Directions (Q7 to Q10): Answer the questions on the basis of the information given below.
A train stops at exactly six intermediate stations A, B, C, D, E and F, in that order, between its originating station and
destination station. At each of the intermediate stations, twice as many people get in as those that get down. The numbers
of people getting down at the intermediate stations are all prime numbers, one cach between 0 and 10, 10 and 20 and so on
up to between 50 and 60, in the order of the stations given above. The difference between the numbers of people getting in
at any two consecutive intermediate stations is at least 20. The total number of passengers getting down in all the
intermediate stations together is an even number. Also no person gets in and gets down at the same station.
7. Which of the following cannot be the number of people getting down at any intermediate station?
(c) 17
(d) 28
Answers
Given :-
- Trains stops at 6 intermediate stations .
- At each of the intermediate stations, twice as many people get in as those that get down.
- The numbers of people getting down at the intermediate stations are all prime numbers, one cach between 0 and 10, 10 and 20 and so on up to between 50 and 60 .
- The total number of passengers getting down in all the intermediate stations together is an even number.
- No person gets in and gets down at the same station.
Solution :-
Case 1 :- Trains stops at 6 intermediate stations .
conclusion :- we have to find 6 prime numbers .
case 2:- all prime numbers, one cach between 0 and 10, 10 and 20 and so on up to between 50 and 60 .
conclusion :- we have to find each prime number between 0-10 , 10-20, 20-30 , 30-40, 40-50, and 50-60 .
Case 3 :- The total number of passengers getting down in all the intermediate stations together is an even number.
conclusion :- As sum of all 6 prime numbers is even, so each of six prime numbers must be odd .
case 4 :- At each of the intermediate stations, twice as many people get in as those that get down.
conclusion :- We have to pick 6 prime numbers, one each from the given ranges such that difference between two consecutively selected prime numbers is at least 10.
Lets start from 1 - 10 :-
→ Prime Numbers from 1 - 10 = 2,3,5,7
2 is an even number so not possible.
Lets take 3 people gets down at station A.
Than,
→ Person gets in = double of gets down = 3 * 2 = 6
Therefore,
→ Person gets in at next stop will be 20 more than first station = 6 + 20 = 26 .
Than,
→ Person gets out at station B = Half of gets in = (26/2) = 13.
Similarly,
→ if 26 gets in at station B , than, 20 more gets in at station C = 26 + 20 = 46 ,
and,
→ gets out at station C = (46/2) = 23.
→ Difference between = (13 - 3) = (23 - 13) = 10
Now,
From 30-40 = Prime numbers are 31, 37 .
As, 31 cant be possible , Difference between gets in will be less than 20.
So,
→ Gets out at station D = 37
Than,
→ gets in = 37*2 = 74
Therefore,
→ gets in at station E = 74 + 20 = 94
Than,
→ gets out at station E = 94/2) = 47. (40 - 50)
Finally, Difference must be 10.
Therefore,
→ gets out at station F will be = 59.
Hence,
→ People gets out at station A, B, C, D, E and F are :-
- 0 - 10 = 3
- 10 - 20 = 13
- 20 - 30 = 23
- 30 - 40 = 37
- 40 - 50 = 47
- 50 - 60 = 59.
Now, we will check options and find that cannot be the number of people getting down at any intermediate station.