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# Truck A gives an average of X miles per gallon of petrol while truck B

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Retired Moderator
Joined: 22 Aug 2013
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Location: India
Truck A gives an average of X miles per gallon of petrol while truck B  [#permalink]

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13 Jul 2018, 10:59
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Difficulty:

55% (hard)

Question Stats:

57% (01:58) correct 43% (01:18) wrong based on 17 sessions

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Truck A gives an average of X miles per gallon of petrol while truck B gives an average of Y miles per gallon of petrol. Both trucks travelled from a city to another, covering a distance of 1500 miles each in this process. What is the difference in the number of gallons of petrol used by the two trucks, for this 1500 mile trip.

(1) X is 20% less than Y.

(2) Y - X = 5.
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Re: Truck A gives an average of X miles per gallon of petrol while truck B  [#permalink]

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13 Jul 2018, 12:42
amanvermagmat wrote:
Truck A gives an average of X miles per gallon of petrol while truck B gives an average of Y miles per gallon of petrol. Both trucks travelled from a city to another, covering a distance of 1500 miles each in this process. What is the difference in the number of gallons of petrol used by the two trucks, for this 1500 mile trip.

(1) X is 20% less than Y.

(2) Y - X = 5.

Avg MPG=Total Miles driven/Total No of gallons used
No of gallons of Truck A used=Miles driven by A/MPG=$$\frac{1500}{X}$$
No of gallons of Truck B used=Miles driven by A/MPG=$$\frac{1500}{Y}$$
So, Difference in the number of gallons of petrol used by the two trucks=$$\frac{1500}{X}-\frac{1500}{Y}$$
St1:-X is 20% less than Y.
Or, X=Y(1-0.2)=0.8Y
One equation two variables, so, we can't determine X and Y. hence insufficient.
St2:-Y - X = 5
One equation two variables, so, we can't determine X and Y. hence insufficient.

Combining , we have,
X=0.8Y & Y - X = 5
So,we can determine X & Y, and subsequently the difference in nos. of gallons.

Ans. (C)
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PKN

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Re: Truck A gives an average of X miles per gallon of petrol while truck B  [#permalink]

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13 Jul 2018, 12:44
amanvermagmat wrote:
Truck A gives an average of X miles per gallon of petrol while truck B gives an average of Y miles per gallon of petrol. Both trucks travelled from a city to another, covering a distance of 1500 miles each in this process. What is the difference in the number of gallons of petrol used by the two trucks, for this 1500 mile trip.

(1) X is 20% less than Y.

(2) Y - X = 5.

According to the Q-stem : A uses 1500/X gallons of petrol & A uses 1500/Y gallons of petrol
Hence the difference in petrol used : 1500/X- 1500/Y =1500(1/X - 1/Y)= 1500{(Y-X)/XY} ........expression 1

Statement 1==> X is 20% less than Y => X=0.8Y Hence, expression 1 ==> 1500{(Y-0.8Y)/0.8Y*Y}........On simplification a factor of Y remains........Not Sufficient
Statement 2==>Y - X = 5 Hence, expression 1 ==> 1500*{5/X*(X+5)}=12.............................Not Sufficient

Statement 1 & 2==> Y=25 & X=20 ..... Thus in expression 1 ==>1500{(25-20)/25*20} ..............Sufficient ....... Hence I would go for option C.
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Re: Truck A gives an average of X miles per gallon of petrol while truck B   [#permalink] 13 Jul 2018, 12:44
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