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Jaime earned enough money by selling seashells at 25 cents each to buy

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Jaime earned enough money by selling seashells at 25 cents each to buy  [#permalink]

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New post 12 Nov 2015, 02:03
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Jaime earned enough money by selling seashells at 25 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?

(A) 5
(B) 11
(C) 17
(D) 25
(E) 30

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Re: Jaime earned enough money by selling seashells at 25 cents each to buy  [#permalink]

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New post 12 Nov 2015, 02:16
25*11=275 , which is exactly divisible by 55
Thus 11 is the minimum
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Re: Jaime earned enough money by selling seashells at 25 cents each to buy  [#permalink]

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New post 12 Nov 2015, 02:57
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1
Let the number of seashells sold by Jamie = x
and the number of paperback books sold = y
Selling price of seashells = 25 cents
Buying price of seashells = 55 cents

Now since all the money earned selling seashells is used to buy the books
25x = 55 y

Prime fatorization of
25 = 5*5
55 = 11* 5

We need to find the LCM of the 2 numbers
LCM = 5^2 * 11
= 25 * 11
= 275

Least number of seashells sold , x = 275/ 25 = 11

Answer B
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Jaime earned enough money by selling seashells at 25 cents each to buy  [#permalink]

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New post 12 Nov 2015, 06:14
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Bunuel wrote:
Jaime earned enough money by selling seashells at 25 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?

(A) 5
(B) 11
(C) 17
(D) 25
(E) 30


His payment is in Multiples of 25 cents

Payment Required is in Multiples of 55 cents

No left over means, Payment Done = Payment Required

i.e. 25x = 55y
i.e. 5x = 11y

i.e. Minimum value of x = 11 (co-efficient of y)
and Minimum value of y = 5 (co-efficient of x)


i.e. Minimum Value of x = 11

Answer: option B
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Re: Jaime earned enough money by selling seashells at 25 cents each to buy  [#permalink]

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New post 30 Nov 2015, 17:01
Hi All,

Since we're asked for the LEAST number of seashells that could have been sold, and the answer choices are numbers, we can TEST THE ANSWERS.

We're given a number of facts to work with:
1) Jamie sells seashells at 25 cents each.
2) Jamie buys books at 55 cents each.
3) Jamie spent ALL the money he earned selling seashells on books.

We're asked for the LEAST number of seashells that Jamie could have sold...

Let's TEST Answer A: 5 seashells...

With 5 seashells, Jamie would have 5(25) = 125 cents. This would allow him to buy 2 books for 110 cents total, but he would then have 15 cents left over. We're told that he spent ALL of his money on books, so this cannot be the correct answer.

Answer B: 11 seashells....

With 11 seashells, Jamie would have 11(25) = 275 cents. This would allow him to buy 5 books for 275 cents total, with no money left over. This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:

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Re: Jaime earned enough money by selling seashells at 25 cents each to buy  [#permalink]

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New post 26 Mar 2017, 14:09
LCM of 25 and 55, that is 275,
There fore least number will be 275/25 =11

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Re: Jaime earned enough money by selling seashells at 25 cents each to buy  [#permalink]

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Re: Jaime earned enough money by selling seashells at 25 cents each to buy   [#permalink] 19 Jan 2019, 08:04
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