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# When an automobile is driven at 70 miles per hour, it uses 0.06 gallon

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Math Expert
Joined: 02 Sep 2009
Posts: 50003
When an automobile is driven at 70 miles per hour, it uses 0.06 gallon  [#permalink]

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31 Oct 2017, 00:08
00:00

Difficulty:

85% (hard)

Question Stats:

36% (01:53) correct 64% (01:47) wrong based on 37 sessions

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When an automobile is driven at 70 miles per hour, it uses 0.06 gallon of gas per mile. When the car is driven at 50 miles per hour, it uses 0.04 gallon of gas per mile. Which of the following relations are possible between the gallons of gas used per mile and the speed at which the car is driven?

I. They are directly proportional.
II. They are indirectly proportional.
III. They are linearly related.

(A) only I
(B) only II
(C) only III
(D) I and III
(E) I, II, and III

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Joined: 13 Apr 2010
Posts: 89
Re: When an automobile is driven at 70 miles per hour, it uses 0.06 gallon  [#permalink]

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31 Oct 2017, 06:00
Bunuel wrote:
When an automobile is driven at 70 miles per hour, it uses 0.06 gallon of gas per mile. When the car is driven at 50 miles per hour, it uses 0.04 gallon of gas per mile. Which of the following relations are possible between the gallons of gas used per mile and the speed at which the car is driven?

I. They are directly proportional.
II. They are indirectly proportional.
III. They are linearly related.

(A) only I
(B) only II
(C) only III
(D) I and III
(E) I, II, and III

I. If they are directly proportional then .
70 = 0.06 * K ; K = 1166.67
50 = 0.04 * K ; K = 1250
Constant has different values . So this statement is Not true

II. If they are indirectly proportional.
70 = K /0.06 ; K = 4.2
50 = K /0.04 ; K = 2
Constant has different values . So this statement is also Not true

III. They are linearly related.
This statement must be true as there is no choice with " None"
Note: If you try to plot this in Coordinate graph then it will be a straight line with a slope. So, the points could be linear .
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Re: When an automobile is driven at 70 miles per hour, it uses 0.06 gallon  [#permalink]

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01 Nov 2017, 17:05
Bunuel wrote:
When an automobile is driven at 70 miles per hour, it uses 0.06 gallon of gas per mile. When the car is driven at 50 miles per hour, it uses 0.04 gallon of gas per mile. Which of the following relations are possible between the gallons of gas used per mile and the speed at which the car is driven?

I. They are directly proportional.
II. They are indirectly proportional.
III. They are linearly related.

(A) only I
(B) only II
(C) only III
(D) I and III
(E) I, II, and III

When two quantities are directly proportional, if one quantity increases (or decreases), so does the other quantity. Moreover, the ratio of the two quantities will be the same. Thus, we must check whether
70/(0.06) = 50/(0.04), or equivalently, whether 70(0.04) = 50(0.06).

We have 70(0.04) = 2.8 and 50(0.06) = 3; thus, we conclude that the two quantities are not directly proportional.

When two quantities are indirectly (inversely) proportional, if one quantity increases (or decreases), the other quantity decreases (or increases). Thus, the two quantities cannot be indirectly proportional.

Since we eliminated statements I and II, and since according to the answer choices one of the statements must be true, we conclude that only statement III is true.

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Re: When an automobile is driven at 70 miles per hour, it uses 0.06 gallon &nbs [#permalink] 01 Nov 2017, 17:05
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