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If k and m are positive integers, what is the remainder when k is divided by m +1?
(1) k-m when divided by m+1 leaves a remainder 1
(2) k/3 and k/2 when divided by m+1 leave a remainder equal to 4 and 3 respectively.
  • 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 aske
  • 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
If k and m are positive integers, what is the remainder when k is divi...
Steps 1 & 2: Understand Question and Draw Inferences
  • k, m are integers > 0
To Find: remainder when k is divided by m +1?
  • Value of r in k = (m+1)x + r,
    • x is an integer ≥ 0
    • where 0 ≤ r < (m+1)
 
Step 3: Analyze Statement 1 independently
  1. k-m when divided by m+1 leaves a remainder 1
  • k – m = (m+1)y + 1, where y is an integer ≥ 0
    • k = (m+1)y + m +1
    • k = (m+1)* ( y +1)
  • Thus, k is divisible by m +1 and hence it leaves a remainder 0
  • r = 0
Sufficient to answer
 
Step 4: Analyze Statement 2 independently
  1. k/3   and k/2  when divided by m+1 leave a remainder equal to 4 and 3 respectively.
  • k/3=(m+1)a+4 , where a is an integer ≥ 0
  • k=(m+1)∗3a+12…………..(1)
    • It seems from above that 12 is the remainder when k is divided by (m+1)
      • However, we know that remainder(i.e. 12) should always be less than the  divisor (i.e. (m+1))
      • Since, we do not know if 12 < m +1. So, we cannot find a unique value of r from it.
  • k/2=(m+1)b+3 , where b is an integer ≥ 0
    • k=(m+1)∗2b+6…………….(2)
    • As discussed in the above case, here also we do not know if 6 < m +1. So, we cannot find a unique value of r from it.
  • Since we need to express k in terms of (m+1), let’s try to eliminate the constants using equations (1) and (2)
  • Carrying out the operation, (2) * 2 – (1), we get
  • Thus k is divisible by (m+1) and hence leaves a remainder 0
  • So, r = 0
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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If k and m are positive integers, what is the remainder when k is divided by m +1?(1) k-m when divided by m+1 leaves a remainder 1(2)k/3and k/2when divided by m+1 leave a remainder equal to 4 and 3 respectively.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)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?
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