding the answer by finding the prime factorization of 71556 and then finding how to combine those factors to get two consecutive integers takes a lot of work.  An average person will get the final answer to the problem in less time than it takes an average person to find the prime factorization -- not to mention the time it takes to play with that prime factorization to find the two page numbers.<br>