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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.

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.

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

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.
_________________

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

Rate problem of Carlos - maybe error on the gmat prep software? :) [#permalink]

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08 Jan 2016, 13:24

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.

If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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08 Jan 2016, 14:24

pepo wrote:

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.

Training for the GMAT will always involve making some mistakes along the way - that's how you'll ultimately hone your GMAT skills and score at a higher level. As you continue to study, you'll find that much of the work that you have to do when answering GMAT questions isn't all that difficult, but it does involve many of the business 'skills' that MBA Programs want to make sure that you have: note-taking, organization, accuracy, attention-to-detail, precision/rounding (when either is asked for), etc.

You mentioned how your calculation proved that Fact 2 was sufficient, but you didn't actually show what your calculation was (or why it was ultimately incorrect). If you can go into a bit more detail about that work, then we should be able to help you make sure that the same mistake doesn't happen again.

Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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10 Jan 2016, 06:06

EMPOWERgmatRichC wrote:

Hi pepo,

Training for the GMAT will always involve making some mistakes along the way - that's how you'll ultimately hone your GMAT skills and score at a higher level. As you continue to study, you'll find that much of the work that you have to do when answering GMAT questions isn't all that difficult, but it does involve many of the business 'skills' that MBA Programs want to make sure that you have: note-taking, organization, accuracy, attention-to-detail, precision/rounding (when either is asked for), etc.

You mentioned how your calculation proved that Fact 2 was sufficient, but you didn't actually show what your calculation was (or why it was ultimately incorrect). If you can go into a bit more detail about that work, then we should be able to help you make sure that the same mistake doesn't happen again.

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

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.

Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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10 Jan 2016, 08:31

pepo wrote:

EMPOWERgmatRichC wrote:

Hi pepo,

Training for the GMAT will always involve making some mistakes along the way - that's how you'll ultimately hone your GMAT skills and score at a higher level. As you continue to study, you'll find that much of the work that you have to do when answering GMAT questions isn't all that difficult, but it does involve many of the business 'skills' that MBA Programs want to make sure that you have: note-taking, organization, accuracy, attention-to-detail, precision/rounding (when either is asked for), etc.

You mentioned how your calculation proved that Fact 2 was sufficient, but you didn't actually show what your calculation was (or why it was ultimately incorrect). If you can go into a bit more detail about that work, then we should be able to help you make sure that the same mistake doesn't happen again.

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

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

Couple of points to mention here. For saying statement 1 is not sufficient, you do not mention anything about the critical value of speed that will give you 31680 feet in 30 minutes. Without mentioning this value, how do you know whether 16 ft/s is sufficient ? What if 16 ft/s WAS the limiting value to give you 6 miles of distance travelled?

Coming back to your analysis of statement 2, when you have speed < 18 ft/s, you have infinite possible values to check and nowhere in the question was it mentioned that the limiting speed is an integer value. So, assuming speed = 17 ONLY had no basis. The limiting value is actually 17.6 ft/s which is still <18 . This is where you made a mistake.

DS questions are specially tricky if you do not follow step by step procedure and should never assume things not given.

Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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10 Jan 2016, 09:04

Engr2012 wrote:

pepo wrote:

EMPOWERgmatRichC wrote:

Hi pepo,

Training for the GMAT will always involve making some mistakes along the way - that's how you'll ultimately hone your GMAT skills and score at a higher level. As you continue to study, you'll find that much of the work that you have to do when answering GMAT questions isn't all that difficult, but it does involve many of the business 'skills' that MBA Programs want to make sure that you have: note-taking, organization, accuracy, attention-to-detail, precision/rounding (when either is asked for), etc.

You mentioned how your calculation proved that Fact 2 was sufficient, but you didn't actually show what your calculation was (or why it was ultimately incorrect). If you can go into a bit more detail about that work, then we should be able to help you make sure that the same mistake doesn't happen again.

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

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

Couple of points to mention here. For saying statement 1 is not sufficient, you do not mention anything about the critical value of speed that will give you 31680 feet in 30 minutes. Without mentioning this value, how do you know whether 16 ft/s is sufficient ? What if 16 ft/s WAS the limiting value to give you 6 miles of distance travelled?

Coming back to your analysis of statement 2, when you have speed < 18 ft/s, you have infinite possible values to check and nowhere in the question was it mentioned that the limiting speed is an integer value. So, assuming speed = 17 ONLY had no basis. The limiting value is actually 17.6 ft/s which is still <18 . This is where you made a mistake.

DS questions are specially tricky if you do not follow step by step procedure and should never assume things not given.

Hope this helps.

Thanks a lot! now it is clear.

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

Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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10 Jan 2016, 09:17

pepo wrote:

Thanks a lot! now it is clear.

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

Based on the GC stats, yes it is a 700-level/hard question but these questions are the ones that you will be able to solve within 2 minutes (by being smart about your calculations!). I never used 17.6 anywhere in my solution but still was able to provide the correct answer.

If you are running short on time, yes you can skip this. You will not know what question got counted in actual GMAT. So give your best shot to the most/all while being smart about your selections.

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.

Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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09 Apr 2016, 13:18

TomB wrote:

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.

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

Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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12 Jun 2016, 23:35

Bunuel wrote:

TomB wrote:

If it took Carlos 1/2 hour to cycle from his house to library was the distance that he cycle greater than 6 miles(1 mile=5280feet) 1) the avg speed at which Carlos cycled from his house to library was greater than 16 feet per second 2) the avg speed at which Carlos cycled from his house to library was less than 18 feet per second

so we know that 16<x<18. (x = avg speed,x=17) what am i missing?

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.

Question is \(d>6\) --> as \(rt=d\) (where \(r\) is the rate in miles per hour) then question becomes: is \(rt=d>6\) --> or is \(r*\frac{1}{2}>6\), as \(t=\frac{1}{2}\) hours --> 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) \(r>16\) 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.

Hi! Does it make sense saying that option A and B tell me the Average speed, and it is nowhere mentioned in the question that he is travelling with constant speed. and thus answer becoms E. PS- I am not getting any other solution

Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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28 Mar 2017, 09:33

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