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# Truck T1 gives an average of M1 miles per gallon of petrol while truck

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Re: Truck T1 gives an average of M1 miles per gallon of petrol while truck [#permalink]
amanvermagmat
Truck T1 gives an average of M1 miles per gallon of petrol while truck T2 gives an average of M2 miles per gallon of petrol. Both trucks travelled from a city to another, covering a distance of 1200 miles each in this process. What is the difference in the number of gallons of petrol used by the two trucks, for this 1200 mile trip.

(1) M1 is 20% less than M2.

(2) 100*M2 = M1*(100 + M2)

Given:
1. Truck T1 gives an average of M1 miles per gallon of petrol while truck T2 gives an average of M2 miles per gallon of petrol.
2. Both trucks travelled from a city to another, covering a distance of 1200 miles each in this process.

Asked: What is the difference in the number of gallons of petrol used by the two trucks, for this 1200 mile trip.

(1) M1 is 20% less than M2.
M1 = .8 M2
Petrol used by T1= 1200/M1 gallons
Petrol used by T2= 1200/M2 gallons
The difference in the number of gallons of petrol used by the two trucks, for this 1200 mile trip = 1200 |1/M1 - 1/M2| = 1200 $$|\frac{M2-M1}{M1M2}|$$
M1 - M2 = .2M2
M1M2 = .8M2M2
$$\frac{M1 - M2}{M1M2} = \frac{1}{4M2}$$
Since M2 is unknown
NOT SUFFICIENT

(2) 100*M2 = M1*(100 + M2)
$$M1 =\frac{100*M2}{(100+M2)}$$
$$M1 - M2 = \frac{100*M2}{(100+M2)} - M2$$
$$M1 - M2 = \frac{(100*M2 - 100*M2 - M2^2)}{(100+M2)}$$
$$M1 - M2 = \frac{(- M2^2)}{(100+M2)}$$
$$\frac{M2 - M1}{M1M2} = \frac{M2^2}{(100+M2)} /\frac{M2*100*M2}{(100+M2)} = \frac{1}{100}$$
Petrol used by T1= 1200/M1 gallons
Petrol used by T2= 1200/M2 gallons
The difference in the number of gallons of petrol used by the two trucks, for this 1200 mile trip = 1200 |1/M1 - 1/M2|= 1200 $$|\frac{M2-M1}{M1M2}|$$ = 1200 / 100 = 12 gallons
SUFFICIENT

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Re: Truck T1 gives an average of M1 miles per gallon of petrol while truck [#permalink]
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