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

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DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
Maria drove a distance without stopping such that she covered first  [#permalink]

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18 Jul 2018, 00:43
15
00:00

Difficulty:

95% (hard)

Question Stats:

25% (02:39) correct 75% (02:55) wrong based on 177 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.
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Joined: 22 Feb 2018
Posts: 348
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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31 Jul 2018, 04:00
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
Joined: 27 Jun 2018
Posts: 1
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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06 Aug 2018, 14:56
2
1
How C is the correct answer. B is sufficient to solve
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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06 Aug 2018, 21:46
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
Joined: 05 Jul 2017
Posts: 27
Maria drove a distance without stopping such that she covered first  [#permalink]

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15 Aug 2018, 20:44
HI @Experts, Could you please provide a solution for this question?
Intern
Joined: 21 May 2018
Posts: 2
Maria drove a distance without stopping such that she covered first  [#permalink]

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17 Aug 2018, 00:30
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
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Joined: 28 Jul 2016
Posts: 135
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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17 Aug 2018, 13:24
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
Joined: 05 Jul 2017
Posts: 27
Re: Maria drove a distance without stopping such that she covered first  [#permalink]

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18 Aug 2018, 00:47
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.
Re: Maria drove a distance without stopping such that she covered first &nbs [#permalink] 18 Aug 2018, 00:47
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