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Difficulty:
65%
(hard)
Question Stats:
69% (03:18) correct
31%
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wrong
based on 2528
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A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?
A. 140
B. 200
C. 250
D. 300
E. 360
PS35502.01
A. 140
B. 200
C. 250
D. 300
E. 360
PS35502.01
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Let the truck used X gallons of fuel travelling at 55mph, then it used (120-X) gallons of fuel travelling at 60mph.
So, in X gallons of fuel travelling at at an economy of 4.5 miles per gallon it traveled 4.5X miles, and in (120-X) gallons of fuel travelling at an economy of 3.5 miles per gallon it traveled 3.5(120-X) miles.
Since the total Distance traveled is 500 miles, the equation becomes:
4.5X + 3.5(120-X) = 500
Solving for X, it comes to 80.
So, distance traveled at a speed of 55mph = 4.5*80 =>360 miles.
Hence, IMO Option E is the answer.
So, in X gallons of fuel travelling at at an economy of 4.5 miles per gallon it traveled 4.5X miles, and in (120-X) gallons of fuel travelling at an economy of 3.5 miles per gallon it traveled 3.5(120-X) miles.
Since the total Distance traveled is 500 miles, the equation becomes:
4.5X + 3.5(120-X) = 500
Solving for X, it comes to 80.
So, distance traveled at a speed of 55mph = 4.5*80 =>360 miles.
Hence, IMO Option E is the answer.
gmatt1476
4.5 miles/gallon = 9/2 miles/gallon at 55 mph
3.5 miles/gallon = 7/2 miles/gallon at 60 mph
500/120 = 4.1667 = 4(1/6) = 25/6 miles/gallon average
Note that we are taking the average of miles/gallon. The weights will be gallons, not miles.
Check this post: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/1 ... -averages/
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (7/2 - 25/6) / (25/6 - 9/2) = (-4/6) / (-1/6) = 2/1
So gallons consumed were in the ratio 2:1 for the two speeds of 55 and 60. Total 120 gallons were consumed so 80 gallons at 55 mph and 40 gallons at 60 mph.
To use 80 gallons, he must have traveled 80*4.5 = 360 miles
Answer (E)
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General Discussion
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let distance covered @ 55mph = x
so mileage would be x/4.5
and @ 60 mph ; 500-x ; mileage 500-x/3.5
solve for
x/4.5+500-x/3.5 = 120
x= 360
IMO E
so mileage would be x/4.5
and @ 60 mph ; 500-x ; mileage 500-x/3.5
solve for
x/4.5+500-x/3.5 = 120
x= 360
IMO E
gmatt1476
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Posts: 1,285
Updated on: 13 Oct 2019, 02:08
Originally posted by CareerGeek on 21 Sep 2019, 05:24.
Last edited by CareerGeek on 13 Oct 2019, 02:08, edited 1 time in total.
Last edited by CareerGeek on 13 Oct 2019, 02:08, edited 1 time in total.
gmatt1476
Let the truck travels x miles at 55mph and remaining 500-x miles at 60mph
For 1 mile, at 55mph, number of gallons used = 1/4.5
For x miles, number of gallons used = x/4.5 = 2x/9
For 1 mile, at 60mph, number of gallons used = 1/3.5
For 500-x miles, number of gallons used = (500 - x)/3.5 = 2(500 - x)/7
Given, Total gallons used = 120
--> 2x/9 + (1000 - 2x)/7 = 120
--> (14x + 9000 - 18x)/63 = 120
--> 9000 - 4x = 7560
--> 4x = 1440
--> x = 360
IMO Option E
akash7gupta11
I agree. This method has one of the best ROI.
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VeritasKarishma
Alternate Method (Also using Weighted Averages)
Method 2:
If the truck went with 55 miles/hr for the whole journey, then it would have gone 4.5 m/g *120 g/tank = 540 miles/tank -> Speed 2
If the truck went with 60 miles/hr for the whole journey, then it would have gone 3.5 m/g *120 g/tank = 420 miles/tank -> Speed 1
Using the w1/w2 formula (where average = 500 miles/tank; weight = tank)
w1/w2 = (A2 - Aavg)/(Aavg - A1) = (540 - 500)/(500 - 420) = 40/80 = 1/2
So while travelling at 55 mph, 2/3 tank * 120 g/tank = 80 g was consumed.
