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# If it took Carol 1/2 hour to cycle from his house to the

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If it took Carol 1/2 hour to cycle from his house to the [#permalink]  13 Nov 2011, 01:16
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Question Stats:

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If it took Carol 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (1mile = 5,280feet)

(1) The average 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-it-took-carlos-1-2-hour-to-cycle-from-his-house-to-129287.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Mar 2014, 00:27, edited 1 time in total.
Edited the question and added the OA.
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Re: Carlos - Ivy 25 [#permalink]  13 Nov 2011, 01:22
enigma123 wrote:
If it took Carol 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (1mile = 5,280feet)
(1) The average 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

Guys - again the OA was not provided but I have gone for C. Can someone please let me whether I am right or wrong?

IMO A.

according to question, d > 16*1/2*60*60
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Re: Carlos - Ivy 25 [#permalink]  13 Nov 2011, 07:35
2
KUDOS
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.
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Re: If it took Carol 1/2 hour to cycle from his house to the [#permalink]  14 Nov 2011, 07:59
5,280 * 6 = 31680
31680/(60*30)= 17.6
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Re: If it took Carol 1/2 hour to cycle from his house to the [#permalink]  14 Nov 2011, 09:08
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Expert's post
enigma123 wrote:
If it took Carol 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (1mile = 5,280feet)
(1) The average 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

Guys - again the OA was not provided but I have gone for C. Can someone please let me whether I am right or wrong?

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.

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Re: If it took Carol 1/2 hour to cycle from his house to the [#permalink]  16 Nov 2011, 09:13
E. Statement 1 says the total traveled was more than 28,800.
Statement 2 says the total traveled was less than 32,400

We need to know if carlos traveled more than 31,680.

We do not know because of the range given if he traveled more or less
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Re: If it took Carol 1/2 hour to cycle from his house to the [#permalink]  25 Mar 2014, 11:58
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Re: If it took Carol 1/2 hour to cycle from his house to the [#permalink]  26 Mar 2014, 00:29
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Expert's post
If it took Carol 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (1mile = 5,280feet)

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) The average speed at which Carlos cycled 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 cycled 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 $$r>17.6$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-it-took-carlos-1-2-hour-to-cycle-from-his-house-to-129287.html[/quote]
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Re: If it took Carol 1/2 hour to cycle from his house to the   [#permalink] 26 Mar 2014, 00:29
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