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

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Bunuel

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26 Dec 2025, 10:00

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GMAT Club Official Explanation:

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?

An average of 252.08 pages per book means:

(total pages)/(total books) = 252.08 = 25208/100 = 6302/25.

Since 6302/25 is in lowest terms, this implies that the total number of pages is a multiple of 6302 and the total number of books is a multiple of 25.

(1) Each shelf contains between 2 and 7 books, inclusive.

With 7 shelves, the total number of books is between 2 * 7 = 14 and 7 * 7 = 49, inclusive. The only multiple of 25 in this range is 25. So the number of books is 25. Sufficient.

(2) The total number of pages across all of her books is less than 10,000.

There is only one multiple of 6,302 less than 10,000, 6,302 itself. Thus, the total number of pages is 6,302 and the number of books is 25. Sufficient.

Answer: D.

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26 Dec 2025, 09:23

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Bunuel

converting 252.08 in fraction
25208/100 or
6302/25 or
12604/50

now using 1)
we get max number of books can be 7*7 = 49 ; only 25 books are possible. hence it is sufficeint alone

now using 2)
total number of pages <10000 so only 6302 is possible. hence it is sufficient alone

each statment is sufficient alone

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26 Dec 2025, 09:37

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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.

total shelves are 7
avg pages per book 252.08
total books be x

total pages / total books = 252.08
total pages = x* 252.08
total pages = x * 252 * 8/100 ; x * 6302 / 25
value of x has to be multiple of 25

#1
each shelf has 2 to 7 inclusive books
possible books 2*7 =14 or 7*7 = 49
25 is possible
sufficient
#2
total number of pages are <10,000
books have to be multiple of 25 , check with 25 , 50
25* 252.08< 10,000 ( sufficient)
50* 252.08 >10,000 ( not possible)
25 is valid

OPTION D is correct

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26 Dec 2025, 09:43

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Lana 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?

Let us assume Lana had n book.
252.08 = 252 8/100 = 252 2/25 = 6302/25
The number of book Lana have is a multiple of 25.

(1) Each shelf contains between 2 and 7 books, inclusive
Number of books she have is between 2*7 = 14 and 7*7 = 49.
She has 25 books
Sufficient

(2) The total number of pages across all of her books is less than 10,000.
Let the number of books she have = n
252.08n < 10,000
n < 10,000/252.08 = 39.66
n < 40
n = 25
She has 25 books
Sufficient

IMO D

Bunuel

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26 Dec 2025, 09:43

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total number of pages can't be decimal
statement 1 says each shelves contain 2 to 7 books
hence if there are 25 books then the total number of pages is 6302
hence statement 1 is sufficient
statement 2 says that total number of pages is less than 10000
if there are 25 books then the total number of pages is 6302
hence statement 2 is sufficient
option d is correct

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26 Dec 2025, 09:44

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Let number of shelves, books, pages be S,B,P
S = 7
P/B = 252.08
P/B = 252 + 8/100 = 252 + 2/25
B is a multiple of 25

S1
2<=B/S<=7
2*7<=B<=7*7
14<=B<=49
B can be 25
Sufficient

S2
P<1000
P/B = 252.08
252.08 < 10000/B
B < 10000/252.08
B<40 (approx)
B can be 25
Sufficient

Answer D

Bunuel

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26 Dec 2025, 10:01

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Bunuel

Mean pages/book = 252.08 = 252 + 0.08 = 252 + 8/100 = 252 + 2/50 = 6302/25

so total pages = 6302/25 x n must be an integer => n must be a multiple of 25

(1) 7 shelves, each has 2 to 7 books => total books is between 7.2 = 14 and 7.7 = 49
Only multiple of 25 in [14,49] is 25 => sufficient

(2) Total pages < 10000
If n = 25, total pages = 252.08 x 25 = 6302 < 10000
if n = 50, total = 12604 > 10000
So the only possible multiple of 25 is 25
Sufficient