To use 80 gallons, he must have traveled 80*4.5 = 360 miles
Method 3: Slowest & Too many calculations
Let distance travelled by 55miles/hr speed be X
Then distance travelled by 60miles/hr speed be 500-X
500m/120g = 500m/((Xm/4.5m/g) + (500-X)m/(3.5m/g))
1/120 = 500/(2X/9 + 2(500-X)/7)
(14x + 500*18 -18X)/63 = 120
-4X = 120 * 63
4X = 500*18 - 120*63 = 4 (125*18 - 30*63)
X = 125*18 - 30*63
X = 360
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Expert reply
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gmatt1476
We can let x = the distance traveled at 55 mph. We can create the equation:
120 = x/4.5 + (500 - x)/3.5
120 = 10x/45 + (5000 - 10x)/35
Multiplying by 315, we have:
37,800 = 70x + 9(5000 - 10x)
37,800 = 70x + 45,000 - 90x
37,800 = 45,000 - 20x
20x = 7200
x = 360
Answer: E
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gmatt1476
Alternative Method: We can use the answer choice to determine the correct answer.
Let's pick B first:
If the truck traveled 200 miles at 55 mph, then it traveled 300 miles at 60 mph.
That means the truck used 200/4.5 gallons of gas at 55 mph, and 300/3.5 gallons of gas at 60.
When you reduce those fractions, you get 400/9 and 600/7
Adding those together, you get approximately 44+86 = 130 total gallons, which is too much.
This means that the truck drove MORE than 200 miles at 55 mph, so A and B are out
Let's pick D next:
If the truck traveled 300 miles at 55 mph, then it traveled 200 miles at 60 mph.
That means the truck used 300/4.5 gallons of gas at 55 mph, and 200/3.5 gallons of gas at 60.
When you reduce those fractions, you get 600/9 and 400/7
Adding those together, you get approximately 67+57 = 124 total gallons, which is STILL too much.
So E has to be the correct answer!
gmatt1476
Sharing the method to solve backwards from answer options
1. If we divide 500 by 120 then we get 4.16 which is closer to 4.5 mpg than 3.5 mpg. This means that the truck traveled more than 50% of the distance at 55 mph than 60 mph
2. As we are asked to find the distance traveled at 55 mph, we now know that it will be > 250, hence options A, B and C can be eliminated straight away
3. Now, lets check D and E
Lets start with option E
1. If 360 miles was traveled at 55 mph, then 360/4.5 = 80 gallons of fuel was utilized when traveling at 55 mph
2. If the remaining 140 miles were traveled at 60 mph, then 140/3.5 = 40 gallons of fuel was utilized when traveling at 60 mph
Summing up the above values gives us 80 + 40 = 120 gallons, which matches the information provided in the question. As we have arrived at the correct answer, we do not need to check option D
Ans. E
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gmatt1476
This is a MIXTURE PROBLEM.
4.5 miles per gallon at a lower speed is combined with 3.5 miles per gallon at a higher speed to yield a MIXTURE with 500 miles per 120 gallons.
The following approach is called ALLIGATION -- a great way to handle mixture problems.
Let L = the lower speed and H = the higher speed.
Step 1: Convert to blue values to fractions over a common denominator
L = 4.5 miles per gallon \(= \frac{9}{2} = \frac{27}{6}\)
H = 3.5 miles per gallon \(= \frac{7}{2} = \frac{21}{6}\)
Whole trip = 500 miles per 120 gallons \(= \frac{500}{120} = \frac{25}{6}\)
Step 2: Plot the 3 numerators on a number line, with the numerators for L and H on the ends and the numerator for the whole trip in the middle
L 27---------25---------21 H
Step 3: Calculate the distances between the numerators.
L 27----2----25----4----21 H
Step 4: Determine the ratio in the mixture.
The ratio of L to H is equal to the RECIPROCAL of the distances in red.
L:H = 4:2 = 2:1
Implication of the resulting ratio:
Of every 3 gallons, 2 gallons are used at the lower speed, while 1 gallon is used at the higher speed.
Thus, 2/3 of the 120 gallons are used at the lower speed:
\(\frac{2}{3}*120 = 80\) gallons
Distance traveled at the lower speed = (4.5 miles per gallon)(80 gallons) = 360 miles
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Number of miles truck travelled at 55 mph is "a" & thus number of gallons truck used @55 mph = a/4.5
Number of miles truck travelled at 60 mph is "500 -a" thus number of gallons truck used @ 60mph = 500-a / 3.5
a/4.5 + (500-a) / 3.5 = 120
Substitute options or solve the equation to get a = 360 miles.
