This is how I did the math more quickly:

Stem: Did he go faster than 12mph?

12*5280/3600 = 6*2*5280/6*6*100 = 528/30 which means: Did he travel faster than 528 feet per 30 seconds?

A) T>16*30 = 480 Not sufficient
B) T<18*30 = 540 Not sufficient

Both) T could be 481 through539 = Not sufficient

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? ( Note: 1 mile = 5280 ft)

(1) The average speed at which Carlos cycles from his house to the library yesterday was greater than 16 feet per second.

(2) The average speed at which Carlos cycles from his house to the library yesterday was less than 18 feet per second.

If the range of the condition is included in that of the question, the condition is sufficient

The question is actually asking whether the car trabels 6miles in 1/2hours, and v(speed rate)>6miles/30min=6*5,280feet/1,800sec=17.6feet/1sec
We have 2 variables (v,d) and 2 equations are given by the conditions, so there is high chance (D) will be the answer.

For condition 1, it is insufficient as v>16 is not included in the range of the question
For condition 2, it is also insufficient as v<18 is not included in the range of the question as well
Looking at the conditions together, 16<v<18 is also not included in the range of the question,
so the answer becomes (E).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Hi all,

I got this question during a CAT of the gmat prep software and I am not sure the result the softwar says is correct. It says E, while for me is B. Here is the question:

"it took Carlos 1/2 hour to cycle from his house to the library, was the distance that he cylced grater than 6 miles? (1 mile = 5,280 feet)

(1) The avrage speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.

(2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.

Now, based on my calculation, with statement B we should figure out that Carlos cycled for sure less than 6 miles, so B is correct, but on the Prep software they say E is correct.

Why?

Thanks a lot

Thanks a lot guys, now it isi much more clear.

Thanks as well for showing me how much ignorant am I :D hahaha

Sure Rich! I will be happy to show you how I worked through the question:

(1) The average speed at which Carlos cycles from his house to the library yesterday was greater than 16 feet per second.

For me is not sufficient because at this rate Carlos could have been cycled a distance less or greater than 6 miles.
Thas this fact is insufficient is quite evident, so I will focus no statement 2.

(2) The average speed at which Carlos cycles from his house to the library yesterday was less than 18 feet per second.

If the speed at which Carlos cycled was less than 18 feet per second, to check if the statement is sufficient, I can take in consideration a speed less than 18 feet/sec., for example 17 feet per second.
So, if Carlos cycled at 17 feet per second, it measn that his rate was also 1020 feet per minute and 30600 feet per 1/2 hour. Dividing 30600 by 5280 (1 mile = 5280 ft) I get 5,79 mile, which is not 6 mile. So, IMO Carlos didn't covered a distance greater or equal than 6 miles and the answer to the question is always NO.

Hope my line of reasoning was understandable, so you can quickly spot my mistake.

Thanks a lot

Thanks a lot! now it is clear.

One more question: is this an hard question? I mean, is this question skippable or it counts?

Hi pepo,

It looks like you knew how to handle the calculations and overall logic just fine. The little mistake you made was in calculating the distance traveled at 17 feet/second and not 18 feet/second. Fact 2 gives us an 'upper limit' based on 18 feet/second, so THAT is the distance that we want to figure out. Anything LESS than THAT distance is possible.

Ultimately, while the work involved in this question was a bit 'thicker' than a typical prompt, the work itself was not 'hard work' (it was unit conversions and some arithmetic) - thus, I would NOT call this a hard question. On Test Day, you have to be responsible for the 'gettable' questions, regardless of how they might be 'ranked.' If you can nail those questions, then you'll end up with an upper-level GMAT score.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

6miles x 5280ft/mile = 31,680 ft.
did he traveled more than 31,680 ft in 30 minutes?

1. suppose 17ft/sec is his speed.
17x60x30 = distance traveled in 30 minutes, or 30,600. so even it he traveled 17ft/min, not enough
but it can be 20 ft/sec as well
20x60x30=36,000 = yes.
A alone is insufficient.

2. if 17ft/sec = then not sufficient
if 17.9ft/sec = then yes

1+2
it can be 16.1 - no or it can be 17.9 yes.

so E.

from the data in the table let's find the border speed to evaluate: 6*5280/(30*60)=17,6
If the average speed was above 17,6 then the distance was over 6 miles, and vice versa
1) NS
2) NS
1+2) NS
Answer is E

Since (1) & (2) Are in rates we should convert 6 miles in 30 minutes into a rate. The Equation is

(1)D = R * T

(2) 6 miles * 5280 = R * (30 minutes * 60 seconds)

(3) Then we isolate R

You can see using cancelling the math is actually not that hard to get it down to 17.6.