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

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

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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 a headstart of <1.3*2*60 = 156 m
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
Sue had a headstart of 2 mins or <156m
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

Distance to cover during the competition = 750 meter
Mary gives Sue a head start of 2 minutes = 120 seconds

(1) Mary swims at a constant rate greater than 1.5 meters per second
Thus, the maximum time taken by Mary to complete the distance = \(\frac{750}{1.5}\) seconds = 500 seconds
Therefore, Mary will complete the distance in < 500 seconds -> (a)

We do not know how long Sue will take to complete the same course.

Not Sufficient.


(2) Sue swims at a constant rate less than 1.3 meters per second
Thus, in 2 minutes head start, Sue will cover a maximum distance of 1.3 * 120 meters = 156 meters
Minimum Distance left for Sue to cover when Mary begins swimming = 750 – 156 meters = 594 meters
Minimum time taken by Sue to complete the distance when Mary begins = 594 / 1.3 seconds = 456.9 seconds
Therefore, Sue will take > 456.9 seconds to swim the distance as Mary begins. -> (b)

We do not know how long Mary will take to complete.

Not Sufficient.


(1) + (2)
From (a)
Time taken by Mary < 500 seconds
From (b)
Time taken by Sue > 456.9 seconds
So depending on the inequality values, Mary can complete the distance before or after Sue.

Not Sufficient.

Answer E

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.

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

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
_________________

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, - not sufficient because we do not know rate of Sue
(2) Sue swims at a constant rate less than 1.3 meters per second - not sufficient because we do not know rate of Mary

Combined still not sufficient because if we assume that Mary swims at rate of 1.6 meters per second, then she can swim 750 meters in 467 seconds. If we assume Sue swims at a rate of 1.3 ( a little less but for sake of rounding, we will assume 1.3) meters per second, then she will need 580 (approx) seconds to swim, but since she was given a head start, she will just need 460 (580-120) seconds. So Mary will be behind. But if Mary swims at rate of 2 meters per second, she will reach end in 375 seconds, thus making her winner. We have two different choices. Hence, E

IMO-E

Sue 2 min ahead of Mary.

(1) Mary swims at a constant rate greater than 1.5 meters per second
Let Speed of Mary = x + 1.5 m/s
No information about Sue speed.
Not sufficient

(2) Sue swims at a constant rate less than 1.3 meters per second
Sue= 1.3 - y m/s
No information about Mary speed.
Not sufficient

Together---
Speed of Mary = x + 1.5 m/s
Sue= 1.3 - y m/s

Limiting case - Let Mary= 1.5 m/s & Sue=1.3 m/s
Mary time = 750/1.5= 500 s & Sue= (750-120*1.3)/1.3=456 s
So Mary will not be able to overtake.

Case 2- Mary=1.4999m/s & Sue=1 m/s
then Mary time=500s & Sue=630s
So Mary overtake Sue

Not Sufficient

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?


Race starts at 0 seconds.
Mary starts at 120 seconds to give headstart to sue



(1) Mary swims at a constant rate greater than 1.5 meters per second
INSUFFICIENT - no info about Sues speed


(2) Sue swims at a constant rate less than 1.3 meters per second
INSUFFICIENT - no info about Mary's speed


(1)&(2)
Mary's minimum speed is > 1.5m/s

So Mary will take MAXIMUM 750/1.5 seconds to reach finish

Mary will take MAX 500 seconds to cover distance.

Mary starts late by 120 seconds, so she will reach finish line BEFORE 620 seconds.



Sues max speed is < 1.3m/s

So Sue will take MINIMUM 750/1.3 seconds to reach finish

=approx 576 seconds

So Sue will reach finish line AFTER 576 seconds.



So, it is possible that sue reaches at 700 (which is after 576) and mary reaches at 600 (before 620).... Mary Overtakes Sue

It is also possible that sue reaches at 600 and mary reaches at 605.... Mary does not overtake sue.

(1)&(2) Both ARE INSUFFICIENT



Answer - E - NONE IS SUFFICIENT

Statement 1- Mary speed>1.5m/s
We have no clue about Sue speed
Insufficient

Statement 2- Sue speed<1.3m/s
We have no clue about Mary speed
Insufficient

Combining 2 equations
1. If sue speed= 1.299999 and Mary speed= 1.500000001
Relative distance= 1.3*120= 156m
Relative speed= 0.2
Minimum distance Mary has to cover to overtake Sue= 156*1.5/0.2 >750
No

2. If sue speed is very large number, let say 10000, then it doesn't matter what speed sue has, Mary will overtake her.

Insufficient

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?

