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805+ Level|   Math Related|         
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 05:36
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Efficiency goes up by 0.2 units for each RPM below 60, so starting from 36 we add 0.2 * (60−R)
-> 36 + 0.2 * (60 - R)
Increased Efficiency -> 48 − 0.2R

Efficiency goes down by 0.15 units for each RPM above 60, so starting from 36 we subtract 0.15 * (R−60)
-> 36 - 0.15 * (R - 60)
Decreased Efficiency -> 45 - 0.15R
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 05:44
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Increased Efficiency where 0 < R < 60

36+ 0.8((60-R)/4)
=36+ 0.2(60-R)
=36+12-0.2R
=48-0.2R

Decreased Efficiency where R > 60

36- 1.2((R-60)/8)
36-0.15(R-60)
36-0.15R+9
45-0.15R
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 05:52
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Machine operates at an efficiency of 36 units per liter of fuel when running at exactly 60 rotations per minute (RPM)
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

We need,
Increased Efficiency formula for the machine’s efficiency when running at R RPM, where 0 < R < 60
Decreased Efficiency formula for the machine’s efficiency when running at R RPM, where R > 60

Now we know that ,

At 60RPM, Efficiency = 36 units/liter
Above 60 RPM, Efficiency decrease = 1.2/8 = 0.15 units/rpm
Below 60 RPM, Efficiency Increase = 0.8/4 = 0.2 units/rpm

For decreased efficiency formula, RPM > 60
=> Efficiency = 36 - 0.15*(R-60) = 36 - 0.15R + 9 = 45 - 0.15R


For increased efficiency formula, RPM < 60
=> Efficiency = 36 + 0.2*(60-R) = 36 + 12 - 0.2R = 48 - 0.2R

Increased Efficiency (for R < 60) = 48 - 0.2R
Decreased Efficiency (for R > 60) = 45 - 0.15R
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 06:02
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Correct Answer: Decreased Efficiency= 45 - 0.15R & Increased Efficiency= 48 - 0.2R
Given we have,

1) Machine operates= 36 units per liter of fuel
2) Efficiency decreases by 1.2 units for every 8 RPM increase above 60
3) Efficiency increases by 0.8 units for every 4 RPM decrease below 60.

Let's found decreased efficiency first,

Here R>60,
Decreased in RPM= R-60
For every 8 RPM we have
Decrease= R-60/8 * 1.2
Efficiency= 36- (R-60)/8 *1.2
= 36- (R-60) * 0.15
= 36- (0.15R - 9)
= 45-0.15R

Similarly we will now find out increased efficiency,

Here R<60,
Increased RPM= 60-R
For every 4 RPM we have,
Increase= 60-R/4 * 0.8
Efficiency= 36 + (60-R)/4 * 0.8
= 36 + (60-R) * 0.2
= 36 + (12 - 0.2R)
= 48 - 0.2 R
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 06:24
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See, for decreased efficiency we can write it as,

DE= 36-(1.2x(R-60)/8)

And for IE we can write it as, 36+(0.8x(60-R)/4)

As we know that base efficiency is 36 and depending on rpm the efficiency reduces by 1.2 unites and increase by 0.8 units respectively to the change in RPM.

So if rpm is reduced by 4 the efficiency should increase by 0.8 units, and for reducing by 8 rpm it would receive by 1.6 units so from here we can create a relationship for the equation so that relationship depends on the amount of rpm's. Incase of increasing rpm, it reduces by 1.2 for every increase of 8 rpm. And for decrease it increases by 0.8.

So when we solve the above equations we find.

IE= 48-0.2R
DE= 45-0.15R
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 06:39
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Option D and Option C are our answers.

Let's understand the information mentioned in the question before trying to answer it.

So the question starts by "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". From here we can tell that for the increase of every 1 RPM over 60 there will be a decrease in efficiency by 0.15 units and for the decrease of every 1 RPM below 60 there will be an increase in efficiency by 0.2 units.
Now the question asks us "a formula for the machine’s efficiency when running at R RPM, where 0 < R < 60 and a formula for the machine’s efficiency when running at R RPM, where R > 60".

