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Bunuel
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A certain car travels 18 miles per gallon of gas on city streets and 3 07 Feb 2020, 06:22
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C
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35% (medium)

Question Stats:

74% (01:51) correct 26% (01:50) wrong based on 89 sessions

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A certain car travels 18 miles per gallon of gas on city streets and 30 miles per gallon of gas on highway. Damaris drives the car to work during the week and travels on city streets and on the highway. She drives the car on the highway more miles than she drives on city streets. How many miles does Damaris drive to work on the highway?

(1) Damaris drives a total of 26 miles.

(2) The car Damaris drives uses 1 gallon of gas to get to work.
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C
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A certain car travels 18 miles per gallon of gas on city streets and 3 11 Feb 2020, 04:10
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Bunuel
A certain car travels 18 miles per gallon of gas on city streets and 30 miles per gallon of gas on highway. Damaris drives the car to work during the week and travels on city streets and on the highway. She drives the car on the highway more miles than she drives on city streets. How many miles does Damaris drive to work on the highway?

(1) Damaris drives a total of 26 miles.

(2) The car Damaris drives uses 1 gallon of gas to get to work.
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Given:
1. A certain car travels 18 miles per gallon of gas on city streets and 30 miles per gallon of gas on highway.
2, Damaris drives the car to work during the week and travels on city streets and on the highway.
3. She drives the car on the highway more miles than she drives on city streets.

Asked: How many miles does Damaris drive to work on the highway?

(1) Damaris drives a total of 26 miles.
It may be inferred from information above that Damaris drives more than 13 miles on the highway.
But number of miles driven on highway can not be determined.
NOT SUFFICIENT

(2) The car Damaris drives uses 1 gallon of gas to get to work.
Damaris drive minimum of 18 miles and maximum of 30 miles on her way to work.
But number of miles driven on highway can not be determined.
NOT SUFFICIENT

(1) + 2)
(1) Damaris drives a total of 26 miles.
(2) The car Damaris drives uses 1 gallon of gas to get to work.
Damaris on average drives @ 26 miles/gallon of gas
Let portion of her highway travel be x
18(1-x) + 30x = 26
18 + 12x = 26
x= 8/12 = 2/3
Damaris drives on highway = 26*2/3 = 52/3 = 17.33 miles
SUFFICIENT

IMO C
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A certain car travels 18 miles per gallon of gas on city streets and 3 11 Feb 2020, 04:27
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Let the number of miles travelled in City and that on Highway be C and H respectively.

Given,

H>C

1 gallon on Highway helps travel 30 miles
1 gallon in City helps travel 18 miles.

Thus,

For 1 mile on Highway, gas required is 1/30th of a gallon

For 1 mile in City, gas required is 1/18th of a gallon

Objective: To find number of miles traveled on Highway.

Statement 1:
Total miles traveled is 26
Thus,
H+C = 26

Multiple combinations are possible.
Hence, not sufficient.

Eliminate A and D

Statement 2:

Total gas used is 1 gallon

So,
H/30 + C/18 = 1
I.e. 3H + 5C = 90
Now, again we have multiple combinations possible as we know that H and C can be fractions also.

Hence, statement 2 is also not sufficient.

Eliminate B

Together,

We have
H+C = 26
3H + 5C = 90

Solving for H and C, we get
H = 20 and C = 6

Hence, C should be the answer.

Quick Verification:

We have H>C
For 20 miles on highway, 20/30 = 2/3rd of a gallon is used
For 6 miles in City, 6/18 = 1/3rd of a gallon is used.

Total gas used is 1 gallon.

Everything checks out properly.


Feel free to tag me for any further clarification.

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A certain car travels 18 miles per gallon of gas on city streets and 3 11 Feb 2020, 06:05
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Bunuel
A certain car travels 18 miles per gallon of gas on city streets and 30 miles per gallon of gas on highway. Damaris drives the car to work during the week and travels on city streets and on the highway. She drives the car on the highway more miles than she drives on city streets. How many miles does Damaris drive to work on the highway?

(1) Damaris drives a total of 26 miles.

(2) The car Damaris drives uses 1 gallon of gas to get to work.
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Solution


Step 1: Analyse Question Stem


    • The car can travel 18 miles per gallon of gas on the city street.
      o So, gallons of gas required to drive 1 mile on City street \(= \frac{1}{18}\)

    • Also, the car can travel 30 miles per gallon of gas on highway.
      o So, gallons of gas required to drive 1 mile on the highway \(= \frac{1}{30}\)
    • Let us assume that Damaris drives c miles on the city street and h miles on the highway to reach work.
    • \(h > c\)
We need to find the value of h.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: Damaris drives a total of 26 miles.
    • According to this statement: \(c+h =26\)
      o since \(h > c\), from above equation we get
         \(h+h > 26\)
         Or,\( h> 13 \)
         However, we cannot determine the exact value of h.
Hence, statement 1 is not sufficient and we can eliminate answer options A and D
Statement 2: The car Damaris drives uses 1 gallon of gas to get to work.
    • According to this statement:\(c*\frac{1}{18} + h*\frac{1}{30} = 1\)
      o or, \(\frac{5c + 3h }{90} = 1\)
      o or, \(5c + 3h = 90\)
         Since \(h > c\), we can write
         \(5h +3h > 90\)
         \(h > 11.25 \)
We know that h > 11.25 but we cannot determine the exact value of h from this statement alone.
Hence, statement 2 is also not sufficient and we can eliminate answer B.

Step 3: Analyse Statements by combining.


    • From statement 1: \(c + h = 26\)
    • From statement 2: \(5c + 3h = 90\)
    • On combining both, we have two equations and two variables, so we can solve to get the value of h.
Thus, the correct answer is Option C.
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A certain car travels 18 miles per gallon of gas on city streets and 3 13 Feb 2020, 20:47
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IMO C
Car on highway gives 30 miles per gallon, and on street gives 18 miles per gallon

Statement 1
GIVES H.MIles + S.Miles = 26
We cannot say directly from this the number of miles from each, INSUFFICIENT

Statement 2
Given total gallons used = 1 gallon .
we don't know any ratio of each one to find the answer from this , so INSUFFICIENT

Statment 1+2 ,

Let Car travels x miles on street , fuel used for x miles will, x/18 gallos ,
Remaining 26-x miles on high way, fuel used for 26-x miles will be , 26-x/30 gallon

Given total gallons = 1 , x/18 + 26-x/30 = 1 ,
30*18 + (26-x)*18 = 18*30,
x = 6 miles , and high way miles = 26-x = 20. SUFFICIENT
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A certain car travels 18 miles per gallon of gas on city streets and 3 18 Sep 2022, 04:00
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rate(city) = 18mpg, rate (highway) = 30 mpg

rate = miles/gallon => r = m/g

miles(total) = miles (c) + miles (h)
r*g (t)= r*g(c) + r*g(h)

1. total miles is 26. But we dont know the miles of c and h, hence NS
2. Total gallon used for work = 1gallon NS

1 & 2

We get the total rate as 26 miles per gallon
and g(c) + g(h) = 1

Put in the above equation and hence Sufficient
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