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Any idea why B is not sufficient?17f/sec is not enough speed

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Ehab Salah Newbie | Next Rank: 10 Posts
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Posted:
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Any idea why B is not sufficient?17f/sec is not enough speed

Post Sat Nov 04, 2017 5:58 am
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Post Tue Nov 07, 2017 8:16 am
Quote:
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,
Brent

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ErikaPrepScholar Master | Next Rank: 500 Posts
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Post Tue Nov 07, 2017 8:05 am
B. Carlos traveled *less than* 18 feet per second. He traveled for 1/2 hour. Converting that into seconds gives:

$$0.5\ hours\ \cdot\ \frac{60\ \min}{1\ hour}\ \cdot\ \frac{60\ \sec}{1\ \min}\ =\ 1800\ \sec$$

So Carlos traveled for 1800 seconds. Combining this information with the rate gives:

$$\frac{18\ feet}{1\ \sec}\ \cdot\ 1800\ \sec\ =\ 32,400\ feet$$

So Carlos traveled *less than* 32,400 feet in total. Converting that into miles gives:

$$32,400\ feet\ \cdot\ \frac{1\ mile}{5,280\ feet}\ =\ 6.13636...$$

So Carlos traveled *less than* 6.13636... miles in total. However, this means that Carlos could have traveled 6.1 miles (greater than 6 miles) or 5.9 miles (less than 6 miles). So B is insufficient.

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