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On a fishing expedition, a group of 13 fishermen caught a total of 160

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On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish
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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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shasadou wrote:
On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish


Hi,
for 160 fish, the average catch is 160/13 that is 11 and half approx..

lets see the statements..
1) The fisherman who caught the third-most fish caught 11 fish.
for making the higher most catches the lowest posible, let everyone from thirdmost to lowest caught equal number of fishes, 11..
so the two topmost will catch= 160-11*11=39
39 will be caught by 2, which means atleast 1 caught>19
Suff

(2) The fisherman who caught the second-most fish caught 12 fish
same as (1), let all from second most to lowest catch equal number of fishes= 12*12=144
so the highest will catch 160-144=16 >15
Suff

D
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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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New post 27 Jun 2016, 11:18
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chetan2u wrote:
shasadou wrote:
On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish


Hi,
for 160 fish, the average catch is 160/13 that is 11 and half approx..

lets see the statements..
1) The fisherman who caught the third-most fish caught 11 fish.
for making the higher most catches the lowest posible, let everyone from thirdmost to lowest caught equal number of fishes, 11..
so the two topmost will catch= 160-11*11=39
39 will be caught by 2, which means atleast 1 caught>19
Suff

(2) The fisherman who caught the second-most fish caught 12 fish
same as (1), let all from second most to lowest catch equal number of fishes= 12*12=144
so the highest will catch 160-144=16 >15
Suff

D



Hi Chethan,

Thanks for the solution, but 160/13 is 12.3 , so we can approximate to 12 as average or any other reason to take 11 as avg ?

Please share your answer for the stat 1 and stat 2 considering 12 as avg.

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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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New post 11 Jul 2016, 18:58
Hi Chetan,
Can you please make me understand that how using Statement 1 how can we say say for sure that 39 fish will be caught by 2 different men. There can be a case where one catches 30 and other catches 9. In the question stem there's no such information :cry:

In statement 2 it tells that 2nd most guy caught 12 so now we can conclusively say that the only remaining guy caught >15. Please help me understand :(

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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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New post 24 Jul 2016, 07:26
shasadou wrote:
On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish



(1) The fisherman who caught the third-most fish caught 11 fish.

total fishermen = 13
since 11 is the third most , we need to minimise the first two
let first two be a and b
to minimise a and b
let all remaining 11 fishermen catch 11 fishes
fishes remaining for a and b = 160-(11*11)=39
now 39 can be divided as 27,12 this gives us minimum b and max a
or, 20,19, which gives us maximum b minimum a
thus the highest , a >12
sufficient

(2) The fisherman who caught the second-most fish caught 12 fish

again to minimise a
let all fishermen catch 12 fishes
therefore a = 160-(12*12) = 160-144=16
therefore sufficient

D

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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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New post 25 Jul 2016, 03:28
atreyaraja wrote:
Hi Chetan,
Can you please make me understand that how using Statement 1 how can we say say for sure that 39 fish will be caught by 2 different men. There can be a case where one catches 30 and other catches 9. In the question stem there's no such information :cry:

In statement 2 it tells that 2nd most guy caught 12 so now we can conclusively say that the only remaining guy caught >15. Please help me understand :(


The question asks Did any one fisherman catch more than 15 fish?
Statement 1 : if 2 fishermans catch total of minimum 39 fishes, then at least one of them will catch more than 15 fishes;
e.g 1,38 2,37 ..... 19,20, .... 38,1.
Sufficient


I hope it's clear to you now.

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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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shasadou wrote:
On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish



There were 13 fishermen and a total of 160 fish. One thing that immediately comes to mind is that many fishermen could have easily caught no fish. So it is certainly possible with either statement that the fisherman who caught maximum number of fish caught, say 100 fish. So more than 15 is certainly possible. What we now need to figure out is whether 15 or less for the fisherman who caught the most is also possible.

(1) The fisherman who caught the third-most fish caught 11 fish.

We need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 10, 10, 10, .... 10, 11, 14, 15
This adds up to only 140 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

(2) The fisherman who caught the second-most fish caught 12 fish.

Again, we need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 11, 11, 11, .... 11, 11, 12, 15
This adds up to only 148 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

Answer (D)
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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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New post 20 Sep 2016, 00:31
VeritasPrepKarishma wrote:
shasadou wrote:
On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish



There were 13 fishermen and a total of 160 fish. One thing that immediately comes to mind is that many fishermen could have easily caught no fish. So it is certainly possible with either statement that the fisherman who caught maximum number of fish caught, say 100 fish. So more than 15 is certainly possible. What we now need to figure out is whether 15 or less for the fisherman who caught the most is also possible.

(1) The fisherman who caught the third-most fish caught 11 fish.

We need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 10, 10, 10, .... 10, 11, 14, 15
This adds up to only 140 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

(2) The fisherman who caught the second-most fish caught 12 fish.

Again, we need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 11, 11, 11, .... 11, 11, 12, 15
This adds up to only 148 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

Answer (D)



Hi Karishma,

Any particular reason for deserting the following case:
1,1,1,1,1,1,1,1,1,1,12,X,X?

Regards,
Ravi

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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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email2vm wrote:
VeritasPrepKarishma wrote:
shasadou wrote:
On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish



There were 13 fishermen and a total of 160 fish. One thing that immediately comes to mind is that many fishermen could have easily caught no fish. So it is certainly possible with either statement that the fisherman who caught maximum number of fish caught, say 100 fish. So more than 15 is certainly possible. What we now need to figure out is whether 15 or less for the fisherman who caught the most is also possible.

(1) The fisherman who caught the third-most fish caught 11 fish.

We need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 10, 10, 10, .... 10, 11, 14, 15
This adds up to only 140 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

(2) The fisherman who caught the second-most fish caught 12 fish.

Again, we need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 11, 11, 11, .... 11, 11, 12, 15
This adds up to only 148 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

Answer (D)



Hi Karishma,

Any particular reason for deserting the following case:
1,1,1,1,1,1,1,1,1,1,12,X,X?

Regards,
Ravi


For which statement are you suggesting this case?

Stmnt 1: Here it will be 1,1,1,1,1,1,1,1,1,1,11,X,Y

Stmnt 2: Here it will be 1,1,1,1,1,1,1,1,1,1,1,12,Y

In both these cases, Y will certainly be more than 15 to get the sum up to 160.
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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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VeritasPrepKarishma wrote:
shasadou wrote:
On a fishing expedition, a group of 13 fishermen caught a total of 160 fish. \ Did any one fisherman catch more than 15 fish?

(1) The fisherman who caught the third-most fish caught 11 fish.

(2) The fisherman who caught the second-most fish caught 12 fish



There were 13 fishermen and a total of 160 fish. One thing that immediately comes to mind is that many fishermen could have easily caught no fish. So it is certainly possible with either statement that the fisherman who caught maximum number of fish caught, say 100 fish. So more than 15 is certainly possible. What we now need to figure out is whether 15 or less for the fisherman who caught the most is also possible.

(1) The fisherman who caught the third-most fish caught 11 fish.

We need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 10, 10, 10, .... 10, 11, 14, 15
This adds up to only 140 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

(2) The fisherman who caught the second-most fish caught 12 fish.

Again, we need to find the case in which the fisherman with most fish caught 15 or less. So other fishermen need to catch as many as they can.
Arranging in ascending order of number of fish caught: 11, 11, 11, .... 11, 11, 12, 15
This adds up to only 148 fish. So the fisherman with most fish MUST HAVE caught more than 15 fish.
Sufficient.

Answer (D)



For statement 1. The fisherman who caught the third-most fish caught 11 fish
Instead of 10, 10, 10, .... 10, 11, 14, 15
can it be 11,11,11, ... 11,11,14,15 , here there are 11 fishermen who caught 3rd-most highest fish
still it is less than 160 , but is it the better way?

thanks

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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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New post 29 Sep 2016, 13:29
Statement 1)

if the third most caught 11 lets just assume fishermen 1-11 caught 11 (to maximize this value)=121
That means fishermen 12 and 13 caught 139 between the two of them. If fisherman 12 caught 14 (maximize this value) then fisherman 13 caught 25. To see if a fisherman caught more than 15 we need to maximize the other values

Statemen 2)
Same approach of maximizing all other values
We'll assume fishermen 1-12 caught 12 fish=144
160-144=16
suff

D

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Re: On a fishing expedition, a group of 13 fishermen caught a total of 160 [#permalink]

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