MGMAT Study Guide 3, Page 187 Question 5

[bhumit920]

The question is as follows:

A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hours, rounded to the nearest hour, then his average speed must be between:

A. 38 and 50 mph
B. 40 and 50 mph
C. 40 and 51 mph
D. 41 and 50 mph
E. 41 and 51 mph

Why did you use the number 225.5 and 5.5 in your calculations when those numbers would clearly round the numbers up to 226 mi. and 6 hours.

Bhank you in advance for your input.

[tim]

BETWEEN x and y means higher than x and lower than y. So when we use 225.5 we are using it appropriately because effectively we are saying it is less than 225.5 miles, which is true..

If you don't like that explanation, then don't use 225.5; instead use the largest number that does round down to 225, i.e. 225.49999999999999999999999999999999999999999999... :)

You'll see you get the same result either way, because 225.4999... = 225.5 anyway! Same reasoning holds of course for the 5.5..

[trevorflint01]

Why is the answer (C) 40 and 51 miles per hour? When you calculate the Maximum speed at 50 1/9 and the Minimum speed at 40 9/11, that answer doesn't make sense.

For example, 40.5 is within the answer range but not within the range for the min and max speed.

Shouldn't the answer be (D) 41 and 50 miles per hour?

[tim]

You have things backwards. I take it you would agree that 50.1 is an acceptable speed? Well, answer C tells us that any acceptable speed MUST be between 40 and 51; this works for our value of 50.1, as well as any other acceptable speed..

Consider D instead, which tells us that any acceptable speed MUST be between 41 and 50. This is NOT true for the value of 50.1, which we have already seen is an acceptable speed..

The question is not asking for an interval in which every value is an acceptable speed; rather it is asking for an interval inside which every acceptable speed will fall. C does that, but D does not. Note that if "0 and 99999 mph" were an answer choice that would work as well, as it accomplishes the same thing C does..