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# If Mary and Sue enter a 750 meter swimming competition in which Mary g

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If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:00
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38% (02:03) correct 62% (02:03) wrong based on 274 sessions

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If Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart, will Mary overtake Sue over the course of the race?

(1) Mary swims at a constant rate greater than 1.5 meters per second
(2) Sue swims at a constant rate less than 1.3 meters per second

 This question was provided by Veritas Prep for the Game of Timers Competition

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If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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Updated on: 12 Jul 2019, 02:20
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If Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart, will Mary overtake Sue over the course of the race?

(1) Mary swims at a constant rate greater than 1.5 meters per second
(2) Sue swims at a constant rate less than 1.3 meters per second

Total distance = 750m. Mary's time = Sue's + 120sec

(1) Mary swims at a constant rate greater than 1.5 meters per second
If mary's speed = 1.5m/s, time taken would be 750/1.5 = 500s (max time)

This is not sufficient since we do not know about Sue's speed

(2) Sue swims at a constant rate less than 1.3 meters per second
If sue's speed = 1.3m/s, time taken = 750/1.3 = 576s (min time)
This is not sufficient since we do not know about Mary's speed

Combining both statements together, mary's time < 500, if speed = 2m/s, time = 375s
sue's time > 576, if speed = 1m/s, time = 750 s

In this scenario Mary will definitely overtake.

However, if mary's speed is close to 1.5, time slightly less than 500s
similarly if sue's speed is close to 1.3m/s, time taken is slightly more than 576s
The difference is < 120 sec
In this scenario Mary will not overtake.

Both statements together are not sufficient.
Option E

Posted from my mobile device

Originally posted by prashanths on 11 Jul 2019, 08:44.
Last edited by prashanths on 12 Jul 2019, 02:20, edited 1 time in total.
##### General Discussion
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:12

from 1: we do not know Sue's rate of swimming, so not suff
from 2: we do not know Mary's swimming rate so not suff
1+2, we know the max and min rates of Mary and Sue with which we can determine if they ever catch up, so C
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:14
because unless we know the speed of both participants we cannot tell that mary could overtake sue or not.
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If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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Updated on: 13 Jul 2019, 04:10
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If Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart, will Mary overtake Sue over the course of the race?

(1) Mary swims at a constant rate greater than 1.5 meters per second
(2) Sue swims at a constant rate less than 1.3 meters per second

Gevin P: Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart
Question Q: Will Mary overtake Sue over the course of the race?

Statement S1:
Mary swims at a constant rate greater than 1.5 meters per second
Mary will complete 750 m in less than 750/1.5 = 500 seconds
Mary will overtake Sue if she covers headstart distance before Sue reaches the end of the race or completes 750 m.
Since Sue's speed is not known
NOT SUFFICIENT

Statement S2:
(2) Sue swims at a constant rate less than 1.3 meters per second
Sue had to swim > 750 - 156 = 594 m before Mary complete 750m
Since Mary's speed is not known
NOT SUFFICIENT

Statement S1 & S2 together:
S1: Mary swims at a constant rate greater than 1.5 meters per second
S2: Sue swims at a constant rate less than 1.3 meters per second

Mary swims the entire distance of 750m in < 750/1.5 = 500 seconds
She swims the balance (>(700-156) or >594 m) in greater than 594/1.3 > 456.92 seconds

If Sue takes more than 500 seconds time to finish than Mary will definitely overtake her, otherwise it will depend on their actual speeds.
NOT SUFFICIENT.

IMO E

Originally posted by Kinshook on 11 Jul 2019, 08:28.
Last edited by Kinshook on 13 Jul 2019, 04:10, edited 3 times in total.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:33
1
(1) Mary swims at a constant rate greater than 1.5 meters per second - Insufficient, No information on Sue's speed
(2) Sue swims at a constant rate less than 1.3 meters per second - Insufficient, No information on Mary's speed
(3) Combined - if at the lowest net speed (Mary-sue) provides that Mary can overtake then sufficient else insufficient.
At lowest - Mary's will be 1.500000..1~1.5 and Sue's 1.2999999999~1.3.
So in 2 minutes Mary will be behind by distance covered by Sue - 1.3*120 = 156.
Net speed gained by Mary per minute is 0.2*60=12 meters/min
To cover 156 Meters Mary will require 13 minutes while sue will complete the race by 750/78~less than 10 minutes - So not enough for Mary to overtake Sue.

As per above logic on (3) - Insufficient IMO E
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:33
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1
E.

Clearly each statement alone is not sufficient since we need some idea about their relative velocity.

Now, for Mary to catch up before finishing line, lets assume RV is the relative velocity of Mary wrt Sue, so RV*2*60 < 750 (for catching up before finishing line) => RV < 6.25 m/s.

Now, from given statements, RV>1.5 - 1.3 = 0.2 m/s

So, RV may very well be more than 6.25 m/s in which case Mary wont catch up before finishing line or may catch up if RV < 6.25 m/s. So cant find out with certainty.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:35
1
If Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart, will Mary overtake Sue over the course of the race?

