Two bicycle wheels, A and B, start rotating at constant speeds at the

Question

Two bicycle wheels, A and B, start rotating at constant speeds at the same time., How many seconds after the wheels start rotatins will wheel B have made 6 more rotations than wheel A?

(1) The rate of rotation of wheel B is three times that of wheel A
(2) The two wheels average 40 revolutions per minute

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Problem Solving Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

PRAGATIOSTWAL · Accepted Answer

I think the answer should be C.

Statement 1: NOT SUFFICIENT. Assuming the speed of the wheel A= x and B=3x, we cannot determine the individual actual speeds (which are required to answer this question).

Statement 2: NOT SUFFICIENT. The average speed also doesn't help to determine the individual actual speeds (which are required to answer this question).

Putting Statement 1 and Statement 2 together
The individual speeds can be determined by the formula: Average Speed= (S1+S2)/2 
40= x+3x/2
x= 20 revolutions per min (Speed of A)
3x= 60 revolutions per min(Speed of B)

Relative Distance= 6 rotations (given in the question stem)
Relative Speed= 60-20 revolutions per min (calculated above)

Time= Relative Distance/Relative Speed
= 6*60/40
= 9 secs

PrasoonGautam · Answer

A since 
State 1 gives the relation required

Statement 2 is insufficient

Posted from my mobile device

Bunuel · Answer

Does anyone else want to try this question?

TOBEATHATPERSON · Answer

I think your avg velocity formula can't be applied in this condition.
2ab/(a+b) is that same Distance different speed but here same time

Posted from my mobile device

PRAGATIOSTWAL · Answer

Thank you for pointing out my mistake. I have corrected my solution/explanation now.

OokandGluk · Answer

@Bunuel Can you please provide the OE for this question. I am a bit confused.

OokandGluk · Answer

@Bunuel, can you please provide the OE for this question. I am a bit confused.

OokandGluk · Answer

I am sorry. I do not understand how you are calculating Average Speed. Why are we doing 2*S1*S2/(S1+S2) instead of your earlier way. I don't understand EDDIE's explanation. Same time but different distance covered so different speed right?

PRAGATIOSTWAL · Answer

OokandGluk : Here's the concept with which we proceeded to calculate Time in this question stem:
Case 1 – When the distance is constant: Average speed = 2xy/x+y; where x and y are the two speeds at which the same distance has been covered. 
Case 2 – When the time taken is constant: Average speed = (x + y)/2; where x and y are the two speeds at which we traveled for the same time.

If you re-read the question requirement, it clearly states that we need to find time (in seconds) when the rotation of Wheel B is more than Wheel A. This means the distance traveled would differ for both wheels within the same time frame. Hence, we'll go with case 2 to calculate the speeds.

bhanu29 · Answer

Given info can be summarized as r1, r2 are individual speed of A and B respectively. t is the time taken for B to go ahead by 6 revolutions
    
 R 
 T 
 D 
 
  A 
 r1 
 t 
 x 
 
  B 
 r2 
 t 
 x+6

To find t, x/r1

Statement 1:
r2 = 3r1
    
 R 
 T 
 D 
 
  A 
 r1 
 t 
 x 
 
  B 
 3r1 
 t 
 x+6

t=x/r1=(x+6)/3r1

3x = x+6
2x = 6
x = 3
t = 3/r1, Insufficient

Statement 2
Average = 40
(x + x + 6)/2t = 40
(x+3)/t=40
t = 40/(x+3)

Combining Statement 1 and 2
x = 3 and t = 40/(x+3)
t = 40/6 minutes (which can be converted to seconds)

Answer  C

Two bicycle wheels, A and B, start rotating at constant speeds at the

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

Two bicycle wheels, A and B, start rotating at constant speeds at the

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