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What is the units digit of (a +b)2 – (a-b)2, where a and b are non-negative integers?
       (1) The difference between any two consecutive multiples of a is 5
       (2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • d)
    EACH statement ALONE is sufficient to answer the question asked
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the units digit of (a +b)2 – (a-b)2, where a and b are n...
Steps 1 & 2: Understand Question and Draw Inferences
Step 3: Analyze Statement 1 independently
  1. The difference between any two consecutive multiples of a is 5
 
  • Let the consecutive multiples of a be a*n and a*(n+1)
  • So, a(n+1) – an = 5
    • an + a – an = 5
    • a = 5
If a = 5, 4ab = 20b. So, irrespective of the value of b, the units digit(20b) = 0.
Sufficient to answer.
 
Step 4: Analyze Statement 2 independently
2.  b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.
 
  • Following cases are possible:
 
  • Units Digit(b) = 0.
    • 0 when multiplied with any integer will have the Units Digit as 0. In this case the units digit(4ab) = 0.
 
  • Units Digit(b) = 5.
    • 5 when multiplied with any even integer will result in units digit of 0. So, Units Digit(4ab) = 0.
As we have a unique answer of Units Digit(4ab), this statement is sufficient to answer.
 
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from steps 3 and 4, this step is not required.
Answer: D
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What is the units digit of (a +b)2 – (a-b)2, where a and b are non-negative integers? (1)The difference between any two consecutive multiples of a is 5 (2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?
Question Description
What is the units digit of (a +b)2 – (a-b)2, where a and b are non-negative integers? (1)The difference between any two consecutive multiples of a is 5 (2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. 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 What is the units digit of (a +b)2 – (a-b)2, where a and b are non-negative integers? (1)The difference between any two consecutive multiples of a is 5 (2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the units digit of (a +b)2 – (a-b)2, where a and b are non-negative integers? (1)The difference between any two consecutive multiples of a is 5 (2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'D'. Can you explain this answer?.
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