Before moving to the question stems, let's analyze the question.
Distance = speed *Time
Distance is 750m

Mary time = t
Sue = t-2

To figure out the answer we need the speed.

(1) Mary swims at a constant rate greater than 1.5 meters per second
This statement is insufficient as we don't know about sue's speed.

(2) Sue swims at a constant rate of fewer than 1.3 meters per second
This statement is insufficient as we don't know the speed of Mary.

Combining the statements: we see that Mary's speed is greater than 90 meters per minute.
Sue's speed is less than 78 meters per minute.

Given the scenario, we cannot tell if mary will overtake Sue. hence combining will be insufficient.

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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:36
1
This is the relative speed question. As both will swim in the same direction we need to find both individual speeds.
Distance = 750 m

1. Mary swims at a constant rate greater than 1.5 meters per second.
Mary speed > 1.5 m/s
but it does not give any idea about sue s speed.
Insufficient.

2. Sue swims at a constant rate of fewer than 1.3 meters per second
Sues speed < 1.3 m/s
but again we dont know about Mary speed.
Insufficient.

Combining both, we have can have a relative speed for both. As we can see also that there is difference between their speeds.
Let Marys speed = 2
and Sues speed = 1
Then the relative speed will be (2-1) m/s.
This is sufficient to answer the question. We dont need to calculate whether Mary will catch Sue or not.

Please hit kudos if you like the solution.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:38
1
A - speed greater than 1.5m/s . Since, there is no greater limit. It can go upto infinite and can be 1.6m/s nevertheless,we cannot get to the concerete answer.

B - on the same line as A. the speed can be almost 0 to 1.3m/s no info about the speed of A hence, inconclusive.

Combining A and B at the border take 1.5m/s at A's speed(90m/min) and 1.3m/s (78m/s)as B's speed.
In 2 minutes B would have travelled 156m
Distance = speed X Time
156 = (90-78) X time
Time = 13 min
In 13+2 min B would have travelled 15X78, which is greater than 750 m --> A will not catch B

if we choose the value of A as 20m/s then A will catch B
so, combining 1st and 2nd statement is inconclusive. Hence,E is the answer.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:38
(1) Speed of Mary > 1.5m/sec > 90m/min

Not sufficient

(2) Speed of Sue < 1.3 m/sec < 78m/min

Not sufficient

(1)+(2) If we consider speed of Mary to be 91 m/min and speed of Sue to be 77m/min

Mary will overtake Sue.

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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:39
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IMO correct ans is C - Explanation given as
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:41
1) Assume Rate of Mary=2.5 and Rate of Sue=1
In 2 mnute headstart, course covered by Sue=120m.
Race Course left to finish race for Sue=630m

Now time taken by Mary to catch Sue=120/2.5=48s
And in 48s Sue would have to still cover 630-48=582m to finish race. Sufficient.

2) Clearly not sufficient.

Hence IMO option A.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:43
1
Total distance = 750 m
Sue starts 2 mins before Mary =120 sec

A. Mary swims at a constant rate greater than 1.5 meters per second
This can be 1.51 or 1.6m/sec or greater than that
This doesn't help us as we don't know Sue's speed
Option A is insufficient

B. Sue swims at a constant rate less than 1.3 meters per second
This can be 1.29 m/s or 1.2 m/s or lesser than that.
This doesn't help us as we don't know Mary's speed
Option B is insufficient.

The answer can either be C or E

The difference between Mary and Sue's time should be >120 sec
If Mary's speed is 1.51 m/s and Sue is 1.29m/s then the time difference nearly equal to 85 sec - This case answer is No
If Mary's speed is 1.6 m/s and Sue is 1.2m/s then the time difference nearly equal to 157 sec - This case answer is Yes

So both options together is insufficient.

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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:48
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IMO : E

If Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart, will Mary overtake Sue over the course of the race?

(1) Mary swims at a constant rate greater than 1.5 meters per second
(2) Sue swims at a constant rate less than 1.3 meters per second

1)if mary swims at 1.5 m per second then she will take 500 seconds to finish.
but we dont know the speed for sue, so this is not sufficient

2)sue swims at less than 1.3 , lets assume 1.3 then she will take 750/1.3 =577 (aprox) seconds to finish.
we dont know the speed of Mary, so not sufficient.

C: from above it is known that Mary can out swim sue in the last 77 seconds but we know that sue already had 120 second head start. so she cannot out swim her at 1.5 m per second, but she might be able to if she swims 3 m per second. but we dont know what is here speed. and there is considerable scope to say that we cant say.

therefore E seems to be the best choice.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:49
1
If Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart, will Mary overtake Sue over the course of the race?

Ok, it is obvious that to solve this problem we have to know speeds od both Mary and sue
(1) Mary swims at a constant rate greater than 1.5 meters per second
Not sufficient. We have to know Sue's speed
(2) Sue swims at a constant rate less than 1.3 meters per second
Not sufficient. We have to know Mary's speed

Taking both statements together. Ok, here it becomes more interesting.
Let's take extremes.
Mary = something a little bit faster than 1,5 m/s
Sue = something a little bit slower than 1,3 m/s

1.3*120 + 1.3*t=1.5t
156=0.2t
t=780
they will meet in 780 sec after 2 min headstart
1,5*780=1170 meters.
So, the answer is no, Mary will not overtake Sue.

Let's take another example.
Mary= 3 m/s
Sue = 0,1 m/s

0.1*120 +0.1t=3t
12=2.9t
t=4.13
3*4.13=12

In this situation, Mary will definitely overtake Sue.

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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:51
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IMO E. [Both statements together are insufficient]

To know if Mary can over take Sue we need to know their respective speeds which are given through the statements. Hence, options A,B and D are eliminated.

Case 1: Mary's speed is 1.51 m/sec and Sue's speed is 1.29 m/secs.
In 2 minutes Sue would have covered 1.29 * 120 = 154.8 meters.
For Mary to overtake Sue it would take her 154.8 / (1.51-1.29 ) seconds = 703.636 seconds.
Hence, the total distance Sue would have travelled would be ( 703 + 120 ) * 1.29 = 1061 meters.
In this case, Mary will not be able to overtake Sue.

Case 2: Mary's speed be 5 m/sec and Sue's speed be 1m/sec.
In 2 minutes Sue would have covered 120 meters.
For Mary to overtake Sue it would take her 120 / (5-1 ) seconds = 30 seconds.
Hence, the total distance Sue would have travelled would be ( 120 + 30 ) * 1 = 150 meters.
In this case, Mary will be able to overtake Sue.

Hence, both statements together are insufficient to answer the question.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:51
2
total distance ; 750 mtrs
time of Mary ; t and Sue ; t+120
#1
Mary swims at a constant rate greater than 1.5 meters per second
but speed of Sue not given ; insufficient
#2
Sue swims at a constant rate less than 1.3 meters per second
speed of Mary not given ; insufficient
from 1 &2
from given info speed of mary is > than speed of sue , but with that we get both yes & no as supposedly if speed of Mary is 1.51 m/sec then time taken by Mary; would be beaten ; else when Mary is at speed 1.62 m/sec she would beat sue
IMO E

If Mary and Sue enter a 750 meter swimming competition in which Mary gives Sue a 2 minute headstart, will Mary overtake Sue over the course of the race?

(1) Mary swims at a constant rate greater than 1.5 meters per second
(2) Sue swims at a constant rate less than 1.3 meters per second
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If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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Updated on: 12 Jul 2019, 02:14
1
I am really cautious when statements say greater or lesser than, because that won't mean a certain number, but imply a range. Any number from the range may affect the result of the problem differently. Thus I understand that I need to check both polar opposites. What popped up first in my mind was C, but the answer shouldn’t be so easy because there is no fun in that.

1 - Case. It’s clear that neither statement itself is sufficient. Thus we will analyze both statements. We know that Sue has $$120$$ second headstart. Keeping this in mind, let’s check whether that headstart can ever help Sue to come first - if Mary swims as slow as possible while Sue swims as fast as possible.

Slowest rate of Mary $$\approx{1.5}$$ meter per second
Fastest rate of Sue $$\approx{1.3}$$ meter per second

Mary spends $$750/1.5=500$$ seconds to reach the finish
Sue spends $$750/1.3\approx{577}$$ seconds to reach the finish

So if they started at the same time Sue would come about $$77$$ seconds later than Mary. However, if Sue started $$120$$ seconds earlier than Mary, then Mary would come about $$43$$ seconds later than Sue. Thus Sue would have a chance to win.

2 – Case. If Mary swims at any speed greater than $$1.7$$ meter per second, then she will definitely be first. Using both statements we are still uncertain who will win. Thus both statements together are insufficient.

Hence E
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Originally posted by JonShukhrat on 11 Jul 2019, 08:55.
Last edited by JonShukhrat on 12 Jul 2019, 02:14, edited 2 times in total.
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Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g  [#permalink]

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11 Jul 2019, 08:58
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E - Took longer than it should, but still original thought C, I am still working on getting better at these problem types.

But my thought process:

1) Insufficient, do not know anything about Sue's rate of speed
2) Insufficient, do not know anything about Mary's rate of speed.

Combine the two:

Even using the extreme of 1.501, Mary would take ~8 mins and 20 seconds to swim the 750 meter distance. Have to convert the rates from second to minute.

Using 1.299 for sue, Sue would complete the 750 ~ 9 mins 40 seconds. However, Sue given a two minute head start would cover ~156 meters in two minutes leaving only 594 meters to finish. Sue would complete this distance in less than ~8 minutes. Mary would never catch here.

Scenario two: if Mary swam 5 meters per second and Sue .5 meters per second, Mary would catch her.
Re: If Mary and Sue enter a 750 meter swimming competition in which Mary g   [#permalink] 11 Jul 2019, 08:58

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