Dan bought x pencils, some at 10 cents each and the rest at 6 cents ea

Question

Dan bought x pencils, some at 10 cents each and the rest at 6 cents each. For the same
amount of money that he spent on these pencils, he could have bought x pencils at 9 cents
each. What is the ratio of the number of 10-cent pencils purchased to the number of 6-cent
pencils purchased?

(A) 1 : 1
(B) 2 : 1
(C) 3 : 1
(D) 4 : 1
(E) 5 : 1

Sabby · Accepted Answer

Hi,

you could do it just as following, it takes a few seconds :

Set y= pencils at 10 cts and x= pencils at 6 cts

9(x+y)=10y+6x
9x+9y=10y+6x
3x=y
y/x=3/1

Answer C)

CrackverbalGMAT · Answer

Let the number of pencils bought at 10 cents = y. The cost = 10y

The number of pencils bought at 6 cents = x - y. The cost = 6(x - y)

The number of pencils bought at 9 cents = x. Therefore the total cost = 9x

Given that the total cost for pencils bought at 10 and 6 cents = Total cost of pencils bought at 9 cents

10y + 6(x - y) = 9x

10y + 6x - 6y = 9x

4y = 3x

x = 4y/3

Price of 10 cent pencils = y and cost of 6 cent pencils = x - y = 4y/3 - y = y/3

Ratio of 10 cent pencils to 6 cent pencils = y : (x - y) = y : y/3 = 3 : 1

Option C

Arun Kumar

rajatchopra1994 · Answer

Explanation:

Bought x pencils at 9 cents means average price per pencil purchased is 9cent.
let x = 4
In order for the average amount to be 9cent i.e. 36 cents total, 
Need to have 3 -10 cent pencils per 6cent pencil.
So the ratio will be 3:1

IMO-C

rajatchopra1994 · Answer

CrackVerbalGMAT  Arun Sir,

Is my approach correct ? Finds your a bit lengthy.

Regards,
Rajat Chopra

CrackverbalGMAT · Answer

Hello Rajatchopra1994 rajatji. Nothing wrong in the approach you have used. I just go by what comes to my mind first. It could be conceptual, plugging in values or eliminating options.

Its good to have different approaches to the same question, lengthy or otherwise. It will help the test takers.

Arun Kumar

bumpbot · Answer

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Dan bought x pencils, some at 10 cents each and the rest at 6 cents ea

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Dan bought x pencils, some at 10 cents each and the rest at 6 cents ea

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