If it took Carlos 1/2 hour to cycle from his house to the library yest

First of all from 16<x<18 you cannot say that x=17. You have the range for x, you cannot take an average and say that x equals to it.

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)

The question asks:

Is \(d>6\) ?

Since \(rt=d\) (where \(r\) is the rate in miles per hour and t = 1/2 hour) then question becomes:

Is \((rt=d)>6\)?

Is \(r*\frac{1}{2}>6\)

Is \(r>12\) miles/hour?

\(12 \ miles/hour = \frac{12*5280}{60*60} \ feet/second = 17.6 \ feet/sec\).

Is \(r>17.6\) feet/sec?

(1) The average speed at which Carlos cycles from his house to the library yesterday was greater than 16 feet per second --> \(r>16\) feet/sec. Not sufficient.

(2) The average speed at which Carlos cycles from his house to the library yesterday was less than 18 feet per second --> \(r<18\) feet/sec. Not sufficient.


(1)+(2) \(16<r<18\) still not sufficient to say whether \(r>17.6\).

Answer: E.
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(1) Avg speed > 16fps
So distance covered > 16*1800 feet = 28800feet or about 5.45miles
So distance > 5.45 miles
Not sufficient

(2) average speed < 18fps
So distance < 18*1800 feet or about 6.14miles
So distance < 6.14miles
Not sufficient

(1)+(2) Distance is between 5.45 and 6.14 miles
Not sufficient to say if it is > 6 miles

Answer = E
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One thing that comes to mind when I read the question above is that the statements give the speed in ft/sec while the question stem asks about a speed in miles/hr. It could be easier to convert the speed of the question stem in ft/sec since that involves only one calculation.

Was his average speed greater than 6miles/half hour or 12 miles/hr?
12 miles/hour = 12*5280/3600 ft/sec = 17.6 ft/sec

Question stem: Was his average speed greater than 17.6 ft/sec?
Now it is a direct comparison.
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Bunuel, is there an specific tag or category for this type of question (more / less questions)? (Not only in rate questions).

Thank you very much!
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Not sure, but try min/max questions: search.php?search_id=tag&tag_id=63 and search.php?search_id=tag&tag_id=42
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Folks, I approached this as a YES / NO DS question, since statement i) was NO and ii) indertiminate - I put A.
ie.Statement 1 alone is sufficient.

I though the question was a yes/ no since the question was "Was the distance greater than 6 miles ?"

Whats wrong with my reasoning.

Thank you.

This is indeed YES/NO DS question, but you don't have a NO answer for (1). If you you convert the question "was the distance that he cycle greater than 6 miles" into the rate you'll get "was \(rate>17.6\) feet/sec?" (Refer to my first post to see how to convert.)

(1) \(r>16\) feet/sec. Not sufficient.
(2) \(r<18\) feet/sec. Not sufficient.

(1)+(2) \(16<r<18\) still not sufficient to say whether \(r>17.6\).

Answer: E.

Hope it's clear.
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6 miles = 5280 * 6 = 31680.

1. For average speed greater than 16 feets for second

In 30 minuts distance travelled = 16 * 60 * 30 > 28800 feets

2. For average speed less than 18 feet for second

In 30 minuts distance travelled = 18 * 60 * 30 < 32400 feets

From both we can not say it travelled more than 31680 feets or not.
So answer is (E)

1/2 hour is 30 minutes which is 1800 seconds.
(i) If average speed is greater than 16 ft/sec, then he cycled more than 1800*16=28800 feet = 28800/5280=2880/528=720/132=180/44=45/11>4 miles
It is not sufficient to say that he cycled more than 6 miles
(ii) If average speed is less than 18 ft/sec, then he cycled less than 1800*18=32400 feet = 32400/5280 = 810/132=405/66=135/22=6 3/22 miles>6 miles
It is not sufficient to say that he cycled more than 6 miles

(i) and (ii) together says that he cycled more than 4 1/11 miles but less than 6 3/22 miles. Again we could not conclude anything about 6 miles.

The answer is E

E

Let's assume distance covered in 30 minutes is 6mi or (6*5280)ft.
Let speed be x ft./s
Distance =speed*time

6*5280=0.5*3600*x
x=17.6 ft./s

1.
x>16

Rephrase the given condition we get
x>17.6 and 16<x<=17.6
Insufficient

2.
x<18

Rephrase the given condition to get
17.6<x<18 and x<=17.6
Insufficient

1+2
Combine and rephrase the two statements to get
16<x<=17.6 and 17.6<x<18
Insufficient

Hence E.

Responding to a pm:

Given: Carol traveled for 1/2 an hour i.e. 30 mins i.e. 1800 sec

Question: Was the distance he cycled greater than 6 miles or rephrase it in terms of speed: Was his speed greater than (5280*6)/1800 feet/sec = 17.6 feet/sec?

We rephrase the question in terms of speed because both the statements give info in terms of speed. If would require more calculations to work on both the statements separately. It is easier to manipulate the question and put it in terms of speed. How do we get the figure of 17.6? We find the speed at which he covers exactly 6 miles in 1/2 an hour. We get this as 17.6 feet/sec (we convert it all to feet and second because the statements give the speeds in these units). Since the question is whether he covered more than 6 miles, we just have to figure whether his speed was more than 17.6 feet/sec. In case his speed was more than 17.6 feet/sec, he would have covered more than 6 miles.

(1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
His speed could have been 16.5 feet/sec or 17.8 feet/sec etc. We do not know whether his speed was greater than 17.6 feet/sec.

