A logistics coordinator planned a delivery route for a truck.

Question

A logistics coordinator planned a delivery route for a truck. Before the route was driven, she estimated the distance the truck would travel and the amount of fuel it would use, and from those estimates she calculated an estimated fuel efficiency in kilometers per liter. After the route was completed, the actual fuel efficiency was calculated from the actual distance driven and the actual amount of fuel used. Did the estimated fuel efficiency differ from the actual fuel efficiency by at most 20% of the actual fuel efficiency?

(1) The estimated distance differed from the actual distance by at most 20% of the actual distance, and the estimated fuel use differed from the actual fuel use by at most 20% of the actual fuel use.

(2) The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.

M47-204

Bunuel · Accepted Answer

GMAT Club Official Solution:

A logistics coordinator planned a delivery route for a truck. Before the route was driven, she estimated the distance the truck would travel and the amount of fuel it would use, and from those estimates she calculated an estimated fuel efficiency in kilometers per liter. After the route was completed, the actual fuel efficiency was calculated from the actual distance driven and the actual amount of fuel used. Did the estimated fuel efficiency differ from the actual fuel efficiency by at most 20% of the actual fuel efficiency?

Let D be the actual distance driven, and let F be the actual amount of fuel used.

Actual fuel efficiency = D/F

The question asks whether the estimated fuel efficiency differed from D/F by at most 20%.

(1) The estimated distance differed from the actual distance by at most 20%, and the estimated fuel use differed from the actual fuel use by at most 20%.

If both estimates were 20% too high, then the estimated fuel efficiency would be:

1.2D/1.2F = D/F

Giving equal efficiencies and thus the answer would be YES.

But if the distance estimate was 20% too high and the fuel-use estimate was 20% too low, then the estimated fuel efficiency would be:

1.2D/0.8F = 1.5 * D/F

This is 50% greater than the actual fuel efficiency, so the answer would be NO.

Not sufficient.

(2) The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.

This gives the absolute errors, but not the actual distance or actual fuel use.

For example, if D = 500 and F = 50, then:

Actual fuel efficiency = 500/50 = 10

Estimated fuel efficiency = (500 + 100)/(50 - 10) = 600/40 = 15

The estimate is 50% greater than the actual value, so the answer is NO.

But if D = 1500 and F = 150, then:

Actual fuel efficiency = 1500/150 = 10

Estimated fuel efficiency = (1500 + 100)/(150 - 10) = 1600/140 = 11.something

The estimate (11.something) differs from 10 by less than 20%.

So the answer is YES.

Not sufficient.

(1)+(2) The same two examples from (2) also satisfy statement (1).

In the first example, 100 is exactly 20% of 500, and 10 is exactly 20% of 50.

In the second example, 100 is less than 20% of 1500, and 10 is less than 20% of 150.

So both statements together can still give NO or YES.

Not sufficient.

Answer: E.

BongBideshini · Answer

Let the actual distance be D and the actual fuel use be F.
Actual fuel efficiency = D/F
Estimated fuel efficiency =  D_e/F_e 
We need to determine whether  0.8D/F ≤ D_e/F_e ≤1.2 D/F  
 Statement (1) 
  0.8D ≤ D_e ≤ 1.2D
0.8F ≤ F_e ≤ 1.2F  
The largest possible ratio occurs when  D_e = 1.2D , F_e = 0.8F: 
 (D_e/F_e )  max =(1.2)/(0.8) (D/F) = 1.5(D/F)  (No) 
The smallest possible ratio occurs when D_e = 0.8D and F_e = 1.2F:
 (D_e/F_e )  min = (0.8)/(1.2) (D/F) = 0.66 (D/F).  (Yes)

Insufficient. 
 Statement (2) 
The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.
Thus:
 D_e = D + 100
F_e = F − 10 
The ratio of estimated efficiency to actual efficiency is:
  ÷ (D/F)
 This depends on the values of D and F.

