All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

a. 44

b. 45

c. 10

d. 12

How can we get the number of pages in the book?

Question

Answer

The given numbers must be divisible by the L. C. M of (7,10,15,21,28)

Answer

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

a. 44

b. 45

c. 10

d. 12

How can we get the number of pages in the book?

Answer

The answer is 10

when u get n=44 by hit and trial, initially there were 44 pages and their sum was (44 × 45)/2 = 990

Since the given sum is 1000, so we can say that the page number 10 was added twice.

Answer

When n(n+1)/2 + x = 1000
by trail and error
44(45)/2 + x =1000 [ taking n as 44]
990 + x = 1000
hence, no. added twice is 10.

I don't know what's wrong in this method

Answer

Solution:
Let's assume that the page number that was added twice is x.

To solve the problem, we need to use the formula for the sum of the first n natural numbers:

Sum of first n natural numbers = n(n+1)/2

We know that the sum obtained by adding all the page numbers is 1000, so we can write:

1 + 2 + 3 + ... + x-1 + x + x+1 + ... + n = 1000

We can simplify this equation by using the formula for the sum of the first n natural numbers:

n(n+1)/2 - x + x + n(n+1)/2 = 1000

Simplifying this equation, we get:

n(n+1) = 2000

We need to find the value of x, which is the page number that was added twice. We know that x is less than or equal to n, so we can try different values of n to find the value of x that satisfies the equation.

If we try n = 44, we get:

44(44+1) = 1980

This value is too small, so we need to try a larger value of n. If we try n = 45, we get:

45(45+1) = 2070

This value is too large, so we need to try a value of n between 44 and 45. If we try n = 44.5, we get:

44.5(44.5+1) = 2022.75

This value is closer to 2000, so we can try values of x around 22.5, which is half of 44.5.

If we try x = 22, we get:

44.5(44.5+1)/2 - 22 + 2(22) = 1000

This equation is true, so the page number that was added twice is 22+1 = 23.

Therefore, the correct answer is option (c) 45.

Answer

Suggest how to check whether the number divisible by 7 or not

Answer

Can u explain me in briefly

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