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A basket of 1430 apples is divided equally among a group of apple love

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A basket of 1430 apples is divided equally among a group of apple love [#permalink]

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New post 19 Jun 2016, 11:24
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A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples did each person get before 45 people joined the feast?

A. 20.
B. 21.
C. 22.
D. 23.
E. 24.
[Reveal] Spoiler: OA

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Re: A basket of 1430 apples is divided equally among a group of apple love [#permalink]

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New post 19 Jun 2016, 12:31
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Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.

Since number of apples per person * total persons = 1430, the answer should be a factor of 1430. Only C is. And that's your answer.
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A basket of 1430 apples is divided equally among a group of apple love [#permalink]

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New post 19 Jun 2016, 12:33
Bunuel wrote:
A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples did each person get before 45 people joined the feast?

A. 20.
B. 21.
C. 22.
D. 23.
E. 24.


Since I didn't know what equation to make, I used the answer choices.

First I wanted to see if 1430 is divisible by anyone of the answer choices. (If non of the answer choices divided the number 1430, I would have simply guessed and moved to another question in actual test.)

A.1430/20 = 143/2
B 1430/21 = 1430/21
C 1430/22 = 65 (I checked this number first.)

If 1430 apple was divided among 65 people, each would have received 22. After addition of 45 people the answer should be 13. 1430/110 = 13.

C is the answer.
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Re: A basket of 1430 apples is divided equally among a group of apple love [#permalink]

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New post 28 Dec 2017, 07:31
Bunuel wrote:
A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples did each person get before 45 people joined the feast?

A. 20.
B. 21.
C. 22.
D. 23.
E. 24.


Hi.
x*y = 1430
(x+45)*(y-9) = 1430
Solve the equation you get the answer
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Re: A basket of 1430 apples is divided equally among a group of apple love [#permalink]

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New post 01 Jan 2018, 03:12
Hi please tell me what is wrong with this approach

let a -> average ( initial )
and n -> number of people ( initial)

(1430) / n - (1430)/ (n+45) = 9


but by solving i am getting very bad value of n.

kindly help
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Re: A basket of 1430 apples is divided equally among a group of apple love [#permalink]

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New post 01 Jan 2018, 03:48
Expert's post
coolnaren wrote:
Hi please tell me what is wrong with this approach

let a -> average ( initial )
and n -> number of people ( initial)

(1430) / n - (1430)/ (n+45) = 9


but by solving i am getting very bad value of n.

kindly help


Your equation is correct and if you plug it into google you will get that n = 65.
Then you would need to divide 1430 by 65 to get answer (C).
But - this is an extremely complex quadratic equation.
If, like on this question, you find yourself in front of such a complex quadratic equation there is a very good chance that you've missed a shortcut. Look for it!
For example, look at the solutions using prime factorization above.
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Re: A basket of 1430 apples is divided equally among a group of apple love   [#permalink] 01 Jan 2018, 03:48
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