Tatto bought a notebook containing 96 pages leaves and numbered them which came to 192 pages. Tappo tore out the latter 25 leaves of the notebook and added the 50 numbers she found on those pages. Which of the following is not true?

a)
She could have found the sum of pages as 1990

b)
She could have found sum of pages as 1275

c)
She could have got sum of pages as 1375

d)
None of these

Correct answer is option 'A'. Can you explain this answer?

Question

Tatto bought a notebook containing 96 pages leaves and numbered them which came to 192 pages. Tappo tore out the latter 25 leaves of the notebook and added the 50 numbers she found on those pages. Which of the following is not true?

a)
She could have found the sum of pages as 1990
b)
She could have found sum of pages as 1275
c)
She could have got sum of pages as 1375
d)
None of these

Correct answer is option 'A'. Can you explain this answer?

Answer

Question is not clear. However we assume that pages were tore are in sequence and from anywhere in the book. Now if 25 pages are tore than first no will always be odd and last no will be even. Like if fist 25 pages are torn the first no is 1 and last no is 50. Odd+ even=always odd and for 25 pages. We can apply rule of ap which is sum = first + last * total no /2 which will be odd * 25 = odd so it cannot be an even no

Answer

Why is 'latter' used?

Answer

Given:
- Notebook contains 96 pages
- Numbered pages came to 192

Let's break down the given information:
- If the notebook contains 96 pages, then it should have 48 leaves (assuming each leaf has 2 pages).
- Since the numbered pages came to 192, it means that all the pages in the notebook have been numbered, including the front and back covers. Therefore, the notebook contains 96 numbered pages.

Now, Tappo tore out the latter 25 leaves of the notebook and added the 50 numbers she found on those pages. This means:
- Tappo tore out 50 pages (25 leaves)
- The sum of the page numbers on these 50 pages is added to the total sum of page numbers in the notebook.

To find the sum of all the page numbers in the notebook, we can use the sum of an arithmetic sequence formula:
S = (n/2)(a + l)
where S is the sum, n is the number of terms, a is the first term, and l is the last term.

Using this formula, we get:
S = (96/2)(1 + 96) = 96 x 97 / 2 = 4656

Now, let's consider the answer choices:
a) She could have found the sum of pages as 1990
- For Tappo to get a sum of 1990, she would have to tear out 52 pages (26 leaves) and add the sum of their page numbers to the sum of the notebook's page numbers.
- The sum of the page numbers on the torn-out pages would be 1990 - 4656 = -2666, which is not possible.

b) She could have found sum of pages as 1275
- For Tappo to get a sum of 1275, she would have to tear out 25 leaves (50 pages) and add the sum of their page numbers to the sum of the notebook's page numbers.
- The sum of the page numbers on the torn-out pages would be 1275 - 4656 = -3381, which is not possible.

c) She could have got sum of pages as 1375
- For Tappo to get a sum of 1375, she would have to tear out 25 leaves (50 pages) and add the sum of their page numbers to the sum of the notebook's page numbers.
- The sum of the page numbers on the torn-out pages would be 1375 - 4656 = -3281, which is not possible.

d) None of these
- This is a possible answer, as options a, b, and c are all not true.

Therefore, the correct answer is option a.

Answer

IF tatto tore out last 25 pages as implied by the word 'latter', one way is to find the sum which turns out to be even = 1050

I have no idea if sum of any 50 numbers will be even or odd as by the logic given in the answer

Answer

No of leaves= 96
pages count= 192

Pages tore= latter 25 leaves = latter 50 pages

So 192-50= 142
which means she tore from 143 to 192

According to Arithmetic progression,
a= 143
n= 50 (25leaves = 50 pages)
d= 1

S(n)= n/2 × [2a + (n-1)d]

S(50) = 50/2 × [2×143 + (50-1)1]

= 25 × [286 + 49]
= 25 × 335
= 8375

Therefore sum of latter 50 pages (25 leaves) = 8375 ,
which matches no option.
So 'D' is the correct option.

The question language is a bit confusing. But acc to what I get, I guess this is the right solution.

Answer

Correct answer is option 'A'.
Explanation

When sum of page numbers of 25 pages it will always be an odd numbers. So, see could not have found the sum of pages as 1990.

Answer

A

Answer

Odd+eve: odd
eve+eve: eve
odd+odd: eve
the page torn (either starting from even or from odd) must end with the same, that is if it had started with odd, it will end with odd and vise versa. so in either of the cases, option b and c is eliminated. there might be a possibility of option d as we don't know the page numbers of the torn pages, we assume the possibility of option a.

Answer

Option A

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