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

[noravoningersleben]

Here is the question from GMATPrep:

"If it took Carlos 1/2 hour ro cycle from his house to the library yesterday, was the distance he cyclced greater than 6 miles?

(1) The averagre 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.

Anwer: (E) Statements (1) and (2) together are not sufficient."

Here is my question / problem:

For Statement (2), when I convert 18 feet per second to miles per second, I get 3/879 miles per second. When I then convert this to miles per hour, I get approximately 11.6 miles per hour. Then, when I multiply this rate (11.6 mph) by the time Carlos spent cycling (1/2 hours), I get 5.8 miles. Thus, if my calculcations are correct, Carlos would not have even cycled a distance of more than 6 miles if his average speed had been 18 feet per second. Therefore, since his speed is less than 18 feet per second, he definitely cannot have cycled a distance greater than 6 miles and Statement (2) is sufficient.

However, the correct answer is (E). Could somebody tell me what I'm doing wrong here?

Thanks in advance for your help!

[noravoningersleben]

Hi all,

Never mind. I figured it out myself! :)

[tomslawsky]

there is no mention of time in either statement

[Ben Ku]

(1) The averagre 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.

Anwer: (E) Statements (1) and (2) together are not sufficient."

Here is my question / problem:

For Statement (2), when I convert 18 feet per second to miles per second, I get 3/879 miles per second. When I then convert this to miles per hour, I get approximately 11.6 miles per hour. Then, when I multiply this rate (11.6 mph) by the time Carlos spent cycling (1/2 hours), I get 5.8 miles. Thus, if my calculcations are correct, Carlos would not have even cycled a distance of more than 6 miles if his average speed had been 18 feet per second. Therefore, since his speed is less than 18 feet per second, he definitely cannot have cycled a distance greater than 6 miles and Statement (2) is sufficient.

However, the correct answer is (E). Could somebody tell me what I'm doing wrong here?

Thanks in advance for your help!


I think it helps to try to rephrase the question. Since rate * time = distance, we can translate the question as:
Is (r)(0.5) > 6?

We can manipulate this by dividing both sides by 0.5. Now it's rephrased as:
Is r > 12 mph?

Noticing that the statements are in feet/second, we should convert 12mph to ft/sec. (12mi/hr) * (1hr/3600 s) * (5280 ft/1 mi) = 5280/300 = 17.6 ft/sec.

Is r > 17.6 ft/sec?

(1) Says r > 16 ft/sec. This is insufficient. r could be less than or greater than 17.6.

(2) says r < 18 ft/sec. This is also insufficient. r could be either less than or greater than 17.6.

Putting (1) and (2) together, 16 < r < 18. We still do not know for sure that r > 17.6. The answer is (E).

Hope that makes sense.

[laklucky]

Here is the question from GMATPrep:

"If it took Carlos 1/2 hour ro cycle from his house to the library yesterday, was the distance he cyclced greater than 6 miles?

(1) The averagre 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.

Anwer: (E) Statements (1) and (2) together are not sufficient."

Here is my question / problem:

For Statement (2), when I convert 18 feet per second to miles per second, I get 3/879 miles per second. When I then convert this to miles per hour, I get approximately 11.6 miles per hour. Then, when I multiply this rate (11.6 mph) by the time Carlos spent cycling (1/2 hours), I get 5.8 miles. Thus, if my calculcations are correct, Carlos would not have even cycled a distance of more than 6 miles if his average speed had been 18 feet per second. Therefore, since his speed is less than 18 feet per second, he definitely cannot have cycled a distance greater than 6 miles and Statement (2) is sufficient.

However, the correct answer is (E). Could somebody tell me what I'm doing wrong here?

Thanks in advance for your help!

Hi, Can you please tell me what is wrong with this reasoning? I understood the solution provided by Ben Ku but I wanted to know how is this wrong?

PS: I have my GMAT in next 10 days. please help! thank you!

[gokul_nair1984]

Calculation mistake:

18ft/sec=12.2mph and 12.2/2=6.1(which is >6).

For other values less than 18ft/sec , the distance may be lesser than 6 miles.

5280 ft = 1 mile
18 ft=(1/5280)*18=.00340miles/sec=.00340*3600=12.272 mph

[RonPurewal]

For Statement (2), when I convert 18 feet per second to miles per second, I get 3/879 miles per second. When I then convert this to miles per hour, I get approximately 11.6 miles per hour.

actually, both of these calculations are mistaken!

the first one isn't off by that much; when you convert 18 ft/s to mi/s, you should get 3/880 mi/s. so this one shouldn't have too much of an effect, since you just somehow got 879 rather than 880 (i wonder how?)

however, when you convert the correct value (3/880) to a decimal, you should get 12.272727..., which is nowhere close to the value that you got.
your value, 3/879, is even a little bit bigger than 3/880 (since its denominator is smaller), so, when you multiply by 3600 in order to convert to mi/hr, you should get a decimal that is even bigger than 12.272727... (like, say, ~ 12.28)

so the problem is just that you've done calculations incorrectly.

[jtslbr]

is there an easy way to convert feet to miles? it seems that multiplying by 5280 is a pretty annoying calculation and it seems that rounding numbers here would not get you to the right answer since the values are so close

[RonPurewal]

is there an easy way to convert feet to miles? it seems that multiplying by 5280 is a pretty annoying calculation and it seems that rounding numbers here would not get you to the right answer since the values are so close

Annoying?
Yes.

Terribly time-consuming?
No.

As in many other instances, you should just get out the proverbial shovel and dig.
We're talking about, what, 10-20 seconds of work? Certainly not a big deal.

Don't talk yourself out of a workable solution!

[EashwarR663]

Hello all

Its been a while since the last post on this question.

I have a basic question - In GMAT are speed measurements assumed to have decimal values. Otherwise, I am going to argue that speed < 18 feet per second means that Carlos rode the bike at a maximum speed of 17 feet per second and yes the distance was less than 6 miles. statement (2) alone is sufficient.

Can someone please answer my question?

[Sage Pearce-Higgins]

Unless the question tells you otherwise, don't assume that the number is an integer. GMAT will often tell you a number is an integer; in other cases, it may or may not be!

[EashwarR663]

Unless the question tells you otherwise, don't assume that the number is an integer. GMAT will often tell you a number is an integer; in other cases, it may or may not be!

Thank you Sage!

[Sage Pearce-Higgins]

You're welcome!