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12 Days of Christmas GMAT Competition 2025 - Day 10: Lena keeps all of

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topgmat25

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27 Dec 2025, 07:09

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Exactly 252.08 means that:

pages/books = 252.08 = 25208/100 = 6302/25

If pages=6302 then books=25
If pages=2*6302 then books=2*25=50
If pages=3*6302 then books=3*25=75
...

books = 25n
pages = 6302n

(1)
2*7 < 25n < 7*7
14 < 25n < 49

n must be 1, books = 25n = 25

Condition (1) is sufficient

(2)
6302n < 10000

n must be 1, books = 25n = 25

Condition (2) is sufficient

The answer is D

geocircle

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27 Dec 2025, 07:25

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Pages = Books * 252.08 = Books * 25208/100 = Books * 6302/25

Books and Pages are integers, so Books is a multiple of 25.

(1)
Books is at least 2*7=14 and at most 7*7=49 -> Books must be 25.

Condition sufficient

(2)
Pages < 10000
If Books=25, Pages=6302
If Books=50, Pages=2*6302 > 10000 -> not possible

Books must be 25.

Condition sufficient

Answer D

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27 Dec 2025, 07:42

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Bunuel

Lena keeps all of her books on 7 wooden shelves. The average (arithmetic mean) number of pages per book in her collection is exactly 252.08. How many books does she have?

(1) Each shelf contains between 2 and 7 books, inclusive.
(2) The total number of pages across all of her books is less than 10,000.

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avg number of pages per book = 252.08 = 25208/100 = 6302/25

So total pages to be an int , number of books should be a multiple of 25

(1) Each shelf contains between 2 and 7 books, inclusive.
min: 2*7 =14
max: 7*7 = 49
only multiple of 25 is 25.

Sufficient.

(2) The total number of pages across all of her books is less than 10,000.
n*252.08 < 10,000
n < 39.67
n <=39
only multiple of 25 is 25.

Sufficient.
Correct Answer: D

redandme21

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27 Dec 2025, 08:12

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7 shelves

N = total number of pages
B = number of books

N/B = 252.08 = 25208/100 = 6302/25

B must be a multiple of 25.
N must be a multiple of 6302.

(1)
Bmin=2*7=14
Bmax=7*7=49

The only multiple of 25 between 14 and 49 is 25. B=25.

Sufficient

(2)
N<10000

The only multiple of 6302 less than 10000 is 6302, so B=25.

Sufficient

IMO D

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27 Dec 2025, 08:14

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Based on the question => Average number of pages per book = 252.08
Converting this to exact fraction => 25208/100=> 6302/25
The Average pages = total pages/ number of books = Total Pages = (6302/25) * N
Number of books has to be a multiple of 25 (25,50,75) as pages can only be integer.

Statement 1 => Each shelf has between 2-7 books => 14<N<49
=> Only possible case is N= 25. Sufficient

Statement 2 => Total pages < 10000
Total pages = 252.08*N (which can only be multiple of 25)
At N=25 => Total Pages = 6302 < 10000
At N=50 => total pages = 12604 > 10000
Only N=25 possible => Sufficient.

Answer => D => Both alone sufficient

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27 Dec 2025, 08:28

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To determine the total number of books Lena has , we must analyse the mathematical constraints provided by the exact average number of pages and the condition in the statements.
Leena's avg number of pages per book is exactly 252.08. This can be written as a mixed fraction
252+8/100 = 252+2/25 = 6302/25

Because the total number of books (n) and total number of pages (T) must both be the integers
Avg = T/n = 6302/25
For the total pages (T) to be a whole number the number of books (n) must be a multiple of 25.

ST 1 : each Shelf contains between 2 and 7 books , inclusive .
Lena has 7 shelves
Min Books : 7 shelves x 2 books / shelf = 14 books .
Max books : 7 Shelves x 7 books /shelf = 49 books.
Within the possible range of 14 to 49 books , the only multiple of 25 is 25.
This definitely identifies that lena has exactly 25 books. Sufficient ✅

ST 2: The total number of pages of her books is less than 10,000
If n = 25 , Total Pages = 25 x 252.08 = 6302 ( This is less than 10,000)
If n = 50 , Total pages = 50 x 252.08 = 12604 ( This is greater than 10,000)
Any higher multiple of 25 will also exceed 10,000 pages.
This confirms that lena must have exactly 25 books.
Sufficient.✅

Vaishbab

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27 Dec 2025, 08:37

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252.08 mean pages means 25208/100 which is essentially 6302/25 pages

[Total Pages (T)]/[No. of Books (B)] = 6302/25

This means T must be B x 6302/25 -------A

I. Each shelf has a minimum of 2 books and a max of 7 books. Which means, the total number of books: 14 <= B <= 49 (since there are 7 shelves)

And since both B & T are supposed to be integers, it's safe to say that B must be divisble by 25 (from A)

The only values in that range that satisfy this requirement is 25.

Hence I is sufficient

II. T < 10000

B x 6302/25 < 10000

B < 250000/6302

B < 39.66

Again, from equation A, we can say that B must be divisble by 25

Therefore, the only nuber that satisfies would be B = 25

Therefore, II is sufficient

Therefore, answer is D.

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27 Dec 2025, 08:51

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avg pages: 252.08 -> 25208/100 -> 6302/25 which gives total pages: T = n*6302/25 // n has to be an integer and a multiple of 25.
7 shelves
A -> 7 shelves each containing 2 to 7 books -> b/w [14,49] -> only 25 present b/w them and satisfies our condition hence A is sufficient.
B -> T < 10,000 -> n < 39.66 -> only possible integer multiple of 25 is 25 -> sufficient

each is sufficient.

side note: just wondering if each 7 shelves had different no. of books.

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27 Dec 2025, 08:58

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The smallest number to multiply 0.08 by to get an integer (and supposedly page number is an integer) is 25, since $25*0.08=2.$
Therefore, the total number of pages is $252.08*25k$, and the minimal value for k=1 is $ 252.08*25 = 6302.$ The total number of books in this case is $b=25k.$

(1) If the maximum number of books per shelf is 7, and there're 7 shelves, then the absolute maximum $b = 7*7=49$, and this only covers one option for k=1, and b=25. Sufficient.

(2) Since for k=2 the number of pages will already be above 12,000, then we only can have k=1 and b=25. Sufficient.

Therefore, the answer is D.