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Barbara spends $95 on books. She buys two different kinds of books: no

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Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 09 Sep 2015, 00:47
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Barbara spends $95 on books. She buys two different kinds of books: novels and comic books. How many novels does Barbara buy?

(1) Barbara pays $5 for each novel and $10 for each comic book.

(2) Barbara buys a total of 11 books.


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Re: Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 09 Sep 2015, 01:37
Bunuel wrote:
Barbara spends $95 on books. She buys two different kinds of books: novels and comic books. How many novels does Barbara buy?

(1) Barbara pays $5 for each novel and $10 for each comic book.

(2) Barbara buys a total of 11 books.


Kudos for a correct solution.

Solution :
Statement1 : 5N + 10 C = 95 ==> N+2C=19 Many values for (N,C) ==> (1,9),(3,8),(5,7)...Insufficient.

Statement2 : If cost of novels is 5 and comics is 10. Then N + 2 C =19 and N +C = 11 ==> N=3 and C=8. But if cost of novels is 10 and comics is 5, then 2N + C =19. So, N=8 and C =3. So, insufficient.

Combined : From the explanation in statement2. N=3. So, sufficient.

Option, C.
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Re: Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 09 Sep 2015, 01:45
Bunuel wrote:
Barbara spends $95 on books. She buys two different kinds of books: novels and comic books. How many novels does Barbara buy?

(1) Barbara pays $5 for each novel and $10 for each comic book.

(2) Barbara buys a total of 11 books.


Kudos for a correct solution.


(1) Barbara pays $5 for each novel and $10 for each comic book:Insufficient-We can have different combinations that are possible.
(2) Barbara buys a total of 11 books:Insufficient-we do not know the price of each type of book

Using both, only one combination is possible i.e 8 comics and 3 novels
8*$10=$80 and 3*$5=$15
Answer C
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Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 09 Sep 2015, 08:18
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.



Barbara spends $95 on books. She buys two different kinds of books: novels and comic books. How many novels does Barbara buy?

(1) Barbara pays $5 for each novel and $10 for each comic book.

(2) Barbara buys a total of 11 books.

Transforming the original condition and the question, we have a typical 2by2 case question as below table.


Here we have 4 variables (a,b,c,d) and 1 equation (ca+db=95) thus we need 3 more equations to match the number of variables and equations. Since there is 1 each in 1) and 2), E is likely the answer. Using both 1) & 2), 1) gives us two equations (c=5, d=10) while 2) gives us 1 (a+b=11) and thus we have 3 equations more. Therefore C is the answer.
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Re: Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 09 Sep 2015, 09:05
Let number of novels = x & comics = y
From statement 1:
5x + 10y = 95 → x + 2y = 19
From statement 2:
x + y = 11
From the above two equations, we have two distinct equations with two variables → Answer: C
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Re: Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 09 Sep 2015, 18:07
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Hi All,

While this question is based around 'system' algebra, the numbers involved are relatively small, so even if you are not 'great' at that type of math, you can still get to the correct answer with a bit of note-taking and 'brute force.'

We're told that Barbara buys 2 types of books (novels and comic books) and spends a total of $95. We're asked how many NOVELS Barbara buys...

1) Barbara pays $5 per novel and $10 per comic book.

'5' and '10' are relatively easy numbers to work with. Since the total spent is $95, you should be able to see (and prove) that there are multiple possibilities...

For example....
1 novel and 9 comic books = $95
3 novels and 8 comic books = $95
5 novels and 7 comic books = $95
Etc.

From this work, you should also recognize a pattern - you can 'trade' one comic book for two novels and spend the same amount of money...
Fact 1 is INSUFFICIENT

2) Barbara bought a total of 11 books.

With the prices of each type of book, this information is not enough to tell us how many Novels she bought.
Fact 2 is INSUFFICIENT

Combined, we know
Total Spend = $95
Novels = $5 each and comic books = $10 each
Total books = 11

From the work that we did in Fact 1, we can use the pattern we discovered to avoid doing any more work.

1 novel and 9 comic books = 10 total books
3 novels and 8 comic books = 11 total books
5 novels and 7 comic books = 12 total books
Etc.

Since 'trading' one comic book gets us 2 novels, the total number of books will vary based on the total number of comic books. The ONLY combination that gives us 11 total books is when there are 3 novels and 8 comic books, so the answer to the question MUST be '3.'
Combined, SUFFICIENT

Final Answer:

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Re: Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 11 Sep 2015, 00:07
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Barbara spends $95 on books. She buys two different kinds of books: novels and comic books. How many novels does Barbara buy?

(1) Barbara pays $5 for each novel and $10 for each comic book.

(2) Barbara buys a total of 11 books.

St 1 --- 95 = 5x +10y ; x- no of novels and y- no of comic
not possible because x could be 17 , 15 and y could be 1, 2 respectively

not sufficient

St 2 -- x+y = 11
But price of novel and comic not given .

hence not sufficent .

together they are . Hence C .... got two equation 95 = 5x +10y and 11= x+y ..... hence sufficient .
Ans C
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Re: Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 14 Sep 2015, 06:57
Bunuel wrote:
Barbara spends $95 on books. She buys two different kinds of books: novels and comic books. How many novels does Barbara buy?

(1) Barbara pays $5 for each novel and $10 for each comic book.

(2) Barbara buys a total of 11 books.


Kudos for a correct solution.


PRINCETON OFFICIAL SOLUTION:

This problem is a little different because it doesn’t have explicit equations in it. But equations are lurking beneath the surface, and you want to translate the words into equations. The question wants to know how many novels Barbara buys. Let’s call this x. We’ll call the number of comic books that Barbara buys y. Fact 1 thus tells us that 5x + 10y = 95 because we know from the setup that Barbara spends $95 on books, and Fact 1 tells us the price of each type of book. This is just one equation, however, so it’s insufficient to solve for x. Fact 2 enables us to write the equation x + y = 11. This is also only one equation, however, so it’s insufficient. When we combine the two statements we have simultaneous equations and thus the data is sufficient. The answer is C.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Barbara spends $95 on books. She buys two different kinds of books: no [#permalink]

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New post 10 Mar 2018, 05:54
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Re: Barbara spends $95 on books. She buys two different kinds of books: no   [#permalink] 10 Mar 2018, 05:54
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