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

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

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23 Sep 2010, 14:10
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jul 2012, 01:36, edited 3 times in total.
Edited the question and added the OA
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23 Sep 2010, 14:25
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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?

(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

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23 Sep 2010, 14:44
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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 $$r>17.6$$.

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11 Dec 2010, 15:42
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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11 Dec 2010, 15:51
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metallicafan wrote:
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!

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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11 Dec 2010, 16:01
Bunuel wrote:
metallicafan wrote:
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!

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

Thanks! Kudos for you
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03 Jan 2011, 05:54
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.
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03 Jan 2011, 06:08
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rjdio wrote:
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 $$r>17.6$$.

Hope it's clear.
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03 Jan 2011, 08:02
Thank you Sir.Crystal clear now.

On the test day - one has to be real level headed.
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03 Jan 2011, 09:24
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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)
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Re: Data sufficiency [#permalink]

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24 Apr 2011, 00:49
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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
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Re: Data sufficiency [#permalink]

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24 Apr 2011, 01:43
agdimple333 wrote:
If it took carlos 1/2 hr to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles?
(1 mile - 5280 feet)

(a) Average speed at which carlos cycled from his house to the library yesterday was greater than 16 ft / sec
(b) Average speed at which carlos cycled from his house to the library yesterday was less than 18 ft/ sec

$$Distance=Speed*time$$

Q: $$D>6\hspace{2} miles$$
I see that Average Speed is given in both statements and time is given in the stem.

$$6=x*\frac{1}{2}$$
$$x=12\hspace{2}miles/hr$$

Q: Is the speed more than 12 miles/hr?

1. Speed > 16 ft/sec

$$16 \hspace{2} \hspace{2} \frac{ft}{sec}=\frac{16*3600}{5280} \hspace{2} \frac{miles}{hr}=\frac{120}{11} \frac{miles}{hr} \approx 11 \hspace{2} \frac{miles}{hr}$$

Speed > 11 miles/h. The speed could be more than 12 miles/hr or less than 12 m/h.

Not Sufficient.

2. Speed < 18 ft/sec

$$18 \hspace{2} \frac{ft}{sec}=\frac{18*3600}{5280} \hspace{2} \frac{miles}{hr}=\frac{135}{11} \hspace{2} \frac{miles}{hr} \approx 12.2 \hspace{2} \frac{miles}{hr}$$

Speed < 12.2 miles/h. The speed could be less than 12 miles/hr or more than 12 m/h.
Not Sufficient.

Combining both;

$$11 \hspace{2} \frac{miles}{h}< Speed < 12.2 \hspace{2} \frac{miles}{h}$$

Speed could be 12.1 miles/h or 11.9 miles/h.
Not Sufficient.

Ans: "E"
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Re: Data sufficiency [#permalink]

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24 Apr 2011, 02:51
agdimple333 wrote:
If it took carlos 1/2 hr to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles?
(1 mile - 5280 feet)

(a) Average speed at which carlos cycled from his house to the library yesterday was greater than 16 ft / sec
(b) Average speed at which carlos cycled from his house to the library yesterday was less than 18 ft/ sec

Lots of similar ways to solve this question - and went for the 30 second solve

Firstly saw we're looking at a question dealing with ranges and that the two rates given were not restricted to integer values.... so aware there is a trap of thinking speed is 17/ft/s.. it isnt!

Next saw that the only way of solving this is by plugging in the values into "s*t = d"

Quick recall or mental calc for an hour's worth of seconds = 60*60 =3600.... (mentally see 6*6 and two zeros) and halved it to 1800. (for some reason my mind goes for half of 36 quicker than 3*6)

So we need to do a quick calc to see where 5280*6 falls around 16*1800 and 18*1800. (leave it as feet, no need to waste time in converting back to miles)

5280 * 6 = 31680 <<<< value x we're looking for
1800 * 16 = 28800 1) insuff as prompt only says x is more than this
1800 * 18 = 32400 2) insuff as prompt only says x is less than this

together we can quickly see that x can be any value between 28800 and 32400 (above and below 31680). insuff. Answer = E
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Last edited by bleemgame on 24 Apr 2011, 08:38, edited 1 time in total.
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Re: Data sufficiency [#permalink]

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24 Apr 2011, 08:01
30 * 60 * 16 = 28800/5280 = 5.something, so NO

he can be driving at 17.9 ft/s = 1800 * 17.9 = 32220

So Distance can be > 6 miles here

(1) is insufficient

(2) is insufficient

(1) + (2) is insufficient
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Re: Data sufficiency [#permalink]

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25 Apr 2011, 18:48
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agdimple333 wrote:
If it took carlos 1/2 hr to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles?
(1 mile - 5280 feet)

(a) Average speed at which carlos cycled from his house to the library yesterday was greater than 16 ft / sec
(b) Average speed at which carlos cycled from his house to the library yesterday was less than 18 ft/ sec

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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Re: DS Rate Problem [#permalink]

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18 Mar 2012, 21:22
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).
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Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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

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27 Jun 2013, 12:22
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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.
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Re: If it took Carlos 1/2 hour to cycle from his house to [#permalink]

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29 Jul 2013, 15:06
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 statements appear to utilize feet, so let's convert miles to feet.

5280*6 = 31,680ft.

Was the distance greater than 31,680 feet?

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

1hour = 60 minutes
1/2hour = 30 minutes
1 minute = 60 seconds
30minutes*60seconds = 1800 seconds.
1800seconds*16feet/second = 28800 feet.
In 30 minutes Carlos travels minimally, 28800 feet. However, we don't know if he travels more than 28800 feet in that 30 minute timespan as the question states simply that he travels greater than 16feet/second.
INSUFFICIENT

(2) The average speed at which Carlos cycles from his house to the library yesterday was less than 18 feet per second.
1hour = 60 minutes
1/2hour = 30 minutes
1 minute = 60 seconds
30minutes*60seconds = 1800 seconds.
1800seconds*18feet/second = 32400 feet.

Here, Carlos travels less than 32400 feet. This means he could travel greater than 6 miles (31680 feet) or he may travel less.
INSUFFICIENT

1+2) He travels more than 16feet/second but less than 18feet/second. There is a possibility he could travel more or less than the 31680 feet the question asks.
INSUFFICIENT

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

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