Option D

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26 Dec 2025, 10:10

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7 shelves
Average number of pages = 252.08=6302/25 ( number of books is a multiple of 25)
(1) each shelf contain between 2 and 7 books, inclusive.
2*7<=number of books<=7*7
14<= number of books <=49
Between this range there is only 1 multiple of 25 whoch is 25 itself.
Sufficient
(2) toatl number of pages across all her books is less than 10,000
If total number of books is 25, total pages = 252.08*25=6,302 (less than 10000)
If total number of books is 50, total pages = 252.08*50=12,604 (more than 10000, no)
Sufficient

D

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26 Dec 2025, 10:34

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total shelves= 7
page per book =252.08
find numb of books
(total pages / total num of books) = 252.08

252* (8/100)
252*(2/25)
6302/25
number of books must be multiple of 25

1) min books=14
max books= 49.
only one multiple of 25.
sufficient.

2) total pages < 10000
avg pages * total books < 10000
total books < 10000- 252.08
total books < 39.66
only one ,multiple of 25.
sufficient

ans is D

Bunuel

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26 Dec 2025, 10:46

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Bunuel

Average = 252.08

= 25208/100 = 12604/50 = 6302/25

Total Pages = Average * Number of books

As the total pages must be an integer, we can conclude the number of books is a multiple of 25.

1) Min Books = 2*7=14
Max Books = 7 * 7 = 49

Between 14 and 49, only one number is a multiple of 25. Its 25 itself. Hence, we can conclude that the number of books is 25

2) Total Pages = 6302/25 * Number of books

If Number of Books = 25, Total pages = 6302
If number of books = 50, total pages = 6302 * 2, which is greater than 10000

Hence, we can conclude that the number of books = 25.

Option D

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26 Dec 2025, 11:41

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let n be number of books
total pages = 252.08*n

1. this shows 14<n<49..Each self can contain any number of books (3 or 5) but of different number of pages. NOT SUFFICIENT
2. 252.08*n < 10000
n<39...n can be anything like 20 or 30.
but no. of pages has to integer, so 252.08*n has to integer. for n<39, only possible value is 25...SUFFICIENT

Ans B

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26 Dec 2025, 12:06

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Bunuel

$Average=\frac{sum}{items}$. We can use this to identify the total number of pages in Lena's books as:

$Average=\frac{25208}{100}=\frac{12604}{50}=\frac{6302}{25}$. This is as far as we can reduce it without getting into decimals.

$average*items=sum$. Since we can't have partial pages, the sum must be a whole number. We already calculated the average so let's sub that in, and let the # of items be represented by x.

$\frac{6302}{25}*x=sum$

Here, it becomes clear that for us to get a whole number on RHS, x must be a multiple of 25, to cancel out the denominator of 25 for the average.

Now we can work on the statements.

Statement 1: We know that she has 7 shelves, and each shelf has min 2 and max 7 books. Therefore the number of books Lena is $14\leq{x}\leq{49}$. Remember that we're looking for multiples of 25. There's only 1 multiple of 25 within this range, which means we can identify exactly how many books she has: 25. Sufficient.

Statement 2: The total number of pages is less than 10,000. So let's go back to where we reduced the number of pages from 25,208 downwards. 6,302 is the only number below 10,000 in that reduction. Taking our average equation again, let's put in 6,302 for the sum.

$\frac{6302}{25}*x=6,302$. Solving for x, we get $x=25$. Thus # of books is again 25. B is sufficient.

Thus, D is our answer.

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26 Dec 2025, 12:13

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avg pages = 252.08 = 6302/25 -> avg pages = tot pages / books -> both the total number of pages and the number of books have to be integers -> the number of books has to be a multiple of 25 -> books =25k (because 6302/25 * books has to equal an integer) (k is a positive integer)

(1) sufficient
7 shelves with 2-7 books
14 ≤ books ≤ 49
considering it must be a multiple of 25, there is only one possible solution -> k=1 -> 25 books

(2) sufficient
tot pages < 10,000
tot pages / avg pages = books
tot pages / (6302/25) = 25k
tot pages = 6302k < 10,000 -> only one possible solution -> k=1 -> 25 books

Answer D. each statement alone is sufficient

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26 Dec 2025, 12:18

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Nice one !

average number of pages per book = 252.08

$252 + \frac{8}{100}$

$252 + \frac{2}{25}$

So dividend is a multiple of 25

$\text{Average number of pages per book} = \frac{\text{Total number of pages}}{\text{Total number of books}}$

statement 1:
each shelf has between 2 and 7 books.

let's assume each has most i.e. 7 books
Total: $7*7 = 49$ books. But 49 is not a multiple of 25.

