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

Question

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.

Bunuel · Accepted Answer

First of all from 166 ? 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) 1617.6 . Answer: E.

shrouded1 · Answer

(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

KarishmaB · Answer

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.

gmatisgood · Answer

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)

metallicafan · Answer

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!

Bunuel · Answer

Not sure, but try min/max questions: search.php?search_id=tag&tag_id=63 and search.php?search_id=tag&tag_id=42

rjdio · Answer

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.

Bunuel · Answer

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) 1617.6 . Answer: E. Hope it's clear.

bagrettin · Answer

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

blink005 · Answer

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

KarishmaB · Answer

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

BrentGMATPrepNow · Answer

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

EMPOWERgmatRichC · Answer

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:  E

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

davidbeckham · Answer

Hi  Bunuel  - is there a compilation of certain conversions that the GMAT may expect us to know? For example, I have never used miles per hour so I did not know the conversion.

Bunuel · Answer

You are not supposed to know that 1 mile = 5280 ft but should be able to convert miles per hour to feet to hour given that 1 mile = 5280 ft. That's why it's given that 1 mile = 5280 ft.

Generally, the question itself will supply the relative conversions, so 1m = 100cm or 1km = 1,000m will be given. Though you should have a few basic ones memorized: 1 hour = 60 minutes, ...

Check other  Conversion problems  to practice in  Special Questions Directory .

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=nainXj3EgZI

CrackverbalGMAT · Answer

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)

Distance = Speed * Time
here we need to check whether the distance covered is greater than 6 miles or not
is Distance > 6 miles ?
Speed * time > 6 miles ?
Speed * 1/2 > 6 ?
Speed > 12 miles/hour ?
Since the unit of speed in the statements are given in feet/sec , we need to convert miles/hour to feet/sec
1 miles/hour = 5280/(60*60) feet/sec = 44/30 feet/sec
12 mile/hour = 12* 44/30 = 17.6 feet/sec
So we can re-frame the question stem as whether the speed is greater than 17.6 feet/sec or not.

(1) The average speed at which Carlos cycles from his house to the library yesterday was greater than 16 feet per second.
Statement 1 is insufficient as we cannot confirm that Speed > 17.6 or not

(2) The average speed at which Carlos cycles from his house to the library yesterday was less than 18 feet per second.
Statement 2 is also insufficient as we cannot confirm that Speed > 17.6 or not

Even though if we combine Statement 1 and 2 , we can only say that 16 feet/sec < speed < 18 feet/sec.
This is not sufficient to answer our question whether the speed is greater than 17.6 feet/sec or not.
If speed is 17 feet/sec, then its a NO and if speed is 17.8 feet /sec then its a Yes
So both Yes and NO is possible as the answer for the question, hence insufficient

Option E is the answer

Thanks,
Clifin J Francis
GMAT SME

iamDARKLORD · Answer

when it say average speed, should we take that value as actual speed? as average speed can be due to anything like if he paused due to obastcales and all etc.

I selected (E) bcz I was not sure due to it

Bunuel · Answer

Your reasoning about average speed is not correct. Average speed is total distance divided by total time, so it can be used directly here. Any speeding up, slowing down, or stopping is already reflected in the average speed, so this does not create any additional uncertainty.

E is correct for a different reason: even together, the statements only give 16 < r < 18, which does not tell us whether r > 17.6.

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

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