Statements (1) and (2) together 
From Statement (2):
 D_e = D + 100
F_e = F − 10 
Using Statement (1):
D + 100 ≤ 1.2D
 ⇒ D ≥ 500 
F − 10 ≥ 0.8F
 ⇒ F ≥ 50

Case 1: 
D = 500, F = 50
 D_e = 600, F_e = 40 
Actual efficiency = 500/50 = 10
Estimated efficiency = 600/40 = 15
Difference = 50%
Answer: No
 Case 2: 
D = 5000, F = 500
 D_e = 5100, F_e = 490 
Actual efficiency = 5000/500 = 10
Estimated efficiency = 5100/490 ≈ 10.41
Difference ≈ 4.1%
Answer: Yes
Since both Yes and No are possible even after combining the statements, the information is insufficient.
 Answer: E

GulfTube · Answer

Question: Is the estimated fuel efficiency within 20% of actual fuel efficiency? 0.8<=Eff(est)/Eff(act)<=1.2 ?

Re-write the question stem for easier use:
Eff(est)/Eff(act) = [ D(est)/D(act) ]/[F(est)/F(act)] so

Question is 0.8<= [ D(est)/D(act) ]/[F(est)/F(act)] <=1.2?

i) \(D_{est}\) is within 20% of \(D_{act}\), and \(F_{est}\) is within 20% of \(F_{act}\).

To establish sufficiency we need to test for cases which yield sufficient and/or not sufficient.

We can maximize D(est)/D(act) and minimize F(est)/F(act) to yield a No. Eff(est)/Eff(act) = 1.2/0.8 = 1.5 which is outside the range of 0.8<=Eff(est)/Eff(act)<=1.2.

Yielding a Yes is easier. Keep numerator and denominator equal 1 i.e. D(est)/D(act) and F(est)=F(act) = 1; this is within the allowed range.

Since we got a Yes and a No , this statement is insufficient.

ii) The coordinator overestimated the distance by 100 kilometers and underestimated the fuel use by 10 liters.

Given: \(D_{est} = D_{act} + 100\) and \(F_{est} = F_{act} - 10\).

We haven't been given what the actual values of fuel and distance are so we can plug in values ourselves. Let's keep the denominator constant (and as close to 1 as possible to keep calculations easier) and change numerator to yield Yes and a No.

\(F_{est} = 990, F_{act} = 1000\). So \(F_{est}/F_{act}\) = 0.99 ~ 1.

Numerator: since we are given that \(D_{est}\) is greater than \(D_{act}\), we know that numerator \(D_{est}/D_{act}\) will be greater than 1. In order to find a Yes and No, we need to test cases where numerator is within the range of >=1 and <=1.2 and another test case where it exceeds it.

\(D_{est}/D_{act}\) = \( D_{act} + 100 /D_{act}\) = \( 1 + 100 /D_{act}\)

We now need only focus on \(100 /D_{act}\), if we minimize it and we get a value as close to 1 as possible which is less than or equal to 1.2, we get a Yes. If we maximize it so that it exceeds 1.2, we get a No.

Let \(D_{act}\) = 1000 so that 100/1000 = 0.1, 1+0.1 = 1.1 which is less than 1.2. Yes

Let \(D_{act}\) = 5 so that 100/5 = 20, 1+20 = 21 which exceeds 1.2. No

Since we got a Yes and a No , this statement is insufficient.

By combining both statements,
For the \(100\text{ km}\) overestimation to be \(\le 20\%\) of \(D_{act}\), \(D_{act}\) must be at least \(500\text{ km}\).
For the \(10\text{ L}\) underestimation to be \(\le 20\%\) of \(F_{act}\), \(F_{act}\) must be at least \(50\text{ L}\).
So, \(D_{act}\) >= 500, and \(F_{act}\)>=50.

We already have a Yes above by taking \(F_{act}\) = 1000 and \(D_{act}\) = 1000 which satisfy these conditions.

In order to get a No, we know that we need to maximize numerator and minimize denominator of [ D(est)/D(act) ]/[F(est)/F(act)]. To maximize the numerator, we take minimum possible value of D(act) = 500 so D(est) = 600. 600/500 = 1.2.

Since we know that the ratio F(est)/F(act) < 1, any values we take for \(F_{act}\)>=50 , the overall fraction will always be greater than 1.2 which exceeds the range.

Example: if F(act) = 50 and F(est) = 40, 40/50 = 0.8 => 1.2/0.8 = 1.5. if F(act) = 1000 and F(est) = 990, 990/1000=0.99 => 1.2/0.99 = 1.212. Both cases exceed the range of <=1.2. Hence this yields a No.

Since we got a Yes and a No by combining statements, answer is E.

A logistics coordinator planned a delivery route for a truck.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

A logistics coordinator planned a delivery route for a truck.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards