2019 · Q14
Consider the following statements:
- 1Unit digit in 17¹⁷⁴ is 7. 2) Difference of the squares of any two odd numbers is always divisible by 8. 3) Adding 1 to the product of two consecutive odd numbers makes it a perfect square.
Which of the above statements are correct?
Elementary MathematicsNumber System
- A1, 2 and 3
- B1 and 2 only
- C2 and 3 only
- D1 and 3 only
Explanation
1) Powers of 7 end in 7, 9, 3, 1 cyclically; 174 = 4x43+2, so 17^174 ends in 9, not 7. False. 2) (2m+1)^2-(2n+1)^2 = 4(m^2+m-n^2-n), and m^2+m = m(m+1) is even, so the difference is a multiple of 8. True. 3) (2n-1)(2n+1)+1 = 4n^2 = (2n)^2, a perfect square. True. Hence statements 2 and 3 only.