Question

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 number of people getting down at the intermediate stations are all prime numbers, one each 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 number 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 (or vice versa) at the same station.

Q: Which of the following cannot be the number of people getting
down at any intermediate station?
47
3
17
23​

Answer 1

Answer:

(c)17

Step-by-step explanation:

We are to just pick 6 prime numbers, one each from the given ranges (i.e. 0 to 10, 11 to 20, 21 to 30, 31 to 40, 41 to 50 and 51 to 60) such that difference between two consecutively selected prime numbers is at least 10.

Also as sum of all 6 prime numbers is even, so each of six prime numbers must be ODD.

It can be easily checked that selected prime numbers can be: 3-13-23-37-47-59 only.

Thus required answer is (c) 17.