To answer the first part of the question i.e. "a formula for the machine’s efficiency when running at R RPM, where 0 < R < 60" let's assume R = 40 which will result in the machine operating at an efficiency of 40 units.

Now let's see which of the following options gives us the above answer.

Option A: 36 - 0.3R, now let's put the above assumed value of R = 40 in the equation.
=>36 - 0.3*40
=>36 - 12 = 24, Does not give us the desired answer. Eliminated

Option B: 36 + 0.2R, now let's put the above assumed value of R = 40 in the equation.
=>36 - 0.2*40
=>36 - 8 = 28, Does not give us the desired answer. Eliminated

Option C: 45 - 0.15R, now let's put the above assumed value of R = 40 in the equation.
=>45 - 0.15*40
=>45 - 6 = 39, Does not give us the desired answer. Eliminated

Option D: 48 - 0.2R, now let's put the above assumed value of R = 40 in the equation.
=>48 - 0.2*40
=>48 - 8 = 40, Gives us the desired answer which we need. Selected

So from here we can tell that Option D will give the formula for the machine’s efficiency when running at R RPM, where 0 < R < 60.

Now let's move on to the second part of the question i.e. "a formula for the machine’s efficiency when running at R RPM, where R > 60" here let's assume R = 140 which will result in the machine operating at an efficiency of 24 units.

Let's see which of the following options gives us the above answer.

Option A: 36 - 0.3R, now let's put the above assumed value of R = 140 in the equation.
=>36 - 0.3*140
=>36 - 42 = -6, Does not give us the desired answer. Eliminated

Option B: 36 + 0.2R, now let's put the above assumed value of R = 140 in the equation.
=>36 - 0.2*140
=>36 - 28 = 8, Does not give us the desired answer. Eliminated

Option C: 45 - 0.15R, now let's put the above assumed value of R = 140 in the equation.
=>45 - 0.15*140
=>45 - 21 = 24, Gives us the desired answer which we need. Selected

So from here we can tell that Option C will give the formula for the machine’s efficiency when running at R RPM, where R > 60.

So from the above calculations we can conclude that only Option D and Option C will give us the required answers.

Bunuel
 


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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.
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 06:54
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Increased efficiency
36+ 0.8(60-R)/4
48-0.2R

Decreased efficiency
36-1.2(R-60)/8
45-0.15R

Ans D, C
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 07:10
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Increased Efficiency
36 + 0.8 * (60 - R) / 4
36 + 0.2 * (60-R)
36 + 12 - 0.2 * R
48 - 0.2 * R

Decreased Efficiency
36 - 1.2 * (R - 60) / 8
36 - 0.15 * (R-60)
36 + 9 - 0.15 * R
45 - 0.15 * R

Correct answers: Increased Efficiency = 48 - 0.2R and Decreased Efficiency = 45 - 0.15R
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 07:15
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For every 4 RPM the efficiency declines by 0.8
Meaning total increased efficiency is 0.8(60-R)/4
So efficiency at R = 36+ 0.8(60-R)/4 = 36+0.2(60-R)= 48-0.2R

For decreased efficiency
The decrease is 1.2(R-60)/8
So efficiency at R = 36 - 1.2(R-60)/8= 36 - 0.15(R-60)= 45-0.15R
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This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



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.
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GMAT Club Olympics 2025 (Day 9): A machine operates at an efficiency 11 Jul 2025, 07:45
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Less than 60:
Increase 0.8 units each 4 RPM
0.8*(60-R)/4 = 0.2*60-0.2R = 12-0.2R

Greater than 60
Decrease 1.2 units each 8 RPM
1.2*(R-60)/8 = 0.15R-0.15*60 = 0.15R-9

Increased Efficiency = 36+12-0.2R = 48-0.2R
Decreased Efficiency = 36-(0.15R-9) = 45-0.15R
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