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QOTD # 12 Each year, the members of a book club select novel
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13 Sep 2016, 06:54
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Each year, the members of a book club select novels and nonfiction books to read. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. Last year, the club met 52 times and discussed 12 books. How many novels did the club discuss last year?
Re: QOTD # 12 Each year, the members of a book club select novel
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13 Sep 2016, 06:57
2
Expert Reply
Explanation
Let n represent the number of novels the club discussed last year. Since the club discussed a total of 12 books, the number of nonfiction books is represented by 12 – n. This, together with the information that the club met 3 times to discuss each novel and 3 times to discuss each nonfiction book, tells you that the number of times the club met last year can be expressed as 3n + 5(12 – n). Since you know that the club met 52 times last year, it follows that 3n + 5(12 – n) = 52.
Re: QOTD # 12 Each year, the members of a book club select novel
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20 Sep 2016, 13:52
2
Expert Reply
Carcass wrote:
Each year, the members of a book club select novels and nonfiction books to read. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. Last year, the club met 52 times and discussed 12 books. How many novels did the club discuss last year?
A) 2 B) 4 C) 5 D) 7 E) 14
We can also solve this question using 2 variables
Let N = number of nonfiction books discussed last year Let V = number of novels discussed last year
Last year, the club discussed 12 books We can write N + V = 12
Last year, the club met 52 times 5N = number of times the club met to discuss nonfiction books 3V = number of times the club met to discuss novels So, we can write 5N + 3V = 52
So, we have the following system: N + V = 12 5N + 3V = 52
Take the top equation and multiply both sides by 5 to get: 5N + 5V = 60 5N + 3V = 52
Now subtract the bottom equation from the top equation to get: 2V = 8 Solve to get: V = 4
Re: QOTD # 12 Each year, the members of a book club select novel
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20 Sep 2016, 14:13
1
Expert Reply
Carcass wrote:
Each year, the members of a book club select novels and nonfiction books to read. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. Last year, the club met 52 times and discussed 12 books. How many novels did the club discuss last year?
A) 2 B) 4 C) 5 D) 7 E) 14
We can also solve this question by TESTING THE ANSWER CHOICES
Answer choice C This answer says that 5 novels were discussed last year Since the club discussed a total of 12 book, we can conclude that the club discussed 7 nonfiction books.
The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. So, the total number of meetings = (3)(5) = 5(7) = 15 + 35 = 50 No good. We're told that there were 52 meeting last year.
NOTE: When we tested answer choice C, we got a total of 50 meetings, and wanted a total of 52 meetings. So, we want MORE meetings. To accomplish this, we need the club to read MORE nonfiction books, since they require more meetings. This means, we need the club to read FEWER novels.
So, let's test... Answer choice B This answer says that 4 novels were discussed last year Since the club discussed a total of 12 book, we can conclude that the club discussed 8 nonfiction books.
The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. So, the total number of meetings = (3)(4) = 5(8) = 12 + 40 = 52 PERFECT! This matches the given information.
Re: QOTD # 12 Each year, the members of a book club select novel
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09 Jun 2020, 01:44
GreenlightTestPrep wrote:
Carcass wrote:
Each year, the members of a book club select novels and nonfiction books to read. The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. Last year, the club met 52 times and discussed 12 books. How many novels did the club discuss last year?
A) 2 B) 4 C) 5 D) 7 E) 14
We can also solve this question by TESTING THE ANSWER CHOICES
Answer choice C This answer says that 5 novels were discussed last year Since the club discussed a total of 12 book, we can conclude that the club discussed 7 nonfiction books.
The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. So, the total number of meetings = (3)(5) = 5(7) = 15 + 35 = 50 No good. We're told that there were 52 meeting last year.
NOTE: When we tested answer choice C, we got a total of 50 meetings, and wanted a total of 52 meetings. So, we want MORE meetings. To accomplish this, we need the club to read MORE nonfiction books, since they require more meetings. This means, we need the club to read FEWER novels.
So, let's test... Answer choice B This answer says that 4 novels were discussed last year Since the club discussed a total of 12 book, we can conclude that the club discussed 8 nonfiction books.
The club meets 3 times to discuss each novel and 5 times to discuss each nonfiction book they select. So, the total number of meetings = (3)(4) = 5(8) = 12 + 40 = 52 PERFECT! This matches the given information.
The reasoning for whether to go upwards or downwards after testing option C looks convoluted to me. Is there an easier way?
In retrospect, I multiplied the novels in the option to 3 (number of times they meet) and subtracted from the total 52, and see if it's divisible by 5. Of the options, only 4 and 14 give numbers 40 and 10 divisible by 5. I then added novels and nonfiction to see if they equal 12.
But yeah, this clarity comes only in retrospect and not during the actual test. So if I test option C, it would be great to have an easier explanation on why we move upwards and not downwards.
Re: QOTD # 12 Each year, the members of a book club select novel
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30 Apr 2022, 20:45
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