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# Of the new vehicles registered in a week, 300 were neither SUVs nor we

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Math Expert
Joined: 02 Sep 2009
Posts: 54696
Of the new vehicles registered in a week, 300 were neither SUVs nor we  [#permalink]

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13 Mar 2016, 10:43
1
00:00

Difficulty:

55% (hard)

Question Stats:

75% (02:50) correct 25% (03:01) wrong based on 78 sessions

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Of the new vehicles registered in a week, 300 were neither SUVs nor were they powered by diesel. 3/4th of the SUVs registered were diesel powered and there were half as many SUVs as there were non SUVs. If SUVs not powered by diesel were a sixth of non SUVs not powered by diesel, how many vehicles registered in the week were powered by diesel?

A. 50
B. 150
C. 200
D. 250
E. 400

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Re: Of the new vehicles registered in a week, 300 were neither SUVs nor we  [#permalink]

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13 Mar 2016, 19:54
2
1
therefore Non diesel SUVs = 1/6 *300 = 50
Let total number of diesel powered SUVs = x
Since 3/4th of the SUVs registered were diesel powered
(1/4)*x = 50
=> x = 200
therefore Diesel powered SUVs = 200 - 50 = 150

there were half as many SUVs as there were non SUVs
Let total number of diesel powered non SUVs = y
150 + 50 = 1/2(300 + y)
=> 200 * 2 = 300 + y
=> y = 100
Number of diesel powered non SUVs = 100

vehicles registered in the week were powered by diesel = 150 + 100 = 250
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Re: Of the new vehicles registered in a week, 300 were neither SUVs nor we  [#permalink]

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13 Mar 2016, 23:08
Bunuel wrote:
Of the new vehicles registered in a week, 300 were neither SUVs nor were they powered by diesel. 3/4th of the SUVs registered were diesel powered and there were half as many SUVs as there were non SUVs. If SUVs not powered by diesel were a sixth of non SUVs not powered by diesel, how many vehicles registered in the week were powered by diesel?

A. 50
B. 150
C. 200
D. 250
E. 400

Supposing that 'x' is the number of vehicles of SUV.
.25*x = non diesel SUV
.75*x = diesel SUV
.5*x = only diesel
By supposition,
.25*x = 1/6*300
=>x = 200
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Re: Of the new vehicles registered in a week, 300 were neither SUVs nor we  [#permalink]

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12 Aug 2017, 10:53
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Re: Of the new vehicles registered in a week, 300 were neither SUVs nor we   [#permalink] 12 Aug 2017, 10:53
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