(option e)
D.S
GMAT SME
Number of miles truck travelled at 60 mph is "500 -a" thus number of gallons truck used @ 60mph = 500-a / 3.5
a/4.5 + (500-a) / 3.5 = 120
Substitute options or solve the equation to get a = 360 miles.
(option e)
D.S
GMAT SME
gmatt1476
chetan2u Bunuel egmat VeritasKarishma ScottTargetTestPrep
I tried backsolving on this question
I started with option C, and calculation the total gallons used, which came out to be 123.7, which is a little more than 120.
But now I got confused whether I should use smaller number or a bigger number so as to get 120.
I thought that maybe a smaller number would work, so I went for B. Which is wrong
So, could you guys help me by clarifying how to decide whether to take a smaller or a bigger option
Chitra657
Chitra657
At the speed of 55, he consumes less fuel per mile (covers 4.5 miles in a gallon)
At the speed of 60, he consumes more fuel per mile (covers only 3.5 miles in a gallon)
We try option (C) which is 250 miles i.e. half of total 500 miles. So if he covers half the distance at 55 and half the distance at 60, he needs 123.7 gallons of fuel. But actually he used only 120 gallons of fuel. So he must have covered more distance at 55 mph because that speed consumes less fuel. Hence you need to try for 300. If it is still more than 120, you know 360 is the answer.
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KarishmaB Can you help explain how one must identify what the weight would be please? and how i should go about for other type of questions
KarishmaB
Hi KarishmaB
could you explain why: Note that we are taking the average of miles/gallon. The weights will be gallons, not miles
I can find the ratio 2:1
But I here, I stuck to define whether the 2 parts of gallon used or the 2 parts of mile travelled.
could you explain why: Note that we are taking the average of miles/gallon. The weights will be gallons, not miles
I can find the ratio 2:1
But I here, I stuck to define whether the 2 parts of gallon used or the 2 parts of mile travelled.
KarishmaB
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Here is a post on how to identify weights in weighted averages: https://anaprep.com/arithmetic-weights- ... d-average/
You can also check out full weighted averages from my content next weekend - 27th to 29th July. We will have a free 3 day trial.
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Found an easier way of solving this rather than delving in equations a
Now see it is saying that for 500 miles it consumed 120 gallons of fuel - if we find the avg we can see it is around 4.167
Now if we see the mileages given in the ques we can notice that for 55mph it is 4.5 m/g and for 60mph it is 3.5m/g which means if he would have travelled equal dist in both the speed that is 250 miles each then the milage should have been 4 ( 4.5+3.5/2) however we can see from above it is greater than 4 that means it travels more in 55mph than 60 mph ( weighted avg concept)
Now looking at choices I can see that only D and E can be suitable options and solving it using these two
And it is most likely that the answer will be and integer and hence when we put it in equations 360/4.5 + 140/3.5 will yield an integer hence most likely it would be answer
You can solve for both 300 and 360 to be confident.
Thanks
Now see it is saying that for 500 miles it consumed 120 gallons of fuel - if we find the avg we can see it is around 4.167
Now if we see the mileages given in the ques we can notice that for 55mph it is 4.5 m/g and for 60mph it is 3.5m/g which means if he would have travelled equal dist in both the speed that is 250 miles each then the milage should have been 4 ( 4.5+3.5/2) however we can see from above it is greater than 4 that means it travels more in 55mph than 60 mph ( weighted avg concept)
Now looking at choices I can see that only D and E can be suitable options and solving it using these two
And it is most likely that the answer will be and integer and hence when we put it in equations 360/4.5 + 140/3.5 will yield an integer hence most likely it would be answer
You can solve for both 300 and 360 to be confident.
Thanks
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when you use alligation of
4.5 .....3.5
4.16
The ratio 2:1 is of gallon, thus divide 120 in 2:1 and not 500
120 gives 80 gallons for 4.5
Thus 80*4.5 = 360 - Option E is answer
4.5 .....3.5
4.16
The ratio 2:1 is of gallon, thus divide 120 in 2:1 and not 500
120 gives 80 gallons for 4.5
Thus 80*4.5 = 360 - Option E is answer
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