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Carlos the racer

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Carlos the racer

by szDave » Thu Jan 24, 2013 7:26 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 = 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.

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.

I thought that the answer is B, but was not right. My equation is: rate*30*60 > 5280 * 6
If the rate is below 18, then it cannot exceed 5280 * 6. How is it possible, that B is not correct, and the answer is E?
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by Brent@GMATPrepNow » Thu Jan 24, 2013 7:50 am
szDave wrote: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 = 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.
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
Last edited by Brent@GMATPrepNow on Sun Oct 18, 2015 8:22 pm, edited 2 times in total.
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by Anurag@Gurome » Thu Jan 24, 2013 6:27 pm
szDave wrote: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 = 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.

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient.

I thought that the answer is B, but was not right. My equation is: rate*30*60 > 5280 * 6
If the rate is below 18, then it cannot exceed 5280 * 6. How is it possible, that B is not correct, and the answer is E?
Distance = speed * time or d = st, where d = distance, s = speed (in mph), t = time
Question is: Is d > 6? or is st > 6 or is s * (1/2) > 6 implies is s > 12 mph
Now convert mph to feet per sec: 12 miles per hour = (12 * 5280)/(60 * 60) = 17.6 feet per sec

So, the question is: Is s > 17.6 feet per sec?

Statement 1: s > 16 feet per sec; clearly NOT sufficient.

Statement 2: s < 18 feet per sec; NOT sufficient.

Combining (1) and (2), 16 < s < 18 is still NOT sufficient to find if s > 17.6 feet per sec.

The correct answer is E.
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by Gurpreet singh » Sun May 29, 2016 9:17 am
Question stem is asking is the distance greater than 6 miles or 31680 feet (6 miles*5289 feet per mile)

time given is 1/2 hr=30 mins=30*60=1800 seconds

st 1- avg speed is greater than 16 miles per second.

Distance =speed(16+ miles/sec)*time(1800 seconds)

Distance-1(D1)
since speed is >16 lets take 16.1 miles per second.
D1=16.1*1800=28980 feet which is < 31680

Distance -2(D2)
Speed =17.9 miles/second

D2=17.9*1800=32220>31680

since we are getting 2 values statement is insufficient.

St-2

Speed<18 miles/second
D1=16.1*1800=28980 feet which is < 31680

Distance -2(D2)
Speed =17.9 miles/second

D2=17.9*1800=32220>31680

since we are getting 2 values statement is insufficient.

Combining both statement we agin get multiple values hence Answer is E
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by [email protected] » Sun May 29, 2016 11:01 am
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

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