vinay1983 wrote:This is the question:
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. 200
B. 50
C. 250
D. 150
E. 400
This is an EITHER/OR problem.
Every vehicle is EITHER an SUV OR a non-SUV.
Every vehicle is EITHER diesel OR non-diesel.
Use a GROUP GRID (also known as a double-matrix) to organize the data.
The key to the grid is the following:
The values in any row or column must add up to the TOTAL of that row or column.
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.
Let total SUVs = 4x.
Since 3/4 of the SUVs are diesel, diesel SUVs = (3/4)(4x) = x.
Since there 1/2 as many SUVs as non-SUVs, non-SUVs = 8x.
Enter this information into the grid:
SUVs not powered by diesel were a sixth of non SUVs not powered by diesel.
Thus, the
x SUVS that are not diesel are equal to 1/6 of the 300 non-SUVS that are not diesel:
x = 1/6 * 300
x = 50.
Resulting grid:
Total diesels = 250.
The correct answer is
C.
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