When (27)56 + (22)38 − (13)50 is solved, which digit will come at its unit…
2019
When (27)56 + (22)38 − (13)50 is solved, which digit will come at its unit place?
- A.
6
- B.
7
- C.
5
- D.
4
Attempted by 173 students.
Show answer & explanation
Correct answer: A
Use only the units digit of each base: the units digits are 7, 2, and 3 respectively.
(27)56: cycle of 7 is 7, 9, 3, 1. Since 56 mod 4 = 0, the units digit is 1.
(22)38: cycle of 2 is 2, 4, 8, 6. Since 38 mod 4 = 2, the units digit is 4.
(13)50: cycle of 3 is 3, 9, 7, 1. Since 50 mod 4 = 2, the units digit is 9.
Combine: 1 + 4 − 9 = −4. Since −4 ≡ 6 (mod 10), the units digit is 6.
Answer: 6