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Each year, the members of a book club select novels and non

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Each year, the members of a book club select novels and non [#permalink] New post 12 Jun 2019, 16:48
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Each year, the members of a book club select novels and nonfiction books to discuss. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. The club met 52 times last year, and at each meeting the club discussed only one book. If the club discussed 12 books last year, how many of the books were novels?

A. 2

B. 4

C. 5

D. 7

E. 14
[Reveal] Spoiler: OA

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Re: Each year, the members of a book club select novels and non [#permalink] New post 12 Jun 2019, 18:20
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Each year, the members of a book club select novels and nonfiction books to discuss. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. The club met 52 times last year, and at each meeting the club discussed only one book. If the club discussed 12 books last year, how many of the books were novels?

With word problems using the phrase "how many" and seeking one specific value from choices listed in numeric order, consider plugging in the choices as a most efficient method for solving the problem without utilizing potentially overly complex algebra.

In this case we see that the choices refer to the number of novels. Start with Choice C - 5.

If there are 5 novels, then 15 meetings focused on novels and then there would have been 7 non-fiction books that were discussed 5 times each for 35 meetings focused on non-fiction. So, if 5 novels were selected there would have been 15 + 35 = 50 total meetings. This does not match the 52 indicated by the problem, so eliminate Choice C.

Now, consider if there need to be more or fewer novels. Since, the total number of meetings is too low and the novels have a lower number of meetings per book, logically eliminate all of the choices larger than 5 novels, so eliminate Choice D and Choice E.

Next, consider Choice B - 4.

If there are 4 novels, then 12 meetings focused on novels and then there would have been 8 non-fiction books that were discussed 5 times each for 40 meetings focused on non-fiction. So if 4 novels were selected there would have been 12 + 40 = 52 total meetings. This matches the 52 indicated by the problem, so select Choice B.
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Re: Each year, the members of a book club select novels and non [#permalink] New post 28 Oct 2019, 14:37
Is there another solution to this? Thanks for the help!
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Re: Each year, the members of a book club select novels and non [#permalink] New post 28 Oct 2019, 15:01
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Carcass wrote:
Each year, the members of a book club select novels and nonfiction books to discuss. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. The club met 52 times last year, and at each meeting the club discussed only one book. If the club discussed 12 books last year, how many of the books were novels?

A. 2

B. 4

C. 5

D. 7

E. 14


Let x = the number of novels discussed
Let y = the number of nonfiction books discussed

The club discussed 12 books last year
We can write: x + y = 12

The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. The club met 52 times last year, and at each meeting the club discussed only one book.
We can write: 3x + 5y = 52


How many of the books were novels?
In other words, solve for x

We have:
x + y = 12
3x + 5y = 52

Take the top equation, and create an equivalent equation by multiplying both sides by 5 to get:
5x + 5y = 60
3x + 5y = 52

Subtract the bottom equation from the top equation to get: 2x = 8
Solve: x = 4

Answer: B

Cheers,
Brent
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Re: Each year, the members of a book club select novels and non [#permalink] New post 28 Oct 2019, 15:09
GreenlightTestPrep wrote:
Carcass wrote:
Each year, the members of a book club select novels and nonfiction books to discuss. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. The club met 52 times last year, and at each meeting the club discussed only one book. If the club discussed 12 books last year, how many of the books were novels?

A. 2

B. 4

C. 5

D. 7

E. 14


Let x = the number of novels discussed
Let y = the number of nonfiction books discussed

The club discussed 12 books last year
We can write: x + y = 12

The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. The club met 52 times last year, and at each meeting the club discussed only one book.
We can write: 3x + 5y = 52


How many of the books were novels?
In other words, solve for x

We have:
x + y = 12
3x + 5y = 52

Take the top equation, and create an equivalent equation by multiplying both sides by 5 to get:
5x + 5y = 60
3x + 5y = 52

Subtract the bottom equation from the top equation to get: 2x = 8
Solve: x = 4

Answer: B

Cheers,
Brent



Thanks Brent!

this is exactly how I solved. except I kept multiplying the 4 with 3 to get a solution of 12. kept wondering why 12 was not an option... So silly!
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Re: Each year, the members of a book club select novels and non [#permalink] New post 28 Oct 2019, 15:14
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bellavarghese wrote:
Thanks Brent!

this is exactly how I solved. except I kept multiplying the 4 with 3 to get a solution of 12. kept wondering why 12 was not an option... So silly!


That's a valid mistake. You were calculating the number of times novels were discussed (rather than the number of novels discussed)

Cheers,
Brent
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Re: Each year, the members of a book club select novels and non   [#permalink] 28 Oct 2019, 15:14
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