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DS - average speed / distance ?!?!

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DS - average speed / distance ?!?!

by minihobel » Tue Jul 21, 2015 8:08 am
Hey,

following Q:

If it took Carlos 1/2 h to cycle from his home to the library, was the distance he cycled GREATER than 6 miles? (note: 1mile = 5280ft)

(1) Average speed from Carlos from his home to the lib. was GREATER than 16ft per second
(2) Av. speed from home to lib. was LESS than 18ft per second.

OA is E

BUT

Let's jump directly to C (both together sufficient - yes/no)

6miles = 31680 ft

from (1) and (2) we get that he ran 17ft per second right?

1 sec - 17ft
10 sec - 170ft
60 sec - 960 ft
30 min - 28800 ft
(60min - 57600 ft)

30 min = 1/2h = 28800 ft < 31680ft so this is a solution right? now, I know that he didn't cycle more than 6miles.

I'm grateful for any explanation guys=)
Thanks in advance

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by GMATGuruNY » Tue Jul 21, 2015 8:11 am
If it took Carlos ½ hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile = 5,280 feet)

(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.
Since the two statements are in terms of FEET PER SECOND, rephrase the question stem in terms of FEET PER SECOND.

1/2 hour = 1800 seconds.
Determine the rate needed to travel 6 miles in 1800 seconds:
(6 miles)/(1800 seconds) * (5280 feet)/(1 mile) = (6*5280)/1800 = 528/30 = 176/10
= 17.6 feet per second.
Note that the units in red CANCEL OUT, leaving the resulting value in terms of feet per second.

Thus, to travel MORE than 6 miles in 1800 seconds, the average speed must be GREATER than 17.6 feet per second.
Question rephrased:
Was the average speed greater than 17.6 feet per second?

The two statements combined indicate only that the average speed was between 16 feet per second and 18 feet per second, implying that the average speed could be less than, equal to, or greater than 17.6 feet per second.
INSUFFICIENT.

The correct answer is E.
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by [email protected] » Tue Jul 21, 2015 8:11 am
Hi minihobel,

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. This is a YES/NO question.

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

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by minihobel » Tue Jul 21, 2015 8:13 am
ok thanks guys... I get it.
Thought there would be only integers in consideration.
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by Brent@GMATPrepNow » Tue Jul 21, 2015 8:42 am
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 feet)

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.
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,
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by Brent@GMATPrepNow » Tue Jul 21, 2015 8:44 am
minihobel wrote:ok thanks guys... I get it.
Thought there would be only integers in consideration.
That's a common mistake. In fact, this mistake is included in our free video Avoiding Common Mistakes - Part II : https://www.gmatprepnow.com/module/gmat- ... cy?id=1105
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by nikhilgmat31 » Wed Jul 22, 2015 12:16 am
Answer is E

32400 > 31680 > 28800
distance can be anywhere between 32400 & 28800 so answer is E Both statement are not sufficient together.
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