21) The number of 10-digit numbers such that the product of any two consecutive digits in the number is a prime number, is (A) 1024 (B) 2048 (C) 512 (D) 64 Share with your friends Share 7 Aditi Jain. answered this Dear Student,The product of any two consecutive digits is a prime number only when one of them is 1 and the other is a prime number.So basically, every other number has to be 1. The other digits have to be 2,3,5, or 7. As we are talking about 10 digit numbers, Case 1:Consider numbers of the form 1x1x1x1x1x, where x = 2,3,5, or 7.For each x you have 4 possible selections (2, 3, 5, 7) - so you multiply 4, 5 times ( for the 5 slots) Possible numbers=4×4×4×4×4=45=210Case 2:Consider numbers of the form x1x1x1x1x1.For each x you have 4 possible selections (2, 3, 5, 7) - you multiply 4, 5 times ( for the 5 slots) Possible numbers=4×4×4×4×4=45=210Thus, total possible numbers=210+210=2×210=211Regards 20 View Full Answer
