Can someone please explain why E is the correct answer I chose C. Let me attempt to explain my logic:

It is given that it took Carlos 30 mins to travel from his house to the library, and we are looking for distance of greater than 6 miles. So using the RT = D formula, we have T = 30 mins, all we need is R to see if D = 6 miles or not.

(1) R = greater than 16 ft/sec, this can be any number greater than 16, so to me I saw this an insufficient.
(2) R = less than 18 ft/sec, this can be any number less than 18, so insufficient as well.

Combined (C), 16<X<18, which would leave us with 17 ft/sec

Now using RT = D, [(R = 17 ft/sec) X (T = 1800 sec (converted 30 mins)) = 30,600 ft
30,600 ft / 5,280ft = approx 5.8 < 6 miles, so definite NO

What am I doing wrong? am I missing something or not seeing something?

You're assuming that the rate can only be an integer. If the rate was 16.1, then you get 5.48 miles. However, if the rate was 17.9, then you get 6.1 miles.
A tip that I find useful in DS is to test out the extremes to make sure you're not overlooking anything.

PS...no need to post images for questions that do not have any necessary diagrams. :D

Thanks Steve! Man those assumptions will kill you every time! :wink:

Well done!

For this problem can someone show a quick way to solve??

It took me the better part of 3 mins to solve

I did figure out the 1 and 2 were insuff

But I was running deep into time so I picked C

To test out the extremes after that 16.1 and 17.9 would take even more time at the point so I guessed on C which is obviously wrong.

Does someone have an approach to these inequality problems that can help me solve it more quicker? (i.e. do you combine the inquality first instead of doing each separate?, etc.)

Thanks!

It took too long because you were starting from the statements (in ft/sec) and solving three times (once for each statement, then for the combination) to answer the question (in miles or miles/hour). Turn that around.

In general, the fastest approach is to go as far as you can with the question rephrase.

RT=D, and T = 1/2 hour
Question: D > 6 miles?

Rephrase:
RT > 6 miles?
R(1/2 hour) > 6 miles?
R > 6 miles / (1/2 hour)?
R > 12 miles/hour?

You could stop there, but since both statements use feet/sec, we save time by converting the question to those units:

R > (12 miles/hour)(5280 ft/mile)(1 hour/60 min)(1 min/60 sec) = (12*5280/60*60) ft/sec?
R > 17.6 ft/sec?

Now you don't have to do any math in order to evaluate the two statements.