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10 Jul 2025, 08:00
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Increased Efficiency: 48 - 0.2R
Decreased Efficiency: 45 - 0.15R
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Difficulty:
95%
(hard)
Question Stats:
60% (02:40) correct
40%
(02:52)
wrong
based on 309
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A machine operates at an efficiency of 36 units per liter of fuel when running at exactly 60 rotations per minute (RPM). Its efficiency decreases by 1.2 units for every 8 RPM increase above 60, and increases by 0.8 units for every 4 RPM decrease below 60.
Select for Increased Efficiency a formula for the machine’s efficiency when running at R RPM, where 0 < R < 60 and select for Decreased Efficiency a formula for the machine’s efficiency when running at R RPM, where R > 60. Make only two selections, one in each column.
| Increased Efficiency | Decreased Efficiency | |
| 36 - 0.3R | ||
| 36 + 0.2R | ||
| 45 - 0.15R | ||
| 48 - 0.2R | ||
| 48 + 0.2R | ||
| 60 - 0.25R |
ShowHide Answer
Official Answer
Increased Efficiency: 48 - 0.2R
Decreased Efficiency: 45 - 0.15R
10 Jul 2025, 08:30
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Bunuel
GMAT Club Official Explanation:
Increased Efficiency (R < 60):
Efficiency increases by 0.8 units for every 4 RPM below 60.
So, number of 4-RPM drops = (60 - R)/4
Increase = 0.8 * (60 - R)/4
Efficiency = 36 + 0.8 * (60 - R)/4 = 48 - 0.2R
Decreased Efficiency (R > 60):
Efficiency decreases by 1.2 units for every 8 RPM above 60.
So, number of 8-RPM increases = (R - 60)/8
Decrease = 1.2 * (R - 60)/8
Efficiency = 36 - 1.2 * (R - 60)/8 = 45 - 0.15R
General Discussion
10 Jul 2025, 09:08
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The formulas for the machine's efficiency are as follows:
For Increased Efficiency (when 0<R<60):
The machine's efficiency increases by 0.8 units for every 4 RPM decrease below 60. This means for every 1 RPM decrease, the efficiency increases by 0.8/4=0.2 units.
The decrease in RPM from 60 is (60−R).
So, the total increase in efficiency is 0.2∗(60−R).
The efficiency formula is 36+0.2∗(60−R)=36+12−0.2R=48−0.2R.
For Decreased Efficiency (when R>60):
The machine's efficiency decreases by 1.2 units for every 8 RPM increase above 60. This means for every 1 RPM increase, the efficiency decreases by 1.2/8=0.15 units.
The increase in RPM from 60 is (R−60).
So, the total decrease in efficiency is 0.15∗(R−60).
The efficiency formula is 36−0.15∗(R−60)=36−0.15R+9=45−0.15R.
Therefore, the correct selections are:
Increased Efficiency: 48−0.2R
Decreased Efficiency: 45−0.15R
For Increased Efficiency (when 0<R<60):
The machine's efficiency increases by 0.8 units for every 4 RPM decrease below 60. This means for every 1 RPM decrease, the efficiency increases by 0.8/4=0.2 units.
The decrease in RPM from 60 is (60−R).
So, the total increase in efficiency is 0.2∗(60−R).
The efficiency formula is 36+0.2∗(60−R)=36+12−0.2R=48−0.2R.
For Decreased Efficiency (when R>60):
The machine's efficiency decreases by 1.2 units for every 8 RPM increase above 60. This means for every 1 RPM increase, the efficiency decreases by 1.2/8=0.15 units.
The increase in RPM from 60 is (R−60).
So, the total decrease in efficiency is 0.15∗(R−60).
The efficiency formula is 36−0.15∗(R−60)=36−0.15R+9=45−0.15R.
Therefore, the correct selections are:
Increased Efficiency: 48−0.2R
Decreased Efficiency: 45−0.15R
