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.

_________________
Emily Sledge
Instructor
ManhattanGMAT

The short cut to this is to stop and think for a second:

1) Lets say he lived exactly 6 miles away. Set up our equation:

D=RT
6miles=R(1/2 hour)
R=12miles per hour

2) Now we realizes that Carlos would have to travel at exactly 12mph to reach the library and live a half hour away. Because the stems give us feet per second we need to convert 12mph into feet per second.

3)

(12miles/1hour)*(5280feet/1mile)*(1hour/60minutes)*(1minute/60seconds)
=5280/300
=528/30
=176/10
=17.6 feet per second

Now we know that he needs to be traveling at 17.6 feet per second to live 6 miles from the library.

4) Evaluating the stems, we see that stem 1 tells us that it could be more or less than 17.6feet per second, so its insufficient.

We also see that stem 2 tells us it could be more or less than 17.6 feet per second, so it is also insufficient.

Taken together, we see that nothing has changed, because it could be still more or less than 17.6 feet per second, so the answer is E, neither stem will help.

5) The key to be able to solve this problem on GMAT day is to realize that you have FEET PER SECOND in the stems, and MILES PER HOUR in the question, and that you need to convert MILES PER HOUR to FEET PER SECOND to analyze the stems. You also need to realize that they give you the #6, and therefor, you should probably figure out a way to use it!

@ benkriger: nicely done.

one add-on comment:


there's no reason you couldn't do the reverse (i.e., convert ft/sec to mi/hr). either will be effective, as long as you create some common unit.

it's easier to convert to ft/sec, though, because two of the three figures are already given in ft/sec. therefore, you only have to do one conversion, vis-à-vis two if you convert to mi/hr.

Emily- You're a Goddess!! Great Explanation!! :-)

I'm glad it helped.

_________________
Ben Ku
Instructor
ManhattanGMAT