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OG quant : Q no 59.

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OG quant : Q no 59.

by NaimaB » Sat Nov 22, 2014 11:28 pm
What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.

OA is A.

I ended up choosing D with below explanation in my mind:

statement 2 gave the rate, it says it will took the wheel 5 hours to complete 100 meter rolling. If it rotates 20 times a hour, then it will rotate 20*5=100 times to cover 100 meter. That is what the question asks, how many times? 100 times!!

I know i am wrong somewhere as the OA is A, but i am not getting where i am wrong. I feel really dumb when i see this kind of wrong answers which i even don't understand why i am wrong. Thanks to BTG forum, where i can ask help at anytime. My scheduled date for the exam is 17 December. Feeling hopeless!
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by GMATGuruNY » Sun Nov 23, 2014 4:38 am
NaimaB wrote:What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.
Number of rotations = (total distance)/(circumference).
Here, the total distance = 100 meters.
To determine the number of rotations, we need to know the circumference of the wheel.

Statement 1: The diameter of the bicycle wheel, including the tire, was 0.5 meter.
Since the diameter of the wheel is known, the circumference of the wheel -- and thus the number of rotations -- can be determined.
SUFFICIENT.

Statement 2: The wheel made twenty 360-degree rotations per minute.
If the total time = 1 minute, then the number of rotations = r*t = 20*1 = 20.
If the total time = 10 minutes, then the number of rotations = r*t = 20*10 = 200.
Since the number of rotations can be different values, INSUFFICIENT.

The correct answer is A.
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by Brent@GMATPrepNow » Sun Nov 23, 2014 7:50 am
NaimaB wrote:What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
(2) The wheel made twenty 360-degree rotations per minute.

OA is A.

I ended up choosing D with below explanation in my mind:

statement 2 gave the rate, it says it will took the wheel 5 hours to complete 100 meter rolling. If it rotates 20 times a hour, then it will rotate 20*5=100 times to cover 100 meter. That is what the question asks, how many times? 100 times!!
Statement 2 tells us how many rotations were made per minute, but we cannot determine how many rotations were made in the 100-meter distance. We need to know the size of the wheel.

Consider these two cases:
case a: the bicycle wheel is HUGE. In fact, let's say that its circumference is 100 meters. So, once the wheel makes ONLY ONE rotation, the wheel has traveled the entire 100-meter distance.
case b: the bicycle wheel is VERY VERY SMALL. In fact, let's say that its circumference is 0.00000001 meters. In this case, the wheel will make MILLIONS OF rotations as it travels the entire 100-meter distance.

Notice, that in both cases, the number of rotations per minute does not help us answer the target question.
In case a, we can can conclude that the wheel takes 3 seconds to travel the 100 meters, but that still doesn't tell us anything about the number of rotations.
Likewise, in case b, we can can conclude that the wheel takes several weeks to travel the 100 meters, but that still doesn't tell us anything about the number of rotations.

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by Brent@GMATPrepNow » Sun Nov 23, 2014 7:59 am
NaimaB wrote:What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?

(1) The diameter of the bicycle wheel, including the tire, was 0.5 meters.
(2) The wheel made twenty 360-degree rotations per minute.
Target question: How many 360-degree rotations does a bicycle wheel made while rolling 100 meters in a straight line?

This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Notice that the number of rotations depends on the SIZE of the wheel. For example, if the bicycle wheel has a circumference of 100 meters, then the wheel makes ONLY ONE rotation during the entire 100-meter distance. Conversely, if the bicycle wheel has a circumference of 0.00000001 meters, then the wheel makes MILLIONS of rotations during the entire 100-meter distance.

Since we need the size of the wheel to answer the target question, we can REPHRASE the target question as...
REPHRASED target question: What is the circumference of the wheel?

Statement 1: The diameter of the bicycle wheel, including the tire, was 0.5 meters
PERFECT.
This tells us (indirectly) the circumference of the wheel.
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: The wheel made twenty 360-degree rotations per minute.
There is no way we can use this information to determine the circumference of the wheel.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by NaimaB » Sun Nov 23, 2014 9:40 am
So i was wrong in thinking that the wheel rolled 100 meter at the given rate (statement 2), but statement 2 actually gives the rate only, not the rate at which it covers 100 meter.
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by Brent@GMATPrepNow » Sun Nov 23, 2014 9:42 am
NaimaB wrote:So i was wrong in thinking that the wheel rolled 100 meter at the given rate (statement 2), but statement 2 actually gives the rate only, not the rate at which it covers 100 meter.
That's right.
We may know the number of rotations per minute, but we don't know how fast the wheel is traveling along the 100 meters.

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