How long, in minutes, did it take a bicycle wheel to roll along a flat

Question

How long, in minutes, did it take a bicycle wheel to roll along a flat, straight 300-meter path?

(1) The wheel made one full 360-degree rotation every 1.5 meters.
(2) The wheel made 18 360-degree rotations per minute.

Bunuel · Accepted Answer

How long, in minutes, did it take a bicycle wheel to roll along a flat, straight 300-meter path?

Time=Distance:Rate, so to get the time we nee to find the rate of the bicycle.

(1) The wheel made one full 360-degree rotation every 1.5 meters --> basically tells us that the circumference of the wheel is 1.5 meters. Not sufficient.

(2) The wheel made 18 360-degree rotations per minute --> the rate of the bicycle is 18 circumference per minute, but since we don't know the length of the circumference then this statement is also insufficient.

(1)+(2) Th rate 18*circumference=18*1.5=27 meter/minute. Sufficient.

Answer: C.

aalba005 · Answer

Went with C. Above explanation is great,

basically we need a time reference and a distance reference to figure out how much time the wheel will take to go any distance, first one gives us the size of the wheel circumference in meters and the second tells us meters per minute using both pieces we can figure out how long it will take to roll any distance amount.

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Distance/Rate Problems: distance-speed-time-word-problems-made-easy-87481.html

All DS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=44
All PS Distance/Rate Problems to practice: search.php?search_id=tag&tag_id=64

Jaisri · Answer

I used 18 as the speed. Basically missed to calculate speed by multiplying number of rotations with circumference. Thanks for the explanation Bunuel!

Vinayprajapati · Answer

An alternate solution may be

T= time taken to cover the entire distance
V= velocity
W= frequency = rev per sec
R= radius of wheel

Distance (300)= v * T = (wr)* T 
Now w is given in second statement
And r is given in first statement

Hence c is the answer

WholeLottaLove · Answer

How long, in minutes, did it take a bicycle wheel to roll along a flat, straight 300-meter path?

(1) The wheel made one full 360-degree rotation every 1.5 meters. 
This tells us nothing about how long it took for the wheel to rotate.
NOT SUFFICIENT

(2) The wheel made 18 360-degree rotations per minute. 
This tells us nothing about the size of the wheel. 
INSUFFICIENT

1+2 we are told the diameter of the wheel and how long it takes to make a set number of rotations.  
The wheel makes 18 full rotations per minute and travels 1.5 meters per rotation. Therefore it travels 24m/minute. 300/24 = 12.5

SUFFICIENT

(C)

madn800 · Answer

EASY way to understand this problem
replace the word 360 degrees with 1 revolution
1.5 mt=1 rev
300 mt=? which is 300/1.5

18 rev = 1 min
300/1.5 rev=? min 
DO not do simplifications as it wastes valuable time.
problem solved>

Asifpirlo · Answer

st(1), nothing about time, so not sufficient.
st(2), 18 × 360-degree rotations in = 1 minute.
but need this data in aspect of meter.
so using both statement together,
18 × 360-degree rotations = 18 × 1.5 = 27meters.

27 meters in = 1 minute
so, 300 meters in = 300/27 = fixed value.
so both together are sufficient. Answer C

longhaul123 · Answer

This is how i did this problem. Kindly let me know if i am wrong. So the total distance is given as 300 meters. So from statement 1 if the wheel can travel for one round by travelling 1.5 mt then for 300 meters it has to go for 200 revolutions. 300/1.5=200 but here we don't know the time taken.
From statement 2, the revolutions per minute is given but we don't know the how many total minutes will it keep revolving , Not sufficient
From 1+2 both unknown values can be found out. Hence C

argerniki · Answer

This can be solved with simple logic without making a single calculation:

Statement 1

We know that one full rotation would move the bicycle 1.5 meters.
To move 300 meters, the tire would have to rotate 200 times.

But  how long  does one rotation take?
If it's a really fast bike and one rotation takes 1 second, then the bike would travel 200 seconds.
But what if it is really slow and one rotation takes 1 minute? Then the bike would travel 200 minutes.

2 different answers ->  NOT SUFF

Statement 2

We know that the wheel made 18 rotations per minute.
At this point, your inner voice might tell you that this is the missing piece from Statement 1. It is tempting to click C but first check whether Statement 2 can be sufficient on its own ( very important! )

We don't know how far the bike travels through 1 rotation.
Again, if it's a really big bike and the tire has a circumference of 100 meters, then it would take 3 rotations and not even take a minute.
But if the bike is really small and the circumference is 1 meter, then we would need 300 rotations and much more time.

Again, 2 different answers ->  NOT SUFF

Combining both statements

From (1) you know the circumference of one rotation and from (2) you know how many rotations per minute.
Combining those facts, you know how many meters the bike travels per minute.
This is enough to calculate how long it would take to travel 300 meters.

Answer C

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

How long, in minutes, did it take a bicycle wheel to roll along a flat

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

How long, in minutes, did it take a bicycle wheel to roll along a flat

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards