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Retired Moderator P
Joined: 22 Aug 2013
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Maria drove a distance without stopping such that she covered first  [#permalink]

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26 00:00

Difficulty:   95% (hard)

Question Stats: 28% (03:16) correct 72% (03:00) wrong based on 277 sessions

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Maria drove a distance without stopping such that she covered first 1/3 of distance in 3 hours and remaining distance in 4 hours. Sarah drove the same distance without stopping such that she drove for first 1/3 of total time at a speed of 60 mph and for remaining time at a speed of 45 mph. What is the total distance that each of them has covered?

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.
Senior Manager  V
Joined: 22 Feb 2018
Posts: 415
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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amanvermagmat wrote:
Maria drove a distance without stopping such that she covered first 1/3 of distance in 3 hours and remaining distance in 4 hours. Sarah drove the same distance without stopping such that she drove for first 1/3 of total time at a speed of 60 mph and for remaining time at a speed of 45 mph. What is the total distance that each of them has covered?

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.

amanvermagmat

I have doubt about the statement 2.

Let $$Av_{Maria}$$ be the Average speed of Maria and $$Av_{Sarah}$$ be the average speed of Sarah

Does Statement 2 means
$$|Av_{Maria}- Av_{Sarah}| = 10$$ or $$Av_{Maria}- Av_{Sarah} = 10$$

Quote:
In the following cases, order is important:
‘ quotient/ ratio of ’ construction If a problems says ‘the ratio of x and y’, it means ‘x divided by y’ NOT 'y divided by x'
‘ difference between/of ’ construction If the problem says ‘the difference of x and y’ it means ‘x – y’

Source: GMAT Club Math Book, Page: 34

According to GC Math Book,Statement 2 means $$Av_{Maria}- Av_{Sarah} = 10$$
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Intern  B
Joined: 27 Jun 2018
Posts: 1
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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2
1
How C is the correct answer. B is sufficient to solve
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1417
Location: India
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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Princ wrote:
amanvermagmat wrote:
Maria drove a distance without stopping such that she covered first 1/3 of distance in 3 hours and remaining distance in 4 hours. Sarah drove the same distance without stopping such that she drove for first 1/3 of total time at a speed of 60 mph and for remaining time at a speed of 45 mph. What is the total distance that each of them has covered?

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.

amanvermagmat

I have doubt about the statement 2.

Let $$Av_{Maria}$$ be the Average speed of Maria and $$Av_{Sarah}$$ be the average speed of Sarah

Does Statement 2 means
$$|Av_{Maria}- Av_{Sarah}| = 10$$ or $$Av_{Maria}- Av_{Sarah} = 10$$

Quote:
In the following cases, order is important:
‘ quotient/ ratio of ’ construction If a problems says ‘the ratio of x and y’, it means ‘x divided by y’ NOT 'y divided by x'
‘ difference between/of ’ construction If the problem says ‘the difference of x and y’ it means ‘x – y’

Source: GMAT Club Math Book, Page: 34

According to GC Math Book,Statement 2 means $$Av_{Maria}- Av_{Sarah} = 10$$

Hello Princ

Sorry for late reply. But as per my understanding, 'difference between x and y' could mean either x-y or y-x, we cant say what unless something else is also mentioned.
Intern  B
Joined: 05 Jul 2017
Posts: 25
Maria drove a distance without stopping such that she covered first  [#permalink]

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HI @Experts, Could you please provide a solution for this question?
Intern  B
Joined: 21 May 2018
Posts: 2
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1
Let's assume 'X' to be the total distance covered by both of them.
The question says that Maria covered X/3 in 4h and the remaining 2X/3 in 4h. Hence, the total time Tm = 7h and average speed Sm = X/7.
Next, Sarah covered X/3 with 60mph(in t1 time) and remaining 2X/3 with 40mph(in t2 time). So total time, T= t1+t2
=> {X/3}/60 + {2X/3}/40 = X/180 + X/60 = X/45.
(1) Statement 1 says Sarah covered X in lesser time than Maria. So x/45 < 7 => X < 315. NOT SUFFICIENT!

(2) Statement 2 says Ss - Sm = 10. Average speed = Total Distance, X/Total Time, T.
Ss = X/(X/45) => 45
Sm = X/7
Hence, 45 - X/7 = 10
315 - X = 70
X = 245.
SUFFICIENT!
Please correct me if I'm wrong Manager  G
Joined: 28 Jul 2016
Posts: 130
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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1
arj93pop wrote:
Let's assume 'X' to be the total distance covered by both of them.
The question says that Maria covered X/3 in 4h and the remaining 2X/3 in 4h. Hence, the total time Tm = 7h and average speed Sm = X/7.
Next, Sarah covered X/3 with 60mph(in t1 time) and remaining 2X/3 with 40mph(in t2 time). So total time, T= t1+t2
=> {X/3}/60 + {2X/3}/40 = X/180 + X/60 = X/45.
(1) Statement 1 says Sarah covered X in lesser time than Maria. So x/45 < 7 => X < 315. NOT SUFFICIENT!

(2) Statement 2 says Ss - Sm = 10. Average speed = Total Distance, X/Total Time, T.
Ss = X/(X/45) => 45
Sm = X/7
Hence, 45 - X/7 = 10
315 - X = 70
X = 245.
SUFFICIENT!
Please correct me if I'm wrong You are wrong here: (2) Statement 2 says Ss - Sm = 10.
Actually statement 2 says that |Ss - Sm| = 10
so it could be 10 or -10
Intern  B
Joined: 05 Jul 2017
Posts: 25
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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LeonidK wrote:
arj93pop wrote:
Let's assume 'X' to be the total distance covered by both of them.
The question says that Maria covered X/3 in 4h and the remaining 2X/3 in 4h. Hence, the total time Tm = 7h and average speed Sm = X/7.
Next, Sarah covered X/3 with 60mph(in t1 time) and remaining 2X/3 with 40mph(in t2 time). So total time, T= t1+t2
=> {X/3}/60 + {2X/3}/40 = X/180 + X/60 = X/45.
(1) Statement 1 says Sarah covered X in lesser time than Maria. So x/45 < 7 => X < 315. NOT SUFFICIENT!

(2) Statement 2 says Ss - Sm = 10. Average speed = Total Distance, X/Total Time, T.
Ss = X/(X/45) => 45
Sm = X/7
Hence, 45 - X/7 = 10
315 - X = 70
X = 245.
SUFFICIENT!
Please correct me if I'm wrong You are wrong here: (2) Statement 2 says Ss - Sm = 10.
Actually statement 2 says that |Ss - Sm| = 10
so it could be 10 or -10

The question says, Sarash covered first 1/3 of time in 60 m/h speed. This doesn't mean 1/3 of the total distance, but what it means is 1/3 of the total time that Sarah spent on the road she drove for 60 m/h and rest 2/3 time that she spent on road for 45 m/h. All the difficulty in this problem lies in this portion only.
Intern  B
Joined: 21 Jan 2018
Posts: 10
Maria drove a distance without stopping such that she covered first  [#permalink]

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amanvermagmat wrote:
Maria drove a distance without stopping such that she covered first 1/3 of distance in 3 hours and remaining distance in 4 hours. Sarah drove the same distance without stopping such that she drove for first 1/3 of total time at a speed of 60 mph and for remaining time at a speed of 45 mph. What is the total distance that each of them has covered?

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.

Let the Total distance Travel by both of them is D miles.

For Maria: (D/3)=S * 3 & (2D/3)=S' * 4
For Sarah: D'=(T/3) * 60 & D"=(2T/3) * 45..... We get D'+D"=D=50T

Statement 1: Time by Sarah < Time by Maria
(D/50) < 7
D < 350 Miles Not Sufficient
Statement 2: Here there are 2 cases:
Case 1: M=S+10
(D/7)=(D/T)+10
(D/7)= 50+10........D=420 Miles
Case 2: M=S-10
(D/7)=(D/T)-10
(D/7)= 50-10........D=280 Miles
Not sufficient.
Both Statement 1 & 2

We get D=280 Miles.

Kindly give me kudos, if u like the post.

Originally posted by sahuiitd on 08 Dec 2018, 04:48.
Last edited by sahuiitd on 09 Dec 2018, 09:35, edited 1 time in total.
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GMAT 1: 420 Q26 V13 GMAT 2: 540 Q44 V21 Maria drove a distance without stopping such that she covered first  [#permalink]

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amanvermagmat wrote:
Maria drove a distance without stopping such that she covered first 1/3 of distance in 3 hours and remaining distance in 4 hours. Sarah drove the same distance without stopping such that she drove for first 1/3 of total time at a speed of 60 mph and for remaining time at a speed of 45 mph. What is the total distance that each of them has covered?

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.

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Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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2
deddex,
Solution is as per sketch:
Attachments WhatsApp Image 2018-12-09 at 21.23.10.jpeg [ 124.32 KiB | Viewed 976 times ]

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Maria drove a distance without stopping such that she covered first  [#permalink]

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Hi prince

Difference between two numbers is always non negative
.

Thanks for pointing out the typo in the book. It will be revised.

Regards

Princ wrote:
amanvermagmat wrote:
Maria drove a distance without stopping such that she covered first 1/3 of distance in 3 hours and remaining distance in 4 hours. Sarah drove the same distance without stopping such that she drove for first 1/3 of total time at a speed of 60 mph and for remaining time at a speed of 45 mph. What is the total distance that each of them has covered?

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.

amanvermagmat

I have doubt about the statement 2.

Let $$Av_{Maria}$$ be the Average speed of Maria and $$Av_{Sarah}$$ be the average speed of Sarah

Does Statement 2 means
$$|Av_{Maria}- Av_{Sarah}| = 10$$ or $$Av_{Maria}- Av_{Sarah} = 10$$

Quote:
In the following cases, order is important:
‘ quotient/ ratio of ’ construction If a problems says ‘the ratio of x and y’, it means ‘x divided by y’ NOT 'y divided by x'
‘ difference between/of ’ construction If the problem says ‘the difference of x and y’ it means ‘x – y’

Source: GMAT Club Math Book, Page: 34

According to GC Math Book,Statement 2 means $$Av_{Maria}- Av_{Sarah} = 10$$

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_________________ Maria drove a distance without stopping such that she covered first   [#permalink] 10 Dec 2018, 04:40
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