Let's discuss a problem from the AMC 2021 Middle Primary Category: Problem 22 which revolves around puzzle.

Question

The biscuit section in a cookbook has 6 pages. The sum of all the page numbers in this section is 147 . What is the number of the last page in this section of the book?

(A) 26
(B) 27
(C) 28
(D) 29
(E) 30

Solution

To number the pages we want $6$ consecutive numbers .

Let's try to check the nearest numbers divisible by $6$.
If we multiply $6 \times 20 = 120$ which is less than the number that we have to get : $147$.

If we multiply $6\times 30 = 180$ which is more than the number that we have to get : $147$.

So the required number will be in between $20$ and $30$.
As the number is bigger than 120 so let's try to take the first number as $20$ then rest of the 5 consecutive numbers.
Adding the numbers: $20+21+22+23+24+25 = 135$. This is less than $147$.
Let's see how much less we are getting: $147 - 135 = 12$.

So, instead of starting from $20$ if we start from $22$ we will get :
$22 + 23+ 24+ 25 +26 + 27 = 147$.

So the last page number is $27$.

What is AMC (Australian Mathematics Competition)?

The Australian Mathematics Competition (AMC) is one of Australia's largest and oldest annual mathematics competitions, aimed at fostering interest and excellence in mathematics among student

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