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10 Aug 2024, 05:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
32% (03:31) correct
68%
(03:11)
wrong
based on 79
sessions
History
Date
Time
Result
Not Attempted Yet
A utilities company sells electrical wiring at $7 per 15 meters, which costs them around $3 per 15 meters to make. If a customer purchases at least 300 meters, the company offers a 10% discount on the rate, with the discount given increasing by 5% for each additional 300 meters, such that 600 meters would receive a 15% discount on the total bill. They must sell less than what length of wire if they wish to have at least a 40% profit margin?
(A) 600 meters
(B) 900 meters
(C) 1200 meters
(D) 1500 meters
(E) 1800 meters
(A) 600 meters
(B) 900 meters
(C) 1200 meters
(D) 1500 meters
(E) 1800 meters
13 Aug 2024, 21:51
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Selling Price: $7 / 15 meters = $0.4667 per meter
Cost Price: $3 / 15 meters = $0.2 per meter
For 300-599 meters (10% discount):
Price after discount: $0.4667 * 0.9 = $0.42 per meter
Profit per meter: $0.42 - $0.2 = $0.22
Profit margin: ($0.22 / $0.42) * 100 = 52.38%
For 600-899 meters (15% discount):
Price after discount: $0.4667 * 0.85 = $0.3967 per meter
Profit per meter: $0.3967 - $0.2 = $0.1967
Profit margin: ($0.1967 / $0.3967) * 100 = 49.58%
For 900-1199 meters (20% discount):
Price after discount: $0.4667 * 0.8 = $0.3734 per meter
Profit per meter: $0.3734 - $0.2 = $0.1734
Profit margin: ($0.1734 / $0.3734) * 100 = 46.44%
For 1200-1499 meters (25% discount):
Price after discount: $0.4667 * 0.75 = $0.35 per meter
Profit per meter: $0.35 - $0.2 = $0.15
Profit margin: ($0.15 / $0.35) * 100 = 42.86%
For 1500-1799 meters (30% discount):
Price after discount: $0.4667 * 0.7 = $0.3267 per meter
Profit per meter: $0.3267 - $0.2 = $0.1267
Profit margin: ($0.1267 / $0.3267) * 100 = 38.78%
We can see that the profit margin drops below 40% when the length reaches 1500 meters.
Therefore, the correct answer is (D) 1500 meters. They must sell less than 1500 meters of wire to maintain at least a 40% profit margin.
This definitely took me a while, hopefully someone has a more time-efficient way of solving this question.
Cost Price: $3 / 15 meters = $0.2 per meter
For 300-599 meters (10% discount):
Price after discount: $0.4667 * 0.9 = $0.42 per meter
Profit per meter: $0.42 - $0.2 = $0.22
Profit margin: ($0.22 / $0.42) * 100 = 52.38%
For 600-899 meters (15% discount):
Price after discount: $0.4667 * 0.85 = $0.3967 per meter
Profit per meter: $0.3967 - $0.2 = $0.1967
Profit margin: ($0.1967 / $0.3967) * 100 = 49.58%
For 900-1199 meters (20% discount):
Price after discount: $0.4667 * 0.8 = $0.3734 per meter
Profit per meter: $0.3734 - $0.2 = $0.1734
Profit margin: ($0.1734 / $0.3734) * 100 = 46.44%
For 1200-1499 meters (25% discount):
Price after discount: $0.4667 * 0.75 = $0.35 per meter
Profit per meter: $0.35 - $0.2 = $0.15
Profit margin: ($0.15 / $0.35) * 100 = 42.86%
For 1500-1799 meters (30% discount):
Price after discount: $0.4667 * 0.7 = $0.3267 per meter
Profit per meter: $0.3267 - $0.2 = $0.1267
Profit margin: ($0.1267 / $0.3267) * 100 = 38.78%
We can see that the profit margin drops below 40% when the length reaches 1500 meters.
Therefore, the correct answer is (D) 1500 meters. They must sell less than 1500 meters of wire to maintain at least a 40% profit margin.
This definitely took me a while, hopefully someone has a more time-efficient way of solving this question.
18 Aug 2024, 06:54
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siddhantvarma I'll have a crack at it, tell me what you think:
So X is the amount of 15 meter wire the company bought, they paid 3x for it
They sell each 15 meters for $7, so they sell the first 20x (300 meters) for 0.9*7*20 = 126, and they paid 60 for it. You can instinctively tell that it's above 40%.
With these questions I always plug in the middle answer and check if it's higher or lower:
1200 meters = 80x.
300 = 0.9 of the original price
600 = 0.85
900 = 0.8
1200 = 0.75 = 3/4
so calculate 80*(3/4)*7 = $420, and it cost the company $240. 24/42 = ≈0.57, or 1-0.57 = 0.43*100 = ≈43% profit margin.
This means that D, 1500, will probably be a bit less than 40% margin, but we can check anyway:
1500 = 0.7*100*7 = $490, and it cost the company 3*100 = $300. 300/490 = 60/98, which again intuitively means that it's a bit more than 60/100. 1-(61/100) = 39% margin, which is below the 40% margin that the company wants.
Thus, the company can sell more than 1200 but less than 1500. Answer D
With this sort of questions I estimate a lot so let me know if this method is not correct.
So X is the amount of 15 meter wire the company bought, they paid 3x for it
They sell each 15 meters for $7, so they sell the first 20x (300 meters) for 0.9*7*20 = 126, and they paid 60 for it. You can instinctively tell that it's above 40%.
With these questions I always plug in the middle answer and check if it's higher or lower:
1200 meters = 80x.
300 = 0.9 of the original price
600 = 0.85
900 = 0.8
1200 = 0.75 = 3/4
so calculate 80*(3/4)*7 = $420, and it cost the company $240. 24/42 = ≈0.57, or 1-0.57 = 0.43*100 = ≈43% profit margin.
This means that D, 1500, will probably be a bit less than 40% margin, but we can check anyway:
1500 = 0.7*100*7 = $490, and it cost the company 3*100 = $300. 300/490 = 60/98, which again intuitively means that it's a bit more than 60/100. 1-(61/100) = 39% margin, which is below the 40% margin that the company wants.
Thus, the company can sell more than 1200 but less than 1500. Answer D
With this sort of questions I estimate a lot so let me know if this method is not correct.