From (1) Mary swims at a constant rate greater than 1.5 meters per second

we get that the range of time is 750/1.5 (Max value of time) = 500
and we can assume a Min value =1 (when speed is 750 m/s)

So range of time for Mary is 1<=T1<=500, and since we do not know anything about Sue, (1) is insufficient.

From (2) Sue swims at a constant rate less than 1.3 meters per second

we get that the range of time is 750/1.3 (Minimum value) = 576 but since it has 2 minute headstart we can assume that Minimum value is 576 - 120 = 456 and we can assume a Maximum value of 1000 - 120 =880(when speed is 0.75 m/s)

So range of time for Sue is 456 <= T2<= 880 and sinde we do not know anything about Sue, (2) is insufficient.

From (1) and (2), also ranges are not sufficient to get an anwser, so (E) is the answer
_________________

Without going into complicated calculation, it is already clear that neither statements on their own sufficient. Combining, we get that Mary swims at least 1.5000000000001 m per second or she can swim 750/1.50000001=500 seconds will take her to swim. Sue can swim at max 1.299999 m per second or 750/1.29999=577 seconds. Since Sue is given a head start of 2 mins, she will reach the end in 577-120=457 sec. In this case, Mary will not catch Sue. But if Mary swims 50 meters per second or 750/50=15 seconds, Mary will win

distance (d) = 700
Sue had 2 mins of head start, it means, by the time Mary started, Sue would have completed a distance of = 2mins x Speed of Sue.
We need to find out whether Mary over takes Sue in this race ?

1) Speed of Mary > 1.5 meters per second (mts), not sufficient, because we don't know the speed of Sue
2) Speed of Sue < 1.3 meters per second (mts), not sufficient, because we don't know the speed of Mary

(1) & (2) --> when Mary is about to start, Sue would have already completed a distance of 2 mins x speed of Sue --> 2x60 (sec)x(<1.3) = (<156 meters), so if Sue continues at a constant rate less than 1.3 mts from this point and Mary continues at a constant rate >1.5 mts, they will meet only around 13 mins after --> 1.5t = 156+1.3t --> t = 13 mins, however, by this time, the race would have completed because race distance is only 700 meters. No, Mary would not over take Sue.

if Mary's speed is 2.0 mts and Sue's is 1.0 mts, then they would meet after 2 mins --> 2.0t = 120 (=1.0x 2minutes - head start) + 1.0t --> t = 2 mins. By this time, both are still within the race distance (700). Yes, Mary would over take Sue.

So, answer is E

IMG_20190712_115429.jpg

IMO-E


(1) Mary swims at a constant rate greater than 1.5 meters per second
Let Speed of Mary = x + 1.5 m/s
No information about Sue speed.
Not sufficient

(2) Sue swims at a constant rate less than 1.3 meters per second
Sue= 1.3 - y m/s
No information about Mary speed.
Not sufficient

Together---
Speed of Mary = x + 1.5 m/s
Sue= 1.3 - y m/s

Let Mary= 1.5 m/s & Sue=1.3 m/s
Mary time = 750/1.5= 500 s & Sue= (750-120*1.3)/1.3=456 s
So Mary will not be able to overtake.

Mary=1.4999m/s & Sue=1 m/s
then Mary time=500s & Sue=630s
So Mary overtake Sue

Not Sufficient

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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?


condition (1) Mary swims at a constant rate greater than 1.5 meters per second mary takes 750/1.5 = 500 or more sec, with 120 sec headstart it takes 620 or less sec . only one variable given so clearly insuficient
condition (2) Sue swims at a constant rate less than 1.3 meters per second sue takes 750/1.3 = 577 or more sec,.only one variable given so clearly insuficient

combined together

mary if speed is slightly more than 1.5m/s then 620 sec and sue takes 577 sec so she wont overtake

but if speed of mary is very high say 75 m/s ( haha with such speed , a light or sound has to swim) then it takes hardly 130 sec and sue 577 mary will overtake .

so both yes and no . so insufficient combined together

ans is E

Statement 1: \(S_M\)>1.5
If \(S_M=2\) and \(S_S=0.5\), Mary will overtake.
But if If \(S_M=2\) and \(S_S=3\), Mary will not.
So, not sufficient.