(2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second
His speed could have been 16.5 feet/sec or 17.8 feet/sec etc. We do not know whether his speed was greater than 17.6 feet/sec.

Same is true even when we have both the statements.

Answer E
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Statement 1: If average speed was more than 16 ft / second = 16/5280 miles /second = 16*3600/5280 = 10.9 miles /hour, then the total distance is more than 10.9*1/2 miles, or more than 5.45 miles. This is insufficient to say whether the distance is more or less than 6 miles. Insufficient.

Statement 2: If the average speed was less than 18 ft/second = 18*3600/5280 miles/hour = 12.27 miles/hour, then the total distance was less than 12.27*(1/2) = 6.13 miles. This may or may not be less than 6 miles. Insufficient.

Combining both the statements, we know that the distance lies between 5.45 and 6.13 miles, but this is not enough to say whether the distance is more or less than 6 miles. Insufficient.

Therefore the answer is (E).

Distance = Speed X Time

Time = 1/2 hour
Speed = S
Ques = Was the distance greater than 6 miles?

If S\(\frac{1}{2}\) = 6, speed becomes 12

when time is constant, speed increases as the distance. So for distance to be greater than 6 miles, speed should be greater than 12mph

So the question can be rephrased as "Was the speed greater than 12mph?"

S1) Speed was greater than 16 F/s -----> \(\frac{16 X 3600}{5280}\) ----------> 10.xxx mph --- Not sufficient

S2) Speed was less than 18 F/s -----------> \(\frac{18 X 3600}{5280}\) ----------> 12.27 mph --- Not sufficient

S1 + S2) 10.xxx < Speed < 12.27 -------- Still can't say for sure that speed was greater than 12. Hence Insufficient.

Choice E.

Target question: Was the distance that he cycled greater than 6 miles?

This question could use some rephrasing. Since the two statements provide speeds in feet per second, let's first see what it means for Carlos to cycle exactly 6 miles in 1/2 an hour.

Distance = 6 miles = (6)(5280) feet
Time = 1/2 hour = 1800 seconds.

Speed = (6)(5280)/1800 = 5280/300 = 176/10
= 17.6 feet per second.

So, in order for Carlos to travel more than 6 miles in 1800 seconds, his average speed must be greater than 17.6 feet per second.

REPHRASED target question: Was Carlo's average speed greater than 17.6 feet per second?

Statement 1: His average speed was greater than 16 feet per second.
So, his speed may have been greater than 17.6 feet per second, or less than 17.6 feet per second.
Since we cannot answer the rephrased target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: His average speed was less than 18 feet per second.
So, his speed may have been greater than 17.6 feet per second, or less than 17.6 feet per second.
Since we cannot answer the rephrased target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We now know that his speed is between 16 feet per second and 18 feet per second.
So, once again, his speed may have been greater than 17.6 feet per second, or less than 17.6 feet per second.

Since we still cannot answer the rephrased target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

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.

Hi All,

Brent has converted the information into feet/second, which absolutely works. Here's another way to solve this problem though:

We're told that Carlos takes 1/2 hour to cycle to the library. We're asked if the distance was greater than 6 miles. The real question is how fast he was traveling; in essence, was it enough to hit more than 6 miles over the course of 1/2 hour. 6 miles = 6(5280 ft) = 31680 ft., so the question is asking if Carlos traveled more than 31,680 feet.

Fact 1: Carlos' speed was > 16 ft/sec.

Let's convert this…

16 ft/sec x 60 secs x 30 mins = 16 x 1800 = 28,800 feet/half-hour

From this, we know how far Carlos traveled AT THE MINIMUM. But we don't know if he traveled 31,680 feet or not.
Fact 1 is INSUFFICIENT

Fact 2: Carlos' speed was < 18 ft/sec.

Let's convert this…

18 ft/sec x 60 secs x 30 mins = 18 x 1800 = 32,400 feet/half-hour

From this, we know how far Carlos traveled AT THE MAXIMUM. But we don't know if he traveled 31,680 feet or not.
Fact 2 is INSUFFICIENT

Combined, we have the range of distances that Carlos traveled: 28,800 < distance traveled < 32,400. From this, we still don't know if Carlos traveled 31,680 feet or not.
Combined INSUFFICIENT

Final Answer:

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

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

Couple of points.

1. Make sure to follow ALL posting guidelines (link in my signatures). Search for a question before you post a new thread. This and many other questions should have been already discussed on GMATCLUB. Merged the topics. Refer above for the solution.

2. For any official questions (official guides, GMATPREP) it is an absolute waste of time if you question the OA or OE.



Remember that 30 minutes = 30*60=1800 seconds. 6 miles = 6*5280 = 31680 feet.

Per statement 1, you are given average speed > 16 ft/s ---> thus in 30 minutes, Carlos travels > 30*60*16 feet ---> > 28800 feet. Nw as the distance is > 28800 we can not be sure whether this value if 29000 or 32000, giving you 2 different answers ---> not sufficient.

Per statement 2, you are given average speed <18 ft/s ---> thus in 30 minutes, Carlos travels < 30*60*18 feet ---> < 32400 feet. Nw if the distance is 32399 feet, then "yes" but if the distance is 31600 feet, the answer is "no". Again, 2 different answers ---> not sufficient.

Combining the 2 statements, 28800 < distance < 32400 , again clearly if the distance is 31600 "no" but if it is 32000 "yes". Again not a unique answer.

E is thus the correct answer.

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

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