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Jeff drove two laps around a track. Was his average speed less than 60

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Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

(1) Jeff's average speed for the first lap was 20 miles per hour.
(2) Jeff's average speed for the second lap was 120 miles per hour.


This was a question that I found in a Manhattan Prep youtube video and they didn't include the answer (argh!!!). The consensus in the comments section says answer B, but I'm struggling to see why that might be. I just spent the past hour learning about how it's impossible to get an average speed that's 2x your first lap, so that leads me to think statement 1 will always be less than 60mph. Statement 2 could be >60 or <60. Therefore I'd pick A. What am I missing?? Thanks!

Link to original video: "Free GMAT Prep Hour: Rates: Distance & Work Questions in GMAT Quant" - youtube com /watch?v=qacow8Cm56Q
Question is at about 1:08

Originally posted by clueless20 on 23 Jun 2020, 23:38.
Last edited by Bunuel on 05 Jul 2020, 02:00, edited 1 time in total.
Edited the OA.
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post Updated on: 24 Jun 2020, 00:16
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clueless20 wrote:
Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

1) Jeff's average speed for the first lap was 20 miles per hour.
2) Jeff's average speed for the second lap was 120 miles per hour.


This was a question that I found in a Manhattan Prep youtube video and they didn't include the answer (argh!!!). The consensus in the comments section says answer B, but I'm struggling to see why that might be. I just spent the past hour learning about how it's impossible to get an average speed that's 2x your first lap, so that leads me to think statement 1 will always be less than 60mph. Statement 2 could be >60 or <60. Therefore I'd pick A. What am I missing?? Thanks!

Link to original video: "Free GMAT Prep Hour: Rates: Distance & Work Questions in GMAT Quant" - youtube com /watch?v=qacow8Cm56Q
Question is at about 1:08


CONCEPT: The average speed is always Greater than half of two speeds given and Less than twice the two speeds

Therefore Statement 2 will be sufficient

Statement 1 is also SUFFICIENT because with one speed 20 average speed has to be less than 40
Average speed \(= \frac{2*20*b}{(20+b)} = \frac{40b}{20+b}\)



Answer: Option D
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Originally posted by GMATinsight on 23 Jun 2020, 23:46.
Last edited by GMATinsight on 24 Jun 2020, 00:16, edited 3 times in total.
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 23 Jun 2020, 23:59
GMATinsight wrote:
clueless20 wrote:
Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

1) Jeff's average speed for the first lap was 20 miles per hour.
2) Jeff's average speed for the second lap was 120 miles per hour.


This was a question that I found in a Manhattan Prep youtube video and they didn't include the answer (argh!!!). The consensus in the comments section says answer B, but I'm struggling to see why that might be. I just spent the past hour learning about how it's impossible to get an average speed that's 2x your first lap, so that leads me to think statement 1 will always be less than 60mph. Statement 2 could be >60 or <60. Therefore I'd pick A. What am I missing?? Thanks!

Link to original video: "Free GMAT Prep Hour: Rates: Distance & Work Questions in GMAT Quant" - youtube com /watch?v=qacow8Cm56Q
Question is at about 1:08


CONCEPT: The average speed is always less than half of two speeds given

Therefore Statement 2 will be sufficient

Statement 1 s NOT sufficient because
Average speed \(= \frac{2*20*b}{(20+b)} = \frac{40b}{20+b}\) can be greater than 60 as well as less than 60 for differnet values of b which is speed of second lap

Answer: Option B



Thanks for the quick reply but can you try explaining another way? I'm not following. Maybe more examples or plugging in numbers would help me see this (also for statement 2 please). Is b in this case the speed of the second lap?

Then to get 60 you'd set 2*20*b / (20+b) = 60
so then 40b = 60(20+b)
40b = 1200+60b
-20b = 1200
b = -60 mph?
This doesn't make sense yet... What else am I missing?
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 24 Jun 2020, 00:17
clueless20 wrote:
This doesn't make sense yet... What else am I missing?


Have made correction in my previous post.
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 24 Jun 2020, 00:48
GMATinsight wrote:
clueless20 wrote:
This doesn't make sense yet... What else am I missing?


Have made correction in my previous post.


Thanks! This makes me feel a little better that I wasn't imagining something.

