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A major airplane manufacturer announced the sale of 150 small airliner

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A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 10 Feb 2015, 08:48
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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%

Kudos for a correct solution.

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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 10 Feb 2015, 10:10
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Answer is (money from mid and large plane)/(total money from all the planes)x 100
=\((175*75+220*60)/(125*150+175*75+220*60) * 100\)
= 58.4%
you could just multiply add divide to get answer.
However sometimes its much better to make it easy we should see if we have any common terms

125*150=(5*5*5)*(2*3*5*5)
175*75=(5*5*7)*(3*5*5)
220*60=(2*2*11*5)*(2*2*3*5)

3*5*5 is common cancel it
Ans becomes
(175+176)/(176+175+250)*100 =~=~ 350/600*100=~=~7/12*100=60% >>> 58% is closest.

Usually you should check to see if the ans options are not close by, if we have options such at 58% 57% 59% then we have to multiply.
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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 11 Feb 2015, 07:54
ynaikavde wrote:
Answer is (money from mid and large plane)/(total money from all the planes)x 100
=\((175*75+220*60)/(125*150+175*75+220*60) * 100\)
= 58.4%
you could just multiply add divide to get answer.
However sometimes its much better to make it easy we should see if we have any common terms

125*150=(5*5*5)*(2*3*5*5)
175*75=(5*5*7)*(3*5*5)
220*60=(2*2*11*5)*(2*2*3*5)

3*5*5 is common cancel it
Ans becomes
(175+176)/(176+175+250)*100 =~=~ 350/600*100=~=~7/12*100=60% >>> 58% is closest.

Usually you should check to see if the ans options are not close by, if we have options such at 58% 57% 59% then we have to multiply.



Is there any other way to solve this. Calculation will take time.
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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 11 Feb 2015, 20:42
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Answer = C. 58%

Equation setup would be as follows:

\(\frac{175*75 + 60*220}{150*125 + 75*175 * 60*220} * 100\)

The above equation has 75 in common; divide the complete equation by 75

\(\frac{175+176}{175+176+250}* 100 \approx{\frac{350}{600} * 100} \approx{\frac{700}{12}} = 58%\)
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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 11 Feb 2015, 21:37
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arunrnair wrote:
ynaikavde wrote:
Answer is (money from mid and large plane)/(total money from all the planes)x 100
=\((175*75+220*60)/(125*150+175*75+220*60) * 100\)
= 58.4%
you could just multiply add divide to get answer.
However sometimes its much better to make it easy we should see if we have any common terms

125*150=(5*5*5)*(2*3*5*5)
175*75=(5*5*7)*(3*5*5)
220*60=(2*2*11*5)*(2*2*3*5)

3*5*5 is common cancel it
Ans becomes
(175+176)/(176+175+250)*100 =~=~ 350/600*100=~=~7/12*100=60% >>> 58% is closest.

Usually you should check to see if the ans options are not close by, if we have options such at 58% 57% 59% then we have to multiply.



Is there any other way to solve this. Calculation will take time.


hi
in this question if you want to avoid calculations, you have to estimate answer..
the price of s/m/l is 125/175/220= approx 5/7/9..
the number of s/m/l is 150/75/60= approx 2/1/1..
now as we have taken 60 as 75 , the ans should be less than what we will get in approximation..
(7*1+9*1)/(7*1+9*1+10*2) =16/26= closer to 62 and the ans has to be less than this so 58 should be the ans
ans C..
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A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 11 Feb 2015, 21:42
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Bunuel 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%

Kudos for a correct solution.


Since you need company's income from large + medium airliners, you can find the average price of these two so that you have one less unit to work with.
Average of 175 and 220 when weights are 75 and 60 respectively (i.e. a ratio of 5:4) - Using scale method, split 45 into 5:4, you will get 25 and 20. So average will be 20 more than 175 i.e. at 195. So you have 135 airliners of price 195.
If you are lost here, check scale method: http://www.veritasprep.com/blog/2011/03 ... -averages/

Company's income from these 135 airliners \(= \frac{135*195}{(135*195 + 150*125)} = \frac{27*39}{(27*39 + 150*5)} = \frac{9*39}{(9*39 + 250)} = 58%\)

Answer (C)
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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 12 Feb 2015, 00:44
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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%


Total income = 150*125+75*175+60*220 = 75*425 + 60*220 = 15*(5*425+4*220) = 15*(2125+880) = 15*3005
Income from large and medium airplanes = 75*175+60*220 = 15*(5*175+4*220) = 15*(875+880) = 15*1755

Required % = 1755*100/3005 %= 175/3% = 58%

OA = C
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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 16 Feb 2015, 05:54
Bunuel 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%

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: C

The company's total revenue is $45,075 million. It sold $18,750 worth of small airliners, $13,125 million worth of medium airliners, and $13,200 million worth of large airliners. The combined total of large and medium airliners was $26,325 or 58% of the total (answer choice C). Be careful that you calculated the correct combination of products sold!

You are not allowed to use a calculator on the GMAT, so using some clever techniques to estimate the answer and save valuable time is very important:

After doing some initial math, you will end up with the following ugly fraction:

26,325/45,075
Then:

1) Factor out a 25; this is clearly possible since the last two digits are a multiple of 25

1053/1803

2) Factor out a 3; this is clearly possible since the sum of the digits of each number is a multiple of 3

351/601
3) Divide numerator and denominator by 6; this will return a number very close to x/100 and can be used to estimate percentage with these answer choices: about 58/100.
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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 10 Aug 2018, 09:32
using ratio, I could make an educated guess:

small airliners is 150 * $125 million, so 75 * 250
medium airliners 75 * $175 million,
large airliners 60 * $220 million

therefore, you can see that medium and large airliners is slightly higher than small, therefore 58 seems correct choice. this was an educated guess.
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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 26 Jan 2019, 13:37
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:

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Re: A major airplane manufacturer announced the sale of 150 small airliner  [#permalink]

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New post 27 Jan 2019, 07:20
Bunuel 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%

\(150:75:60\,\,\mathop = \limits^{:\,15} \,\,10:5:4\)

\(? = {{5 \cdot 175 + 4 \cdot 220} \over {10 \cdot 125 + 5 \cdot 175 + 4 \cdot 220}}\,\, = \,\,{{5\left( {100 + 70 + 5 + 88 \cdot 2} \right)} \over {5\left( {125 \cdot 2 + 100 + 70 + 5 + 88 \cdot 2} \right)}}\,\, = \,\,{{351} \over {601}}\mathop \cong \limits^{\left( * \right)} \,\,\,59\%\)

\(\left( * \right)\,\,\,\,{{350} \over {600}} = {{350} \over 6}\% = {{360 - 10} \over 6} \cong 59\%\)


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

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Re: A major airplane manufacturer announced the sale of 150 small airliner   [#permalink] 27 Jan 2019, 07:20
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