In an endurance race, a car drove the whole race at a constant speed

I think the answer should be B...

3 MILES PER MINUTE = 180 MILES PER HOUR

statement 1 tells us that the time taken by the car was more than 2 hours...
If the car took 2 hrs 30 minutes to travel , then the total distance would be 450...
If the car took 3 hrs to travel, the total distance would be 540.. not sufficient..

Statement 2- the time taken by car was less than 2.75 hours... Even if the car took exact 2.75 hrs , then the total distance would be 495 , which is less than 500... Statement b gives a definite no...

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Hello,

Greetings for the day!

This is an easy question which tests you on the basic concepts of Speed, Time and Distance. The variable to be found out in this question is Distance.
Distance = Speed x Time

The data given in the question says that the car drove at a speed of 3 miles per minute. Since there are 60 minutes in an hour, we can conclude that the speed of the car is 180 mph. Since this data is given in the question, this can be used at any stage of the solution.

Let us look at the data given in Statement I. Statement I says that the time taken by the car to cover D was more than 2 hours.
If the time is 3 hours, D = 180 x 3 = 540 miles. In this case, we can answer the main question with a YES.
If the time is 2.5 hours, D = 180 x 2.5 = 450 miles. In this case, we can answer the main question with a NO.

Since we are getting both a YES and a NO as an answer to the main question when we use the data given in statement I, statement I is insufficient.

Now, let us look at the data given in Statement II. Statement II says that the time taken by the car to cover D was less than 2.75 hours.
This means that, the time cannot be equal to 2.75 hours.
If the time is 2.75 hours, D = 180 x 2.75 = 495 miles, which is definitely less than 500 miles.
Since the time cannot be EQUAL to 2.75 hours and has to be lesser, clearly, the distance travelled by the car D, will be less than 500 miles. Hence, we can answer the question with a NO, which is a unique answer.

So, there we go. The answer option is B.

A few pointers before we wrap up.

In questions on Speed, Time and Distance, always be wary of the mistakes that you may commit if you do not convert values to the appropriate units. In this question, speed was given in miles per minute but the time was given in hours. So, it was imperative that we converted the speed to miles per hour.

This question represents a very common DS trap and the trap is in the question. The question wants you to answer with a YES or a NO, as to whether D is more than 500 miles. A very common mistake that students do on such questions is that they try to prove that D is more than 500 miles; in other words, they try to get a YES as an answer, while, a NO also is an acceptable answer.

Also, with the first statement, a lot of students tend to try only integral values for the time, not realizing that values like 2.5 can easily disprove the statement.

Hope this helps.
Cheers!

Solution

Given:
In this question, we are given

• In an endurance race, a car drove the whole race at a constant speed of 3 miles per minute to cover the total race distance D.

To find:
We need to determine

• Whether the value of D greater than 500 miles or not.

Approach and Working:

• Speed of the car = 3 miles per minute = (3 x 60) miles per hour = 180 miles per hour

As we already know the constant speed of the car is 180 miles per hour, to determine whether D was more than 500 miles or not, we need to know the time duration for which the car was driven.

Analysing Statement 1
As per the information given in statement 1, the car took more than 2 hours to complete the race.
From this statement, we can say that

• The car drove more than (180 x 2) = 360 miles in the race.
• However, we cannot say whether the distance the car was driven was more than 500 miles or not.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, the car took less than 2.75 hours to complete the race.
From this statement, we can say that

• The car drove less than (180 x 2.75) = 495 miles in the race.
• Therefore, we can definitely say that the distance the car was driven was not more than 500 miles.

Hence, statement 2 is sufficient to answer the question.

Hence, the correct answer is option B.

First glance - rate problem involving distance. Also note that the rate is given in miles per MINUTE. Make sure to remember to convert to hours if required by statements.

Statement 1: Convert 3 miles per minute to miles per hour. We have 180 miles per hour. 500 miles is more than 2 hours, yet less than 3 hours. This could be yes/no, so [b]not sufficient.
[/b]

Statement 2: Less than 2.75 hours -- 180 times 11/4 = 45*11 --> 9*5*11 --> 99*5 (less than 500). Since less than this, this statement is sufficient because always no.

Answer is B.

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