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20 Feb 2019, 15:13
1
00:00

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
Intern
Joined: 27 Nov 2018
Posts: 30

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20 Feb 2019, 15:35
1
Isn’t the answer $8? Can you (or someone) give an explanation [size=80][b][i]Posted from my mobile device[/i][/b][/size] e-GMAT Representative Joined: 04 Jan 2015 Posts: 3074 Re: A boy purchased some chocolates from a shop for$ 120. In the next sho  [#permalink]

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20 Feb 2019, 20:49
1

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.

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: A boy purchased some chocolates from a shop for $120. In the next sho [#permalink] ### Show Tags 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 _________________ e-GMAT Representative Joined: 04 Jan 2015 Posts: 3074 Re: A boy purchased some chocolates from a shop for$ 120. In the next sho  [#permalink]

### Show Tags

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.

_________________