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A store has a parking lot which contains 70 parking spaces. Each row

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A store has a parking lot which contains 70 parking spaces. Each row [#permalink]

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New post 16 Oct 2017, 10:23
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A store has a parking lot which contains 70 parking spaces. Each row in the parking lot contains the same number of parking spaces. The store has bought additional property in order to build an addition to the store. When the addition is built, 2 parking spaces will be lost from each row; however, 4 more rows will be added to the parking lot. After the addition is built, the parking lot will still have 70 parking spaces, and each row will contain the same number of parking spaces as every other row. How many rows were in the parking lot before the addition was built?

(A) 5
(B) 6
(C) 7
(D) 10
(E) 14
[Reveal] Spoiler: OA

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Re: A store has a parking lot which contains 70 parking spaces. Each row [#permalink]

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New post 16 Oct 2017, 11:29
Let the number of rows initially be 'n'. Since each row has same number of parking spaces, and total spaces are 70, 'n' must be a factor of 70. (option B is out)

Now, after we add 4 more rows, even if we reduce number of parking spaces per row, still every row has same number of spaces and total spaces are still 70. So 'n+4' also must be a factor of 70.

So n and n+4 both must be factors of 70. Only 10 from the given options fit the value of 'n' (because 10+4 = 14 is also a factor of 70).

So D answer

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Re: A store has a parking lot which contains 70 parking spaces. Each row [#permalink]

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New post 16 Oct 2017, 11:35
We know that there are 70 spots to begin with and 70 spots to end with.

Before the new construction we have 70=x*y where x is the number of rows and y is the # of spots per row.
After the construction we have 70=(x+4)*(y-2).

We know that both x and y must be positive integers, so I thought the best way was to find factors of 70 that fit both equations. Factors besides 70 and 1 are 10,7, 14, 5. The only way it works is if x=10 and y=7 and we are looking to solve for x, so the answer is D.

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A store has a parking lot which contains 70 parking spaces. Each row [#permalink]

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New post 23 Oct 2017, 08:18
Factors of 70=
1x70 ; 2x35 ; 5x14 ; 7x10

Now, given that one factor is reduced by 2 and other increased by 4 to retain same value, we know that
7x10 changed to (7-2)x(10+4) i.e. 5x14.

As number of rows increased by 4, we can deduce from above that initially there were 10 rows.

Hence, Ans D

Kudos [?]: 18 [0], given: 19

A store has a parking lot which contains 70 parking spaces. Each row   [#permalink] 23 Oct 2017, 08:18
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