Now for statement 2... wouldn't this be insufficient? If the speed for the first lap was 40 mph, then the average for the two laps could be 60 mph, but if the speed for the first lap was 60 mph, then the average for both would be 80 mph. Is this thinking correct? So the answer would just be A?
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 24 Jun 2020, 01:31
GMATinsight wrote:
clueless20 wrote:
Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

1) Jeff's average speed for the first lap was 20 miles per hour.
2) Jeff's average speed for the second lap was 120 miles per hour.


This was a question that I found in a Manhattan Prep youtube video and they didn't include the answer (argh!!!). The consensus in the comments section says answer B, but I'm struggling to see why that might be. I just spent the past hour learning about how it's impossible to get an average speed that's 2x your first lap, so that leads me to think statement 1 will always be less than 60mph. Statement 2 could be >60 or <60. Therefore I'd pick A. What am I missing?? Thanks!

Link to original video: "Free GMAT Prep Hour: Rates: Distance & Work Questions in GMAT Quant" - youtube com /watch?v=qacow8Cm56Q
Question is at about 1:08


CONCEPT: The average speed is always Greater than half of two speeds given and Less than twice the two speeds

Therefore Statement 2 will be sufficient

Statement 1 is also SUFFICIENT because with one speed 20 average speed has to be less than 40
Average speed \(= \frac{2*20*b}{(20+b)} = \frac{40b}{20+b}\)



Answer: Option D


I still don't understand how Stmt(2) alone is sufficient.
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post Updated on: 03 Jul 2020, 23:30
GMATinsight wrote:
clueless20 wrote:
Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

1) Jeff's average speed for the first lap was 20 miles per hour.
2) Jeff's average speed for the second lap was 120 miles per hour.


This was a question that I found in a Manhattan Prep youtube video and they didn't include the answer (argh!!!). The consensus in the comments section says answer B, but I'm struggling to see why that might be. I just spent the past hour learning about how it's impossible to get an average speed that's 2x your first lap, so that leads me to think statement 1 will always be less than 60mph. Statement 2 could be >60 or <60. Therefore I'd pick A. What am I missing?? Thanks!

Link to original video: "Free GMAT Prep Hour: Rates: Distance & Work Questions in GMAT Quant" - youtube com /watch?v=qacow8Cm56Q
Question is at about 1:08


CONCEPT: The average speed is always Greater than half of two speeds given and Less than twice the two speeds

Therefore Statement 2 will be sufficient

Statement 1 is also SUFFICIENT because with one speed 20 average speed has to be less than 40
Average speed \(= \frac{2*20*b}{(20+b)} = \frac{40b}{20+b}\)



Answer: Option D


Hi GMATinsight, could you please elaborate some more on why Statement 1 is sufficient? I personally think the answer is B because:
Statement 1
First round = given; ave. 20 mph
Second round
1. Ave. speed could be 20 mph, by which the average speed of 2 laps is under 60
2. Ave. speed could be 110 mph, by which the average speed of 2 laps is 65 mph
This means that Statement 1 is NOT SUFFICIENT

Statement 2
Second round = given; 120 mph
First round
1. Ave. speed could be 1 mph, by which the average speed of 2 laps is 61
2. If ave. speed is 0, the average speed of 2 laps would be 60.
This means that Statement 2 is SUFFICIENT

ANS. B

Maybe I am missing out on something? If so, please tell me!

Originally posted by WBogey on 24 Jun 2020, 02:09.
Last edited by WBogey on 03 Jul 2020, 23:30, edited 1 time in total.
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 24 Jun 2020, 04:10
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I am unsure how B alone is sufficient?

-> If average speed for lap 2 is 120 mph, lets say he drove 2 hours at this speed -> (120)(2) = 240 miles in 1 lap.
-> Lets say he drove the first lap 1 mph -> (1)(t) = 240, therefore it theoretically took 240 hours for the first lap.
-> Average speed = total distance/total time = (2)(240)/(240+2) = 1.98 mph

Can someone please tell me where I am a faulting here?
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 28 Jun 2020, 03:32
GMATinsight, could you explain?
I can't understand how B only is sufficient.
For ex, if the average speed for the first lap is 240 mph. Each lap = 120 miles
=> Completing first lap needs 0.5h, second lap needs 1h
=> Average speed = 240 : 1.5 = 160 mph > 60
However, if the average speed for the first lap is only 20 km/h and each lap = 120 miles
=> Average speed = 240 : 7 = 34.2 mph < 60
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 03 Jul 2020, 06:27
Bunuel
Please help!
The question didn't mention speed to be constant.
:)
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 03 Jul 2020, 10:09
clueless20 wrote:
Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

(1) Jeff's average speed for the first lap was 20 miles per hour.
(2) Jeff's average speed for the second lap was 120 miles per hour.


