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A boy purchased some chocolates from a shop for $ 120. In the next sho

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A boy purchased some chocolates from a shop for $ 120. In the next sho  [#permalink]

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New post 20 Feb 2019, 15:13
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

61% (02:05) correct 39% (02:38) wrong based on 17 sessions

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A boy purchased some chocolates from a shop for $ 120. In the next shop he found that the price per piece of chocolate is $ 3 less than that charged at the previous shop, and as such he could have purchased 2 more chocolates. How many chocolates did he buy from the first shop?

A)7
B)8
C)9
D)10
E)15
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Re: A boy purchased some chocolates from a shop for $ 120. In the next sho  [#permalink]

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New post 20 Feb 2019, 15:29
let each piece of chocolate priced at x dollars, and he bought a pieces.
ax=120
(a+2)(x-3)=120
from testing the answers you'd get 8 pieces of chocolate, each priced at 15 each from the first shop.
Unless the question meant to ask how many pieces he bought from SECOND shop, then the answer should be B - 8 pieces.
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Re: A boy purchased some chocolates from a shop for $ 120. In the next sho  [#permalink]

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New post 20 Feb 2019, 15:35
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Isn’t the answer $8? Can you (or someone) give an explanation

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Re: A boy purchased some chocolates from a shop for $ 120. In the next sho  [#permalink]

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New post 20 Feb 2019, 20:49
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Solution – Using Options



Given:
    • A boy purchased some chocolates from a shop for $120.
    • In the next shop he found that the price per piece of chocolate is $3 less than that charged at the previous shop.
    • Because of the lower price in the next shop, he figured out that he could have purchased 2 more chocolates in the next shop, compared to what he bought originally.

To find:
    • The number of chocolates he bought from the first shop

Approach and Working:
We know that 120/number of chocolates = price per chocolate

For the first shop,
    • 120/number of chocolates bought = price per chocolate
    • Therefore, number of chocolates bought must be a factor of 120 (at this point, we can discard option A and option C)

For the second shop,
    • 120/(number of chocolates bought + 2) = price per chocolate – 3
    • Therefore, (number of chocolates bought + 2) must also be a factor of 120 (at this point, we can discard option E)

At this point, we can check the remaining two options.
If number of chocolates bought = 8, then
    • Price per chocolate in the first shop = \(\frac{120}{8} = 15\)
    • Price per chocolate in the second shop = \(\frac{120}{(8 + 2)} = 12\)
    • And, 15 – 12 = 3, which satisfies our given condition.

Hence, the correct answer is option B.

Answer: B

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Re: A boy purchased some chocolates from a shop for $ 120. In the next sho  [#permalink]

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New post 20 Feb 2019, 20:52

Solution – Using 1 Variable



Given:
    • A boy purchased some chocolates from a shop for $120.
    • In the next shop he found that the price per piece of chocolate is $3 less than that charged at the previous shop.
    • Because of the lower price in the next shop, he figured out that he could have purchased 2 more chocolates in the next shop, compared to what he bought originally.

To find:
    • The number of chocolates he bought from the first shop

Approach and Working:
Let us assume that the number of chocolates he bought from the first shop is n.
    • Price per chocolate in the first shop = \(\frac{120}{n}\)

Number of chocolates he could have bought from the second shop = n + 2
    • Price per chocolate in the second shop = \(\frac{120}{(n + 2)}\)

As per the given information,
    • \(\frac{120}{n} – \frac{120}{n+2} = 3\)
    Simplifying, we get n = 8

Hence, the correct answer is option B.

Answer: B

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Re: A boy purchased some chocolates from a shop for $ 120. In the next sho  [#permalink]

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New post 20 Feb 2019, 20:56

Solution – Using 2 Variables



Given:
    • A boy purchased some chocolates from a shop for $120.
    • In the next shop he found that the price per piece of chocolate is $3 less than that charged at the previous shop.
    • Because of the lower price in the next shop, he figured out that he could have purchased 2 more chocolates in the next shop, compared to what he bought originally.

To find:
    • The number of chocolates he bought from the first shop

Approach and Working:
Let us assume that the number of chocolates he bought from the first shop is n, and the price of each chocolate in the first shop is p
    • Therefore, we can say n x p = 120 …… (1)

Number of chocolates he could have bought from the second shop = n + 2
And the price of each chocolate in the second shop = p – 3
    • Therefore, we can say that (n + 2) (p – 3) = 120 …… (2)

Solving the equations (1) and (2), we get n = 8 and p = 15

Hence, the correct answer is option B.

Answer: B

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Re: A boy purchased some chocolates from a shop for $ 120. In the next sho   [#permalink] 20 Feb 2019, 20:56
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