Latest Campus Aptitude Question SOLUTION: 1,2,3,4,5,6,7 are arranged such that sum of two successive numbers is a prime number. For example, 1234765 (i.e. 1+2=3, 2+3=5, 3+4=7....) 1. How many such possible combinations o

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(#M40157200) CAMPUS Logical Reasoning question permutation and combination Keep an EYE

1,2,3,4,5,6,7 are arranged such that sum of two successive numbers is a prime number. For example, 1234765 (i.e. 1+2=3, 2+3=5, 3+4=7....)
1. How many such possible combinations occur?
2. How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
3. How many numbers will come on 4th position(xxx_xxx)?

Asked In Campus NIDHISH (7 years ago)

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rc  (7 years ago)

We have to follow a systematic approach for this question. We know that if at all two consecutive numbers be prime, they should not be even in the first place. So we arrange even numbers in even places, odd numbers in odd places.
2 should not have 7 as its neighbor
4 should not have 5 as its neighbor
6 should not have 3 as its neighbor
Case 1:
__ 2 ____ 4 ____ 6 __
x7 x7,5 x5,3 x3
So fix, 3 or 1 in between 2 and 4. We get the following options with reverse case also.
5234167, 7614325
5234761, 1674325
1234765, 5674321
3214765, 5674123

Case 2:
__ 2 ____ 6 ____ 4 __
x7 x7,3 x3,5 x5

5216743, 3476125
3256147, 7416523
3256741, 1476523
1256743, 3476521

Case 3:
__ 4 ____ 2 ____ 6 __
x5 x5,7 x7,3 x3

3412567, 7652143
7432165, 5612347
7432561, 1652347
1432567, 7652341
Answer 1: Total possibilities are 24.
Answer 2: 4 possibilities.
Answer 3: 3 possibilities.

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