This was a question that I found in a Manhattan Prep youtube video and they didn't include the answer (argh!!!). The consensus in the comments section says answer B, but I'm struggling to see why that might be. I just spent the past hour learning about how it's impossible to get an average speed that's 2x your first lap, so that leads me to think statement 1 will always be less than 60mph. Statement 2 could be >60 or <60. Therefore I'd pick A. What am I missing?? Thanks!

Link to original video: "Free GMAT Prep Hour: Rates: Distance & Work Questions in GMAT Quant" - youtube com /watch?v=qacow8Cm56Q
Question is at about 1:08


The answer should be D. May we request for some expert's opinion?
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 03 Jul 2020, 23:55
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Let the length of 1 lap be \(d\)
Avg Speed for first lap = \(A\)
Avg Speed for second lap = \(B\)

So the total time taken is \(\frac{d}{A}+\frac{d}{B}\)
Total time taken if overall average speed is \(60 = \frac{2d}{60}=\frac{d}{30}\)

The question asks, is \(\frac{d}{A}+\frac{d}{B}>\frac{d}{30}\)? or is \(\frac{1}{A}+\frac{1}{B}>\frac{1}{30}\)?

(1) Jeff's average speed for the first lap was 20 miles per hour.

\(\frac{1}{A}=\frac{1}{20}\).

Since \(\frac{1}{20}\) is already greater than \(\frac{1}{30}\), then yes, \(\frac{1}{A}+\frac{1}{B}>\frac{1}{30}\)

1 is sufficient

(2) Jeff's average speed for the second lap was 120 miles per hour.

\(\frac{1}{120}\) is less than \(\frac{1}{30}\) so we need to know the value of A to determine if \(\frac{1}{A}+\frac{1}{B}>\frac{1}{30}\)

2 is not sufficient

Answer is (A)

nick1816 can you verify the OA and post a solution?
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 04 Jul 2020, 13:50
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firas92 bhai tere answer galat nhi hote ;) IMO it should be A too.

Suppose length of 1 lap= D
Time taken to complete first lap =x
Time taken to complete second lap =y

Average speed of 2 laps = \(\frac{2D}{x+y}\)

\(0< \frac{2D}{x+y}< 2(\frac{D}{x})\).......since y>0

or

\(0< \frac{2D}{x+y}< 2(\frac{D}{y})\).......since x>0


Statement 1- Average speed of Jeff for the 2 laps < 2*20 <60

sufficient

Statement 2- Average speed of Jeff for the 2 laps < 2*120

Hence it can can be less than 60 or can be greater than 60.

Insufficient
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 05 Jul 2020, 01:31
ccooley Bunuel yashikaaggarwal could you please provide with the final OA and OE?
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Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 05 Jul 2020, 03:03
GMATinsight wrote:
clueless20 wrote:
Jeff drove two laps around a track. Was his average speed less than 60 miles per hour for the two laps?

1) Jeff's average speed for the first lap was 20 miles per hour.
2) Jeff's average speed for the second lap was 120 miles per hour.


CONCEPT: The average speed is always Greater than half of two speeds given and Less than twice the two speeds

Therefore Statement 2 will be sufficient

Statement 1 is also SUFFICIENT because with one speed 20 average speed has to be less than 40
Average speed \(= \frac{2*20*b}{(20+b)} = \frac{40b}{20+b}\)

Answer: Option D


I think you mean: The average speed is always LESS than half of two speeds.

Also I think you mean: Less than twice the lowest speed.

Also, it is must be mentioned that the above rule is a special case when distance is the same.

Example:

D =100 S1=2, t1=50 & S2=5, t2=20

Average speed = 200/70 = 2.85 which less than average of 2 speeds and less than twice the lowest speed.

