At a sale all books were priced equally and all magazines were priced

Question

At a sale all books were priced equally and all magazines were priced equally. What was the price of 3 books and 4 magazines at the sale?

(1) At the sale the price of a book was $1.45 more than the price of a magazine.

(2) At the sale the price of 6 books and 8 magazines was $43.70.

ID 10738

Nikkb · Answer

price of books =B
price of magazines =M
Find: price of 3 books and 4 magazines => 3B +4M = ?

(1) At the sale the price of a book was $1.45 more than the price of a magazine.
=> B = 1.45+M
to find total cost we need to know value of 1 of the parameters with above equation
=? 3B+4M = 3(1.45+M)+4M = some value in M form. 
Not sufficient

(2) At the sale the price of 6 books and 8 magazines was $43.70. 
=>6B+8M = 43.70
=> 2(3B+4M)=43.70
=>3B+4M =21.85 . Answer
Sufficient

Answer: B

Kimberly77 · Answer

Thanks for explanation  Nikkb . From statement 1, if we get M value, can we not put M into B = 1.45+M to get B value therefore it's sufficent? Am I missing something? Thanks for your time in advanced.

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

We know that all books were priced equally and all magazines were priced equally. 
Let the price of a book = $x and the price of a magazine = $y.

The price of 3 books and 4 magazines is to be found out. This means, we need to calculate the value of 3x + 4y.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  At the sale the price of a book was $1.45 more than the price of a magazine.

This means, x = y + 1.45.
Without knowing the value of y, we cannot calculate the value of x. Neither do we have any data about the total money paid for a set of books and magazines.

This data is insufficient to find the value of 3x + 4y.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:  At the sale the price of 6 books and 8 magazines was $43.70.

Therefore, 6x + 8y = 43.70.

Upon careful observation, we see that 6x + 8y = 2 * (3x + 4y).

If 2 * (3x + 4y) = 43.70,

3x + 4y =  \frac{43.70 }{ 2} .

The data given in statement 2 is sufficient to find a unqiue value of 3x + 4y.
Statement 2 alone is sufficient. Answer options C and E can be eliminated.

The correct answer option is B.

GMATWhizTeam · Answer

Thanks for explanation  Nikkb . From statement 1, if we get M value, can we not put M into B = 1.45+M to get B value therefore it's sufficent? Am I missing something? Thanks for your time in advanced.

Kimberly, happy to answer your question.

In fact, a part of your question answers itself. When you say “IF we get M value, then can we not put M into the equation?..” Where do we get this M from? It’s neither given in the question nor in statement I. 
So, I hope it’s clear that’s not possible.

In questions like these which involve solving Linear equations, you have to remember a cardinal rule of Algebra:    To obtain a unique solution / solution set, Number of independent equations = Number of unknowns.

Now, from statement 1, how many equations could we form? Just ONE. Do we have the second equation? Clearly not. That’s sufficient reason, as per Algebra, to conclude that the information given is insufficient to solve for the variables. If you cannot solve for the variables, you cannot find out the value of the expression 3x + 4y.

Hope that helps!

Kimberly77 · Answer

Kimberly, happy to answer your question.

In fact, a part of your question answers itself. When you say “IF we get M value, then can we not put M into the equation?..” Where do we get this M from? It’s neither given in the question nor in statement I. 
So, I hope it’s clear that’s not possible.

In questions like these which involve solving Linear equations, you have to remember a cardinal rule of Algebra:    To obtain a unique solution / solution set, Number of independent equations = Number of unknowns.

Now, from statement 1, how many equations could we form? Just ONE. Do we have the second equation? Clearly not. That’s sufficient reason, as per Algebra, to conclude that the information given is insufficient to solve for the variables. If you cannot solve for the variables, you cannot find out the value of the expression 3x + 4y.

Hope that helps!

Thanks  GMATWhizTeam  for your reply.
From Statement 1, was thinking substituting given info into 3B+4M = 0, we can get M=-3/7. Therefore thought we can use this value back into 3B+4M to get B ?

BottomJee · Answer

OFFICIAL EXPLANATION

At a sale, each book sold for one amount and each magazine sold for another amount. Determine the cost of 3 books and 4 magazines.

Letting b represent the price, in dollars, of each book and m represent the price, in dollars, of each magazine, determine the value, in dollars, of 3b + 4m.

(1) Given that b = m + 1.45, if m = 2.00, for example, then b = 2.00 + 1.45 = 3.45, and hence 3b + 4m = 3(3.45) + 4(2.00) = 18.35. But if m = 4.00, for example, then b = 4.00 + 1.45 = 5.45, and hence 3b + 4m = 3(5.45) + 4(4.00) = 32.35; NOT sufficient.

(2) It is given that 6b + 8m = 43.70, so 2(3b + 4m) = 43.70, and hence 3b + 4m = 21.85; SUFFICIENT.

The correct answer is B; statement 2 alone is sufficient.

bumpbot · Answer

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At a sale all books were priced equally and all magazines were priced

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