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

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amanvermagmat
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Truck T1 gives an average of M1 miles per gallon of petrol while truck [#permalink] Truck T1 gives an average of M1 miles per gallon of petrol while truck   13 Jul 2018, 11:03
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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)
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Re: Truck T1 gives an average of M1 miles per gallon of petrol while truck [#permalink] Truck T1 gives an average of M1 miles per gallon of petrol while truck   13 Jul 2018, 12:32
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)


According to the Q-stem : T1 uses 1200/M1 gallons of petrol & T2 uses 1200/M2 gallons of petrol
Hence the difference in petrol used : 1200/M1- 1200/M2 =1200(1/M1 - 1/M2)= 1200{(M2-M1)/M1M2} ........expression 1

Statement 1==> M1 is 20% less than M2 => M1=0.8M2 Hence, expression 1 ==> 1200{(M2-0.8M2)/0.8M2*M2}................Not Sufficient
Statement 2==>100*M2 = M1*(100 + M2) ==> 100*M2 = 100*M1 + M1*M2 ==>100(M2 -M1) = M1*M2 ==>(M2 -M1)/M1*M2=1/100
Hence, expression 1 ==> 1200*(1/100)=12............................................................................................SUFFICIENT........Hence I would go for option B.
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Re: Truck T1 gives an average of M1 miles per gallon of petrol while truck [#permalink] Truck T1 gives an average of M1 miles per gallon of petrol while truck   13 Jul 2018, 12:54
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)

Avg MPG=Total Miles driven/Total No of gallons used
No of gallons of Truck T1 used=Miles driven by T1/MPG=\(\frac{1200}{M1}\)
No of gallons of Truck T2 used=Miles driven by T2/MPG=\(\frac{1200}{M2}\)
So, Difference in the number of gallons of petrol used by the two trucks=\(\frac{1200}{M1}-\frac{1200}{M2}\)=\(1200\frac{(M2-M1)}{M1M2}\)-------------(a)
St1:-M1 is 20% less than M2.
Or, M1=M2(1-0.2)=0.8M2
One equation two variables, so, we can't determine M1 and M2. hence insufficient.
St2:- 100*M2 = M1*(100 + M2)
Or,100*M2-100M1=M1*M2
Or, 100(M2-M1)=M1*M2
Or, \(\frac{(M2-M1)}{M1M2}\)=\(\frac{1}{100}\)
Substituting above in (a) we can determine the desired difference.

Hence, sufficient.

Ans. (B)
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Re: Truck T1 gives an average of M1 miles per gallon of petrol while truck [#permalink] Truck T1 gives an average of M1 miles per gallon of petrol while truck   22 Aug 2019, 03:07
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] Truck T1 gives an average of M1 miles per gallon of petrol while truck   05 Nov 2022, 08:18
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Re: Truck T1 gives an average of M1 miles per gallon of petrol while truck [#permalink]
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