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A certain store sells two types of pens: one type for $2 per pen and

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A certain store sells two types of pens: one type for $2 per pen and  [#permalink]

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New post 12 Jul 2018, 04:47
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Question Stats:

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A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can buy?


A. 9
B. 10
C. 11
D. 12
E. 20

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A certain store sells two types of pens: one type for $2 per pen and  [#permalink]

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New post 12 Jul 2018, 04:56
Bunuel wrote:
A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can buy?


A. 9
B. 10
C. 11
D. 12
E. 20



As 2 is the lower price between 2 types of pens we have to buy max pen spending 2 $ types in order to maximize the no. of pens.

So, 11 * 2$ + $3 = 25 $

Total no of pens = 11 + 1 =12

thus the best answer is D.

It's mentioned in the question paper that a buyer can spend up to 25$.
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Re: A certain store sells two types of pens: one type for $2 per pen and  [#permalink]

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New post 12 Jul 2018, 04:59
If the only goal is to purchase as many pens as possible and quality doesn't matter pick up the cheap pens
for $24 you can purchase twelve $2 pens

P.S please prompt me what exactly "up to $25" means: \(<=25\) or \(<25\)
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Re: A certain store sells two types of pens: one type for $2 per pen and  [#permalink]

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New post 12 Jul 2018, 05:07

Solution



Given:

    • One type of pen costs $2 per pen.
    • Another type of pen costs $3 per pen.

To find:
    • Greatest number of pens a customer can buy if the customer spend up to $25.

Approach and Working:

    • Greatest number of pens a customer can buy:
    o if the customer spend maximum amount i.e $25.
    o And, he buys more numbers of cheapest pen.
       Hence, he will maximum of $2 pen.

    • Let the customer buys x pen of $2 and y pen of $3.
      o 2x+3y=25
      o Hence, he either buy 12 pens that will cost him $24.
      o Or, he can buy one $3 pen and eleven $2 pen that will cost him $25.

    • Hence, in every case, he will buy 12 pens only.

Hence, the correct answer is option D.

Answer: D
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A certain store sells two types of pens: one type for $2 per pen and  [#permalink]

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New post 12 Jul 2018, 05:20
LevanKhukhunashvili wrote:
If the only goal is to purchase as many pens as possible and quality doesn't matter pick up the cheap pens
for $24 you can purchase twelve $2 pens

P.S please prompt me what exactly "up to $25" means: \(<=25\) or \(<25\)



up to 25$ means maximum limit is 25 but if it is required u can spend less than 25. Up to 25 means you are not allowed to cross 25$.

So, < = 25.

Thanks.
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Re: A certain store sells two types of pens: one type for $2 per pen and  [#permalink]

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New post 12 Jul 2018, 06:37
Seconded. The answer is D (12)

Given:

    • One type of pen costs $2 per pen.
    • Another type of pen costs $3 per pen.

To find:
    • Greatest number of pens a customer can buy if the customer spend up to $25.

Approach and Working:

    • Greatest number of pens a customer can buy:
    o if the customer spend maximum amount i.e $25.
    o And, he buys more numbers of cheapest pen.
       Hence, he will maximum of $2 pen.

    • Let the customer buys x pen of $2 and y pen of $3.
      o 2x+3y=25
      o Hence, he either buy 12 pens that will cost him $24.
      o Or, he can buy one $3 pen and eleven $2 pen that will cost him $25.

    • Hence, in every case, he will buy 12 pens only.

Hence, the correct answer is option D.

Answer: D[/quote]
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Re: A certain store sells two types of pens: one type for $2 per pen and &nbs [#permalink] 12 Jul 2018, 06:37
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