The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD

Question

The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD is equal to the cost of 4 pencils and the cost of book is equal to the cost of 6 pens. What is the ratio of the cost of a book to the cost of a CD ?

A) 9 : 4
B) 4 : 9
C) 2 :3
D) 3 : 2
E) 2 : 1

A) 9 : 4
B) 4 : 9
C) 2 :3
D) 3 : 2
E) 2 : 1

generis · Answer

The purposely NOT fancy way.

Everything is defined in terms of pens and pencils. Take the ratio of pens and pencils and define one in terms of the other.

(1)  4 pens cost the same as 6 pencils
4 PN = 6 PC
6 PC = 4 PN
PC =  \frac{4}{6}=\frac{2}{3} PN

(2)  One CD costs the same as 4 pencils
1CD = 4PC
CD cost in   PNs  ?
From above, PC =  \frac{2}{3}  PN
So 1CD = (4 * \frac{2}{3} PN) 
1 CD =  \frac{8}{3}  PN

(3)  One book cost the same as 6 pens
1B = 6PN

(4)  Book and CD cost in terms of PENS
1B = 6PN
1CD =  \frac{8}{3} PN

(5)  Ratio of book cost to CD cost?
 \frac{B}{CD}=\frac{6}{(\frac{8}{3})}=(6*\frac{3}{8})=\frac{18}{8}=\frac{9}{4}

Answer A

jxav · Answer

We can solve it by making the unit of comparison the same.

4 pens=6 pencils so 1 pen=1.5 pencils.

Cost of CD=4 pencils
Cost of Book=6 pens or 9 pencils.

Cost of Book to Cost of CD ratio=9:4. Ans is A.

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GMATGuruNY · Answer

Let 4 pens = 6 pencils = 12 cents, implying that each pen = 3 cents and that each pencil = 2 cents.
Cost of a book = cost of 6 3-cent pens = 6*3 = 18 cents.
Cost of a CD = cost of 4 2-cent pencils = 4*2 = 8 cents.
Resulting ratio:
18:8 = 9:4.

A

neelesh1508 · Answer

Given,

4 Pen = 6 Pencil
=> 1 Pen = 6/4 Pencil
=> 1 Pen = 3/2 Pencil ..... Equation 1

Also given,

1 Book = 6 Pen ...... Equation 2

And

1 CD = 4 Pencil ....... Equation 3

We need to find out below ratio

Book : CD

Substitute the value of Book and CD in terms of Pen and Pencil from equation 2 and 3 respectively

=> 6 Pen : 4 Pencil
=> 1 Pen : 4/6 Pencil
=> 1 Pen : 2/3 Pencil

Substitute the value of 1 Pen in terms of Pencil from equation 1

=> 3/2 Pencil : 2/3 Pencil
=> 9 Pencil : 4 Pencil
Cancel the Pencil form both the sides
=> 9 : 4

Hence, the expected ratio is 9:4.

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JeffTargetTestPrep · Answer

We can let each pen cost 6 cents and each pencil cost 4 cents (notice that the cost of 4 pens is 24 cents and so is the cost of 6 pencils). So a CD would cost 4 x 4 = 16 cents and a book would cost 6 x 6 = 36 cents. Therefore, the ratio of the cost of a book to that of a CD is 36 : 16, or 9 : 4.

Answer: A

TheNightKing · Answer

I solved with the same approach. 
Assume Cost of each item to be : Pen=6, Pencil=4, CD becomes 16 and book becomes 36.
We need to find 36:16 which is 9:4.
Hence A

bumpbot · Answer

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The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD

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The cost of 4 pens is equal to the cost of 6 pencils. The cost of a CD

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