So possible option is only 25

sufficient

Statement 2:

Total number of pages < 10000

Total number of books * Average number of pages per book = Total number of pages

assume total number of books = 25
Then, $25 * 252.08 =6,302$

assume total number of books = 50
Then, $50 * 252.08 =12,604$

So only 25 is possible.

sufficient

Ans: Option D

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26 Dec 2025, 12:52

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given books are kept in total of 7 wooden shelves and for complete collection the mean no. of pages per book=252.08.
need to find the total no. of books=??
1. no. of books per shelf is between 2 and 7 i.e. 3 or 4 or 5 or 6
still we don't know the total no. of pages of all the books , so insufficient to find the total no. of books.
2. total no. of pages in the complete collection is less than 10,000
still insufficient as exact no. of pages in the collection not known.
even if we take 1 and 2 together its still not sufficient

so E.

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26 Dec 2025, 14:42

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Bunuel

Given :

7 shelves

Pages / Book = 252.08

Statement 1 :

So total book could be between 14 - 49 .

Insufficient

Statement 2 :

Total pages < 10,000

Insufficient

Statement 1 + 2 :

252.08 * 25 = 6,302 (Except 25 there is no other number between 14 - 49 where we will get integer when multiplying it with average pages)

so Yes Total books = 25

Sufficient

Ans - C

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26 Dec 2025, 20:49

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Given that the mean number of pages is 252.08

Point 2) The total number of pages she has is less than 10,000. Now we know that pages can't be in decimal (Practically), we try to convert the mean to a whole number.A little knowledge of the table of 8 will tell us that the nearest hundreds of 8 can be achieved at 200, with *25, which gives us 252.08 *25 = 6302. The next one will take us above 10k, and hence our answer will be 25.

Point 1) The number of books per shelf is between 2 & 7. This means that the range of books is 14 to 49. From the above point, we can see that the only number within this range is 25.

And hence the answer can be deduced from both the statements individually.

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26 Dec 2025, 23:01

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Let 'n' be the total number of books
Total pages = 252.08 x n
Simplify the decimal:
=(6302/25 ) * n (So, n must be a multiple of 25)
Statement 1:
number of books is 2 to 7 inclusive
So for 7 shelves 'n' number of books must be between , 7*2 =14 to 7*7 =49
So only multiple of 25 is 25 between 14<25<49
So 25 books
Statement 2
Total pages <10,000
(6302/25)*n <10,000
n<39.66
As total number of books cannot be decimal and n has to be a multiple of 25
So n = 25

Option (D) each alone is sufficient

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26 Dec 2025, 23:16

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Good Question , and full of traps again. At first glance it feels that nothing is sufficient but inner feeling was telling that I am missing something. Let's solve this:

Lena keeps all of her books on 7 wooden shelves. The average number of pages per book in her collection is 252.08.

So , Sum of all pages on book set = 252.08*total books.

Total books will be integer and Sum of all pages on book set should also be an integer. This implies that total books will have specific integer values. Bingo , this is a very important observation.

Now let's look at the statement 1:

(1) It says Each book shelve contains books in the interval [2,7]. So Min number of total books will be 14. Max no of books will be 49.
Now observe 252.08. This can become integer if we multiply it with 5 multiples. So we have to check from 15,20,25,30,35,40,45 which one it takes. If more than 1 values are present this statement will be insufficient and if one value is present then it will be sufficient. While checking, I observed one pattern and came to conclude that it will be 25 only. So Total books will be 25.

Statement 1 is sufficient.

(2) Now it says total pages will be less than 10000. If total books are 25 then total pages are 6302. So I was left with 50. Let's check on 50. It is also giving integer value but more than 10K pages. And below 14 value , no value gives an integer. So again Total books will be 25.

Statement 2 is sufficient.

Answer is D.

PS. Integer observation is just playing a key role here. If that's missed , you are gone.

Bunuel