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OG-17 Problem solving

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OG-17 Problem solving

by Joy Shaha » Sun Jan 22, 2017 11:26 am

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Q. Thabo owns exactly 140 books, and each book is either paperback fiction,
paperback nonfiction, or hardcover nonfiction. If he owns 20 more
paperback nonfiction books than hardcover nonfiction books, and twice as
many paperback fiction books as paperback nonfiction books, how many
hardcover books nonfiction books does Thabo own?
A) 10 B) 20 C) 30 D) 40 E) 50
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by DavidG@VeritasPrep » Sun Jan 22, 2017 4:26 pm
Joy Shaha wrote:Q. Thabo owns exactly 140 books, and each book is either paperback fiction,
paperback nonfiction, or hardcover nonfiction. If he owns 20 more
paperback nonfiction books than hardcover nonfiction books, and twice as
many paperback fiction books as paperback nonfiction books, how many
hardcover books nonfiction books does Thabo own?
A) 10 B) 20 C) 30 D) 40 E) 50
Designate hardcover nonfiction as H
If there are 20 more paperback nonfiction than hardcover nonfiction, then we can designate paperback nonfiction as H + 20
If there are twice as many paperback fiction books as paperback non-fiction, then we can designate paperback fiction as 2* [H + 20}

The three categories sum to 140, so H + H + 20 + 2(H + 20) = 140 --> H + H + 20 + 2H + 40 = 140 ---> 4H = 80 ---> H = 20

The answer is B
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by DavidG@VeritasPrep » Sun Jan 22, 2017 4:29 pm
Joy Shaha wrote:Q. Thabo owns exactly 140 books, and each book is either paperback fiction,
paperback nonfiction, or hardcover nonfiction. If he owns 20 more
paperback nonfiction books than hardcover nonfiction books, and twice as
many paperback fiction books as paperback nonfiction books, how many
hardcover books nonfiction books does Thabo own?
A) 10 B) 20 C) 30 D) 40 E) 50
Or Back-solve.

Say we try C, 30. If there were 30 hardcover non-fiction, there'd be 20 more, or 50, paperback non-fiction. And because there are twice as many paperback fiction as non-fiction, there'd be 50*2 or 100 paperback fiction books. We'd have a total of 30 + 50 + 100 = 180. We know we actually have 140 books, so C is too big. Eliminate C, D and E.

Test A, 10. If there were 10 hardcover non-fiction, there'd be 20 more, or 30, paperback non-fiction. And because there are twice as many paperback fiction as non-fiction, there'd be 30*2 or 60 paperback fiction books. We'd have a total of 10 + 30 + 60 = 100. But there are 140 books total, so A is too small. Eliminate A.

All that's left is B
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by Jay@ManhattanReview » Sun Jan 22, 2017 9:06 pm
Joy Shaha wrote:Q. Thabo owns exactly 140 books, and each book is either paperback fiction,
paperback nonfiction, or hardcover nonfiction. If he owns 20 more
paperback nonfiction books than hardcover nonfiction books, and twice as
many paperback fiction books as paperback nonfiction books, how many
hardcover books nonfiction books does Thabo own?
A) 10 B) 20 C) 30 D) 40 E) 50
Hi Joy,

This is a simple question; I try to understand what could be a challenge with you. Though a couple fo experts have already answered beautifully, I see that one of the challenges with this one could be, "how to start with assuming a variable for hardcover nonfiction books. Why not start with paperback fiction or with paperback nonfiction."

So let's say the number of paperback fictions = x, paperback nonfictions = y, and hardcover nonfictions = z.

The second sentence in the questions states that 'If he owns 20 more paperback nonfiction books than hardcover nonfiction books,'

Since the comparison is with hardcover nonfiction (z), we have to put paperback nonfiction (y) in terms of z, thus y = z + 20.

Similarly, the third sentence is, '[In he owns} twice as many paperback fiction books as paperback nonfiction books.'

Thus, x = 2y

Or, x = 2*(z+20) = 2z+40

Now, we know that the total number of books = 140,

Thus, 140 = x+y+z = (2z+40) + (z+20) + z =140

=> 4z + 60 = 140
=> z = 20.

Answer B

Hope this helps!

-Jay
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by [email protected] » Mon Jan 23, 2017 10:46 am
Hi Joy Shaha,

This question can be solved by TESTing THE ANSWERS. We're given several facts to work with:

1) Total number of books = 140 and there are only 3 types of books.
2) Paperback Nonfiction = 20 + Hardcover Nonfiction
3) Paperback Fiction = 2(Paperback Nonfiction)

We're asked for the number of Hardcover Nonfiction books.

Given the 2nd and 3rd facts, we can arrange the books from greatest number to least number:

Paperback Fiction > Paperback Nonfiction > Hardcover Fiction.

This means that the SMALLEST group of books will be the Hardcover Nonfiction books. Thus, we should TEST one of the smaller answers first!

Let's TEST Answer B: 20 books

IF....
Hardcover Nonfiction = 20
Paperback Nonfiction = 40
Paperback Fiction = 80
Total = 20 + 40 + 80 = 140
This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer: B

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by Scott@TargetTestPrep » Fri Jan 27, 2017 9:42 am
Joy Shaha wrote:Q. Thabo owns exactly 140 books, and each book is either paperback fiction,
paperback nonfiction, or hardcover nonfiction. If he owns 20 more
paperback nonfiction books than hardcover nonfiction books, and twice as
many paperback fiction books as paperback nonfiction books, how many
hardcover books nonfiction books does Thabo own?
A) 10 B) 20 C) 30 D) 40 E) 50
We are given that Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction.

We can let f = the number of paperback fiction books, n = the number of paperback nonfiction books, and h = the number of hardcover nonfiction books.

Since Thabo has 140 books, we can say:

f + n + h = 140

We are also given that Thabo owns 20 more paperback nonfiction books than hardcover nonfiction books and twice as many paperback fiction books as paperback nonfiction books. Thus, we can say:

n = 20 + h

AND

f = 2n

We need to determine how many hardcover nonfiction books Thabo owns.

Since we have the variable n in each equation, we should express each variable in terms of n.

h = n - 20 and f = 2n

Finally, we can substitute n - 20 for h and 2n for f in the equation f + n + h = 140, so we have:

2n + n + n - 20 = 140

4n = 160

n = 40

Thus, Thabo owns 40 - 20 = 20 hardcover nonfiction books.

Answer: B

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Re: OG-17 Problem solving

by Bijaya Krushna Mohapatra » Fri Jan 17, 2020 8:48 pm
total book 140 = PF +PN +HN

LET HN = X

PN = X + 20

PF = 2( X+20) = 2X +40

SO total = 2x+ 40 +x +20 +x =140

4x+60 = 140

4x = 80

x=20 ( Answer B)
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