Statement 2: \(S_S\)<1.3
If \(S_M=2\) and \(S_S=0.5\), Mary will overtake.
But if If \(S_M=0.2\) and \(S_S=0.5\), Mary will not.
So, not sufficient.

Combining Statements 1 & 2
\(S_M\)>1.5 and \(S_S\)<1.3
Substituting these limiting values (\(S_M\)=1.5 and \(S_S\)=1.3), we find that distance travelled by Sue in the first 2 mins is 1.3x120=156 m and that by Mary is 0.
Mary starts after this 2 mins period.
So, time taken by Sue for completing the rest of the race \(T_S\) = (750-156)/1.3 = 495 s
Time taken by Mary to complete the race \(T_M\) = 750/1.5=500 s

But we know that \(T_M\)<500 s and \(T_S\)>495 s
If speed is such that \(T_M\)=498 s and \(T_S\)=496 s, Mary will not overtake.
If speed is such that \(T_M\)=490 s and \(T_S\)=500 s, Mary will overtake.

Hence, both statements are insufficient and (E) is the answer.

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
--> Swimming speed of Mary (Vm) > 1.5 m/s = 90 km/min.
(1) is NOT SUFFICIENT, because we don't know the swimming speed of Sue


(2) Sue swims at a constant rate less than 1.3 meters per second
--> Swimming speed of Sue (Vs) < 1.3 m/s = 78 km/min.
(2) is NOT SUFFICIENT, because we don't know the swimming speed of Mary


Combining both statements
CASE NO. 1: Assuming Mary swims at min. constant rate (~90 km/min) and Sue at max. constant rate (~78 km/min),
- Time (from the start) when Sue and Mary meets: 90 km/min * (t-2min) = 78 km/min * t ---> t = 15 mins
- Distance (from the start) when Sue and Mary meets: 90 km/min * (15-2min) = 1170 m > 750 m
- In Case no. 1, Mary will not overtake Sue for 750-m race for considered swimming speed.

CASE NO. 2: Assuming Mary swims at min. constant rate (~90 km/min) and Sue at ~54 km/min ,
- Time (from the start) when Sue and Mary meets: 90 km/min * (t-2min) = 54 km/min * t ---> t = 5 mins
- Distance (from the start) when Sue and Mary meets: 90 km/min * (5-2min) = 270 m << 750 m
- In Case no. 2, Mary will overtake Sue for 750-m race for considered swimming speed.

Even if we consider both statements, we will not be able to determine whether Mary will overtake Sue.


Correct answer is (E)

Speed of Mary= \(S_M\)
Speed of Sue=\(S_S\)
Time taken by Mary=\(t_M\)
Time taken by Sue=\(t_S\)
Also, \(t_S\)=\(t_M\) +120 ---> Given

If Mary over takes Sue then \(S_M\)*\(t_M\)=\(S_S\) *\(t_M\) <750, i,e, the point at which they meet, the distance from the starting line will be less than 750.
If not, then \(S_M\)*\(t_M\)=\(S_S\) *\(t_S\) \(\geq {750}\)



(1) Mary swims at a constant rate greater than 1.5 meters per second ---> \(S_M\)>1.5 m/s ---> Not sufficient
(2) Sue swims at a constant rate less than 1.3 meters per second---->\(S_S\)<1.3 m/s -----> Not Sufficient

(1)+(2)
Lets consider the limiting values for time being for speeds. \(S_M\)=1.5 \(S_S\)=1.3

1.5 * \(t_M\) =1.3* (\(t_M\) +120)
\(t_M\) = 780
d= \(S_M\)*\(t_M\)= 1.5* 780 =1170 m, This means they don't meet before 750 m => Mary doesnt over take Sue.

But, if \(S_M\)=1.6 \(S_S\)=1.2
1.6* \(t_M\) =1.2* (\(t_M\) +120)
\(t_M\) = 360
d= \(S_M\)*\(t_M\)= 1.6* 360= 576 m,This means they meet at a distance of 576 m from starting line => Mary does over take Sue.

Both outcomes possible, both (1) and (2) together also not sufficient.

Hence, Ans: E