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When an automobile is driven at 70 miles per hour, it uses 0.06 gallon 31 Oct 2017, 00:08
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

Question Stats:

29% (02:04) correct 71% (01:41) wrong based on 100 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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C
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When an automobile is driven at 70 miles per hour, it uses 0.06 gallon 31 Oct 2017, 06:00
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Bunuel
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
Show more

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"
Answer is C
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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When an automobile is driven at 70 miles per hour, it uses 0.06 gallon 01 Nov 2017, 17:05
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Bunuel
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
Show more


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.

Answer: C
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When an automobile is driven at 70 miles per hour, it uses 0.06 gallon 20 Nov 2020, 00:56
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As the miles per hour goes up ---------> so does the gallons used per mile

they can NOT be "Indirectly" Proportional


if they are DIRECTLY Proportional -----> then the Same Proportional Increase in the Miles per Hour should result in the Same Proportional Increase in the gallons used per mile


Proportional Increase in M.P.H. -----> (70 - 50) / 50 = 20/50 = 2/5 -------> Increased by 2/5

the gallons per mile @ 50 mph is = .04

a (2/5) Proportional Increase would be = .04 + (2/5)(.04) = .04 + (.4)(.04) -----> does NOT equal .06 gallons per mile that is used at 70 mph


they are NOT Directly Related


However, they are "Linearly Related"

As the Miles per hour INCREASES from 50 to 70 -------> there is a corresponding INCREASE in the gallons used per mile from 0.4 to .06


-C-

Only III. they are only linearly related
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When an automobile is driven at 70 miles per hour, it uses 0.06 gallon 20 Nov 2020, 01:21
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Bunuel
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
Show more

Instance 1:
Speed = 70 mph, Mileage = .06 gallons/mile

Instance 2:
Speed = 50 mph, Mileage = .04 gallons/mile

I. They are directly proportional.

In this case, \(\frac{S1}{M1} = \frac{S2}{M2}\)
But \(\frac{70}{.06} \neq \frac{50}{.04}\)

Not correct

II. They are indirectly proportional.

In this case, S1 * M1 = S2 * M2
But \(70 * .06 \neq 50 * .04\)

Not correct

III. They are linearly related.
You can draw a line between any two distinct points so these two points will be linearly related.
This is correct.

Answer (C)
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When an automobile is driven at 70 miles per hour, it uses 0.06 gallon 05 Jul 2024, 05:28
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