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A group of 10 athletes was competing in a marathon race. If the range

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A group of 10 athletes was competing in a marathon race. If the range  [#permalink]

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New post 07 Nov 2019, 03:23
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A group of 10 athletes was competing in a marathon race. If the range of the distance run by the athletes was 10 kilometers, did the total distance run by the athletes exceed 200 kilometers?

(1) The distance covered by one of the athletes was more than 30 kilometers.

(2) The total distance covered by 5 athletes was 125 kilometers.


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A group of 10 athletes was competing in a marathon race. If the range  [#permalink]

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New post Updated on: 08 Nov 2019, 09:52
Bunuel wrote:
A group of 10 athletes was competing in a marathon race. If the range of the distance run by the athletes was 10 kilometers, did the total distance run by the athletes exceed 200 kilometers?

(1) The distance covered by one of the athletes was more than 30 kilometers.

(2) The total distance covered by 5 athletes was 125 kilometers.


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range = highest- lowest = 10 ; did the total distance run by the athletes exceed 200 kilometers

#1
The distance covered by one of the athletes was more than 30 kilometers.
so 31 and least speed - 21 ; (21*9)+30 ; 219 ; sufficient
#2
The total distance covered by 5 athletes was 125 kilometers.
125+ 5 other distance ; not know insuffieint
IMO A

Originally posted by Archit3110 on 07 Nov 2019, 12:08.
Last edited by Archit3110 on 08 Nov 2019, 09:52, edited 1 time in total.
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A group of 10 athletes was competing in a marathon race. If the range  [#permalink]

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New post 07 Nov 2019, 12:59
Statement 1-

Minm possible distance travelled by other athlete>20

Total distance travelled by all athlete>(30-10)*9+30= 210

Sufficient

STATEMENT 2-

total distance travelled >= 5*(25-15)+125=175

Insufficient

Archit3110 wrote:
Bunuel wrote:
A group of 10 athletes was competing in a marathon race. If the range of the distance run by the athletes was 10 kilometers, did the total distance run by the athletes exceed 200 kilometers?

(1) The distance covered by one of the athletes was more than 30 kilometers.

(2) The total distance covered by 5 athletes was 125 kilometers.


Are You Up For the Challenge: 700 Level Questions


range = highest- lowest
#1
The distance covered by one of the athletes was more than 30 kilometers.
other value distance not know insufficeint
#2
The total distance covered by 5 athletes was 125 kilometers.
125+ 5 other distance ; not know insuffieint
from 1 &2
30 is inclusive of 125 or not + balance 5/6 athlete distance not know insufficient
IMO E
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Re: A group of 10 athletes was competing in a marathon race. If the range  [#permalink]

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New post 08 Nov 2019, 09:57
nick1816
I misread and initially solved the question thinking that it had asked to find range ... :?
see the highlighted part it says one of them is >30 so the speed to be considered should be ; ( 21*9)+31 ; 219 sufficient


nick1816 wrote:
Statement 1-

Minm possible distance travelled by other athlete>20

Total distance travelled by all athlete>(30-10)*9+30= 210

Sufficient

STATEMENT 2-

total distance travelled >= 5*(25-15)+125=175

Insufficient

Archit3110 wrote:
Bunuel wrote:
A group of 10 athletes was competing in a marathon race. If the range of the distance run by the athletes was 10 kilometers, did the total distance run by the athletes exceed 200 kilometers?

(1) The distance covered by one of the athletes was more than 30 kilometers.

(2) The total distance covered by 5 athletes was 125 kilometers.


Are You Up For the Challenge: 700 Level Questions


range = highest- lowest
#1
The distance covered by one of the athletes was more than 30 kilometers.
other value distance not know insufficeint
#2
The total distance covered by 5 athletes was 125 kilometers.
125+ 5 other distance ; not know insuffieint
from 1 &2
30 is inclusive of 125 or not + balance 5/6 athlete distance not know insufficient
IMO E
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Re: A group of 10 athletes was competing in a marathon race. If the range  [#permalink]

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New post 08 Nov 2019, 10:33
Archit3110
That is why i used sign of 'greater than', not 'greater than or equal to'. Highlighted part is still incorrect; it doesn't affect the answer tho. You can't assume distance travelled by the athlete is an integral number. It's not given.


[quote="Archit3110"]nick1816
I misread and initially solved the question thinking that it had asked to find range ... :?
see the highlighted part it says one of them is >30 so the speed to be considered should be ; ( 21*9)+31 ; 219 sufficient
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A group of 10 athletes was competing in a marathon race. If the range  [#permalink]

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New post 08 Nov 2019, 10:59
Bunuel wrote:
A group of 10 athletes was competing in a marathon race. If the range of the distance run by the athletes was 10 kilometers, did the total distance run by the athletes exceed 200 kilometers?

(1) The distance covered by one of the athletes was more than 30 kilometers.

(2) The total distance covered by 5 athletes was 125 kilometers.


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Range of distance = 10
Total Distance run by 10 athletes > 200 ?

Statement 1)
Distance covered by one athlete > 30
Let's take minimum integer possible value for that = 31
So, possible least run distance by an athlete = 31 - 10 = 21
Total distance = 21*9 + 31 = 220

Hence, the more the value of distance covered by one athlete the more the total distance.

SUFFICIENT.

Statement 2)
Distance covered by 5 athletes = 125
Case - I:
Let the maximum distance covered possible by athletes is x.
x + 4(x - 10) = 125
5x = 165
x = 33

Now, lowest possible distance covered = 23
Total possible distance covered by 10 athletes = 125 + 23*5 = 240 YES
OR

Case - II:
Let y be minimum possible distance covered.
So, y + 4(y + 10) = 125
5y = 85
y = 17

Now, Since lowest possible distance is 17
Total possible distance covered by 10 athletes = 125 + 17 * 5 = 210 YES
OR
Total possible distance covered by 10 athletes = 125 + 17 * 5 = 210 YES

Case III:
Average distance covered by 5 athletes = 125 / 5 = 25
Thus least possible distance run by athlete = 25 - 10 = 15

So, Total possible distance covered by 10 athletes = 125 + 15 * 5 = 200 NO

ALTERNATIVELY:
Let x be the maximum possible distance covered by athlete so that any distance more than it would result in total distance greater than 200.
So, x + 9 * (x - 10) > 200
10x - 90 > 200
x > 29

Let y be the minimum possible distance covered by athlete so that any distance more than it would result in total distance greater than 200.
So, y + 9 * (y + 10) > 200
10y + 90 > 200
y > 11

As from Statement 1, x > 30 it is SUFFICIENT.

In Statement 2, the maximum and minimum are established leading to total distance greater than 200(refer first solution).
But, the average of 5 athletes = 25
leading to minimum possible distance of 15 for rest of the 5 athletes, consequently total distance of exactly 200.
INSUFFICIENT.

IMO Answer A.
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A group of 10 athletes was competing in a marathon race. If the range   [#permalink] 08 Nov 2019, 10:59
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