# Logical

The fitness school marathon attracted 16 entrants this year. Each of the five houses entered a team of three runners and field was made up by sports master, Alamkhir, who is the sixteenth runner. The school houses were competing for trophy. The nu…

The fitness school marathon attracted 16 entrants this year. Each of the five houses entered a team of three runners and field was made up by sports master, Alamkhir, who is the sixteenth runner. The school houses were competing for trophy. The number number of points by each entrant would be equals to his finishing position. The five houses tied for the cup, their totals being equal, although no two competitors tied for the same position. In order to determine the order in which houses should keep the trophy for 73 days each in year, they multiplied the finishers positions together in each house. The house with the smallest product, Black, would hold the trophy first and so on to the house with the largest product, Blue who held it last. But per chance Green and White houses still tied, and had to be separated by toss of the coin.

Mr Alamkhir later noted that no house had two finishers in consecutive positions although green house would have achieved this had Mr Alamkhir himself not managed to get between two of the runners in race...

ques1) the possible position of Mr alamkhir is
a) 1 only
b) 6 only
c) 11 only
d) 6 or 11

ques2) the possible positions of white house are
a) 4,6,15
b)3,10,12
c)3,5,12
d)6,11,16

ques3) the product of black house is
a) 136
b) 360
c) 120
d)128

ques 4)which of the following is a possible combination of the red, the second house?
a)2,11,16
b)2,9,14
c)5,11,15
d)1,4,18

The fitness school marathon attracted 16 entrants this year. Each of the five houses entered a team of three runners and field was made up by sports master, Alamkhir, who is the sixteenth runner. The school houses were competing for trophy. The number number of points by each entrant would be equals to his finishing position. The five houses tied for the cup, their totals being equal, although no two competitors tied for the same position. In order to determine the order in which houses should keep the trophy for 73 days each in year, they multiplied the finishers positions together in each house. The house with the smallest product, Black, would hold the trophy first and so on to the house with the largest product, Blue who held it last. But per chance Green and White houses still tied, and had to be separated by toss of the coin.

Mr Alamkhir later noted that no house had two finishers in consecutive positions although green house would have achieved this had Mr Alamkhir himself not managed to get between two of the runners in race...

ques1) the possible position of Mr alamkhir is
a) 1 only
b) 6 only
c) 11 only
d) 6 or 11

ques2) the possible positions of white house are
a) 4,6,15
b)3,10,12
c)3,5,12
d)6,11,16

ques3) the product of black house is
a) 136
b) 360
c) 120
d)128

ques 4)which of the following is a possible combination of the red, the second house?
a)2,11,16
b)2,9,14
c)5,11,15
d)1,4,18

a good question.. did by trial n error only.. took quite some time..

1. c) 11 only..
2. a) 4,6,15
3. d) 128..
4. b) 2,9,14..

excellent work @ash i will be highly thankful if you could throw some light on your approach....

rahulsharma3154 Says
excellent work @ash i will be highly thankful if you could throw some light on your approach....

add all numbers from 1 to 16 which gives 136 as the sum.. now since the players are divided into 5 teams of 3 players each. the sum should be divisible by 5.. so the sixteenth player should be 1st or 6th or 11th..
if he is 1st then the total of 1 team will be (135/5)=27.. if 6th then 26.. else 25..
try and arrange all ranks giving the sum as 27 first.. if its possible.. then check their product.. two of them should come same.. if not so.. try with sum as 26...

little time consuming but its a matter of 4 ques.. and it didnt took me that long also..

the answer will come with the 16th player coming 11th.. also to select between green and white (the one with same products) you have to check the condition that green would have two consecutive ranks if the sixteenth player would not have been there.. so it has 10th and 12th rank..

try with these conditions you will get the answer.. hope it helps..