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A major airplane manufacturer announced the sale of 150

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A major airplane manufacturer announced the sale of 150

by swerve » Fri Jan 25, 2019 9:35 am

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A major airplane manufacturer announced the sale of 150 small airliners at $125 million each, 75 medium sized airliners at $175 million each, and 60 large airliners at $220 million each. What percentage of the company's income came from large and medium airliners?

A. 29%
B. 41%
C. 58%
D. 69%
E. 70%

The OA is C

Source: Veritas Prep
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by [email protected] » Fri Jan 25, 2019 11:34 am
Hi All,

We're told that a major airplane manufacturer announced the sale of 150 small airliners at $125 million each, 75 medium sized airliners at $175 million each, and 60 large airliners at $220 million each. We're asked for the percentage of the company's income that came from large and medium airliners. While this question appears to involve a lot of math, you can actually simplify it by taking advantage of the ratios involved; the answers are 'spaced out' enough that you can also use estimation to avoid some of the math.

Since the question asks for the PERCENTAGE of the total revenue, we can simplify the ratio of the types of planes. Based on the given information, the ratio of small airliners to medium airlines to large airliners is 150:75:60. Each of those numbers is a multiple of 15, so the ratio can be 'reduced' to 10:5:4. Using those numbers, we'd have revenues of...

Small: (10)($125 mill.) = $1250 mill
Medium: (5)($175 mill.) = $875 mill
Large: (4)($220 mill.) = $880 mill
Total = $1250 + $875 + $880 = $3005 million

The percent of that total that is Medium and Large airliners is (875 + 880)/($3005) = $1755/3005 = approximately 1800/3000 = about 18/30 = about 3/5 = about 60%. There's only one answer that's close...

Final Answer: C

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by fskilnik@GMATH » Sun Jan 27, 2019 6:06 am
swerve wrote:A major airplane manufacturer announced the sale of 150 small airliners at $125 million each, 75 medium sized airliners at $175 million each, and 60 large airliners at $220 million each. What percentage of the company's income came from large and medium airliners?

A. 29%
B. 41%
C. 58%
D. 69%
E. 70%
Source: Veritas Prep
$$150:75:60\,\,\mathop = \limits^{:\,15} \,\,10:5:4$$
$$? = {{5 \cdot 175 + 4 \cdot 220} \over {10 \cdot 125 + 5 \cdot 175 + 4 \cdot 220}}\,\, = \,\,{{5\left( {100 + 70 + 5 + 88 \cdot 2} \right)} \over {5\left( {125 \cdot 2 + 100 + 70 + 5 + 88 \cdot 2} \right)}}\,\, = \,\,{{351} \over {601}}\mathop \cong \limits^{\left( * \right)} \,\,\,59\% $$
$$\left( * \right)\,\,\,\,{{350} \over {600}} = {{350} \over 6}\% = {{360 - 10} \over 6} \cong 59\% $$


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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