Can you elaborate?
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 05 Jul 2020, 04:51
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Well I solved it like this,

Distance of one lap = D
Let Time taken at first lap = T1 , Speed = X
Time taken at second lap = T2 , Speed = Y

Average Speed = Total Distance/Total time taken.
As = 2D/ T1+T2
Also, T1=D/X and T2 = D/Y

As = 2D*XY/D(X+Y)
As = 2XY/X+Y

To find : 2XY/X+Y < 60

Statement 1: X = 20
2*20*Y/20+Y
Let,
Case 1: 2XY/X+Y > 60
40Y/20+Y > 60
40Y > 1200+60Y
-1200 > 20Y
Y < -60 (not possible)

Case 2: 2XY/X+Y = 60
40Y/20+Y = 60
40Y = 1200+60Y
-1200 = 20Y
Y = -60 (not possible)

Case 3: 2XY/X+Y < 60
40Y/20+Y < 60
40Y < 1200+60Y
-1200 < 20Y
Y > -60 (possible) {any possible value greater than zero of Y will never make an average greater than 60} , {because speed can't be negative unlike other two cases}

(Sufficient)

Statement 2: Y = 120
2*120*X/20+X
Let,
Case 1: 2XY/X+Y > 60
240X/120+X > 60
240X > 7200+60X
180X > 7200
X > 40

Case 2: 2XY/X+Y = 60
240X/120+X = 60
240X = 7200+60X
180X = 7200
X = 40

Case 3: 2XY/X+Y < 60
240X/120+X < 60
240X < 7200+60X
180X < 7200
X < 40
{infinite many Values possible, hence insufficient}

Answer is A.

momen Kritisood I hope this will be helpful.

Posted from my mobile device
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 06 Jul 2020, 21:09
nick1816 wrote:
firas92 bhai tere answer galat nhi hote ;) IMO it should be A too.

Suppose length of 1 lap= D
Time taken to complete first lap =x
Time taken to complete second lap =y

Average speed of 2 laps = \(\frac{2D}{x+y}\)

\(0< \frac{2D}{x+y}< 2(\frac{D}{x})\).......since y>0

or

\(0< \frac{2D}{x+y}< 2(\frac{D}{y})\).......since x>0


Statement 1- Average speed of Jeff for the 2 laps < 2*20 <60

sufficient

Statement 2- Average speed of Jeff for the 2 laps < 2*120

Hence it can can be less than 60 or can be greater than 60.

Insufficient


nick, to summarise have you used the following understanding: Maximum average speed cannot be more than or equal to twice the lower speed ?
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 07 Jul 2020, 13:41
Hi,

The question is to verify whether the average speed is less than 60 miles per hour or not.
We can see very beautiful numbers out there 20 miles per hour, 60 miles per hour and 120 miles per hour.
So for the convenience of this problem i will consider 120 miles is the distance covered in one lap.
So 2 lapse will account for 240 miles.
Average speed = Total dist/Total time
We know average speed limit = 60mph
Therefore total time = 240/6= 4 hours. This means for a avg speed of 60 miles per hour the body should move 240miles in 4 hours

Statement 1: 20 miles per hour in one lap
Now if we consider the time taken alone in this lap= 120/20= 6hours.
So minimum is 6 hours so we can not achieve avg speed of 60mph because minimum time is 6hours and above
So this statement alone is sufficient

Statement 2: 120mph in 2nd lap
Tim taken = 120/120 =1 hour
Now since we do not know the speed of other lap we cant conclude the total time is less than 4 hours or more than 4 hours.
This statement alone is not sufficient.

Answer A.

Please hit the kudos button if you like this approach
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 07 Jul 2020, 14:18
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Kritisood

That's exactly what you can inferred from my solution. If distance covered in the 2 trips is equal, maximum average speed cannot be more than or equal to twice the lower speed.
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Re: Jeff drove two laps around a track. Was his average speed less than 60  [#permalink]

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New post 07 Jul 2020, 18:13
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Kritisood wrote:
nick1816 wrote:
firas92 bhai tere answer galat nhi hote ;) IMO it should be A too.

Suppose length of 1 lap= D
Time taken to complete first lap =x
Time taken to complete second lap =y

Average speed of 2 laps = \(\frac{2D}{x+y}\)

\(0< \frac{2D}{x+y}< 2(\frac{D}{x})\).......since y>0

or

\(0< \frac{2D}{x+y}< 2(\frac{D}{y})\).......since x>0


Statement 1- Average speed of Jeff for the 2 laps < 2*20 <60

sufficient

Statement 2- Average speed of Jeff for the 2 laps < 2*120

Hence it can can be less than 60 or can be greater than 60.

Insufficient


nick, to summarise have you used the following understanding: Maximum average speed cannot be more than or equal to twice the lower speed ?


I hope you find this link useful by one of the best instructors.
https://www.beatthegmat.com/reiko-drove ... 06985.html
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Re: Jeff drove two laps around a track. Was his average speed less than 60   [#permalink] 07 Jul 2020, 18:13

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