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# In a parking lot, 1/3 of the vehicles are black and 1/5 of the remaind

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In a parking lot, 1/3 of the vehicles are black and 1/5 of the remaind  [#permalink]

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19 Aug 2018, 09:12
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Difficulty:

15% (low)

Question Stats:

93% (01:17) correct 7% (01:09) wrong based on 20 sessions

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In a parking lot, $$\frac{1}{3}$$ of the vehicles are black and $$\frac{1}{5}$$ of the remainder are white. How many vehicles could be parked on the lot?

(A) 8
(B) 12
(C) 20
(D) 30
(E) 35

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Re: In a parking lot, 1/3 of the vehicles are black and 1/5 of the remaind  [#permalink]

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19 Aug 2018, 09:19
$$\frac{1}{3}$$ Black. The remainder is $$\frac{2}{3}$$.
And $$\frac{1}{5}$$ of $$\frac{2}{3}$$ is $$\frac{2}{15}$$.
LCM of the denominator 3,15 is 15. Hence the number of the vehicle in the parking lot should be a multiple of 15. 30 is a multiple.
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Re: In a parking lot, 1/3 of the vehicles are black and 1/5 of the remaind  [#permalink]

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19 Aug 2018, 10:53
2
Bunuel wrote:
In a parking lot, $$\frac{1}{3}$$ of the vehicles are black and $$\frac{1}{5}$$ of the remainder are white. How many vehicles could be parked on the lot?

(A) 8
(B) 12
(C) 20
(D) 30
(E) 35

Solve by backsolving
Since 1/3 of the vehicles are black eliminate A, C, E, since these are not multiples of 3 and no. of cars must be a whole number.
Check D, 1/3 of 30 = 10, Remaining =20, which is divisible by 5.
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Re: In a parking lot, 1/3 of the vehicles are black and 1/5 of the remaind  [#permalink]

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19 Aug 2018, 10:59
Let total vehicles be x.
Then (1/3 of x)+(2/15 of x) should be an integer.
So, 6/15 of x is an integer
x=30 from the options fulfils this condition,hence D is the correct choice.

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Re: In a parking lot, 1/3 of the vehicles are black and 1/5 of the remaind   [#permalink] 19 Aug 2018, 10:59
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