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nousernamefine
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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 05:11
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Check options- Fictional 3X, non fictional X
Hardcover fictional- 2.4X, 1.8X of these local
Check whatever X (1.8X be an integer)

A. 15 Total =4X
X=3.75
1.8X Not an Integer, Incorrect

B Total Books 4X= 20
X=5
1.8X=9

Correct


Ans B

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A library has both fiction and nonfiction books. Of the fiction books, 4/5 are hardcover, and 3/4 of these hardcover books are authored by local writers. If the number of fiction books is three times the number of nonfiction books, what is the least total number of books in the library?

A. 15
B. 20
C. 40
D. 60
E. 80

 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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Akshay1298
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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 05:25
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Let the fiction books be F and the non-fiction books be NF respectively.

As per the ratio, F : NF = 3 : 1;

Option A is not divisible by 4.

Therefore 20 is divisible by 4.

Option B
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__Poisonivy__
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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 05:30
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Let the no. of Non. Fiction books= B
Given, no. of fiction books is thrice the no. of non. fict.= 3B

Hardcover Fiction books= 4/5x 3B= 12B/5

Hardcover fiction books of local writers= 3/4x 12B/5= 9B/5.

Total no. of books (fiction, non-fiction)= B+3B= 4B

Now, for integral values of B, it should be a multiple of 5 because the no. of hardcover fiction books and hardcover fiction books by local writers is of the form= X/5 (12B/5, 9B/5 respectively.)

So, the smallest val.=5

So, no. of non. fiction books =5
no. of fiction book= 15
Total no. of books= 20

for verification-
no. of hardcover fiction books=12
no. of hardcover fictional books by local writers= 9

So, all the values are integers, which are valid.

Ans- 20
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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 06:05
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Total books are 3NF + NF = 4NF

Given F = 3*NF
So the total number of books must be in the form of 4*k
Since we are looking for the least number possible let's try with 20

20 = 4X -> NF are 5 and Fictions are 15
Fictions 15 and 4/5 are hardcover so hardcover will be 12 and Non-hardcover will be 3.
12 are hardcover from which 3/4 are from authorised authors which is 9 books and 3 will be from non authored local writers.

This gives us all integer solutions and answer 20 is correct
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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 06:19
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let f = no. of fiction books
n = no. of non fiction books

f=3n

4/5th of fiction are hardcover
=4/5 * f = 4/5 * 3n = 12n/5

3/4th of hardcover are authored by local writers
=3/4 * 12n/5
= 9n/5

total no. of books
f+n=n+3n = 4n

For the total number of books to be a whole number, both the number of hardcover fiction books 12n/5 and the number of local writer fiction books 9n/5 must be whole numbers
==> n must be a multiple of 5.

the smallest value of n that satisfies the equation = 5

least total no. of books in library is 4*5 = 20

Option B
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A library has both fiction and nonfiction books. Of the fiction books, 4/5 are hardcover, and 3/4 of these hardcover books are authored by local writers. If the number of fiction books is three times the number of nonfiction books, what is the least total number of books in the library?

A. 15
B. 20
C. 40
D. 60
E. 80

 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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chloepham
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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 06:27
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The number of books has to be integer.

4/5 are hardcover ==> At least 5 fiction books (where X=1 or 5X books).

But we have fiction books = 3 x nonfiction books
==> The least fiction books is 3 x 5X = 15 books
==> Nonfiction book is 5

So the least total will be 5 + 15 = 20 books
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A library has both fiction and nonfiction books. Of the fiction books, 4/5 are hardcover, and 3/4 of these hardcover books are authored by local writers. If the number of fiction books is three times the number of nonfiction books, what is the least total number of books in the library?

A. 15
B. 20
C. 40
D. 60
E. 80

 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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maddscientistt
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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 07:08
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Let N be the number of nonfiction books. Then, the number of fiction books is 3N

Hardcover fiction books = 12N/5
Local author hardcover fiction books = 9N/5

For 9N/5 to be an integer, N must be a multiple of 5. The smallest such N is 5

if N is 5, 3N = 15

Total books = 5 + 15 = 20

Answer is Option B


Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A library has both fiction and nonfiction books. Of the fiction books, 4/5 are hardcover, and 3/4 of these hardcover books are authored by local writers. If the number of fiction books is three times the number of nonfiction books, what is the least total number of books in the library?

A. 15
B. 20
C. 40
D. 60
E. 80

 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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12 Days of Christmas GMAT Competition - Day 10: A library has both 28 Dec 2024, 08:10
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Let F be no. of fictional books and nF be non fictional, then total books would be F + nF which should be an positive integer.

F=3nF ; Of the fiction books, 4/5 are hardcover. Of these hardcover fiction books, 3/4 are authored by local writers.
ie: LA books = 3/4 * 4/5 * 3nF which should be integer. it implies nF should be a multiple of 5 . Try with nF = 5 => F= 15 total books = 20.
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