UPSC Exam  >  UPSC Questions  >  Find the units digit of 53n + 95m, where m an... Start Learning for Free
Find the units digit of 53n + 95m, where m and n are positive integers
  1. m is an odd integer
  2. n is an even integer
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
  • c)
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
  • d)
    EACH statement ALONE is sufficient.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Find the units digit of 53n + 95m, where m and n are positive integers...
Given: 53n 95m, where m and n are positive integers
m is an odd integer
n is an even integer

To find: Units digit of 53n 95m

Approach:
We need to find the units digit of the given expression which is the remainder obtained when the expression is divided by 10.

Statement 1: m = 1
If m = 1, then 95m = 95 and its units digit is 5.
Now, we need to find the units digit of 53n 95. If we observe the units digit of powers of 5, it repeats after every 4 powers. The units digit of 5, 5^2, 5^3, 5^4, 5^5, … is 5, 25, 125, 625, 3125, …
Hence, the units digit of 53n 95 will depend on the value of n. If n = 2, then 53n = 253 and the units digit of 253 + 5 = 8. If n = 4, then 53n = 2053 and the units digit of 2053 + 5 = 8. If n = 6, then 53n = 20553 and the units digit of 20553 + 5 = 8. The pattern repeats after every 4 values of n. Hence, the units digit of the given expression will be 8 when m = 1 and n is even.
Therefore, statement 1 alone is sufficient.

Statement 2: n = 2
If n = 2, then 53n = 253 and the units digit of 53n is 3.
Now, we need to find the units digit of 53n 95m. If we observe the units digit of powers of 9, it repeats after every 2 powers. The units digit of 9, 9^2, 9^3, 9^4, … is 9, 81, 729, 6561, …
Hence, the units digit of 95m will depend on the value of m. If m = 1, then the units digit of 95m + 3 = 8. If m = 3, then the units digit of 95m + 3 = 2. The pattern repeats after every 2 values of m. Hence, the units digit of the given expression will be 8 when n = 2 and m is odd.
Therefore, statement 2 alone is not sufficient.

Hence, the correct answer is option A. Statement 1 alone is sufficient but statement 2 alone is not sufficient.
Free Test
Community Answer
Find the units digit of 53n + 95m, where m and n are positive integers...
Choice a. the cyclicity of units digit of 5 is 1 meaning units digit is always 5. cyclicity of units digit of 9 is 2 and the digits vary as 2 and 9. so knowing either the power is odd or even gives out the units digit of 9. knowing m is sufficient
Explore Courses for UPSC exam

Top Courses for UPSC

Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?
Question Description
Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC. Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Find the units digit of 53n + 95m, where m and n are positive integers m is an odd integer n is an even integera)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice UPSC tests.
Explore Courses for UPSC exam

Top Courses for UPSC

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev