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If r and s are positive integers, what is the remainder when r + s is divided by 3?
(1) rs is divisible by 9
(2) s is divisible by 3
  • 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 ask
  • 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 'E'. Can you explain this answer?
Most Upvoted Answer
If r and s are positive integers, what is the remainder when r + s is ...
E should be the option
First of all, if we divide some number by 3, we can have only 3 remainders which are 0,1,2; i.e, either the number is of the form 3k or 3k+1 or 3k+2.
Now we have to find the remainder of r+s and we are provided with 2 statements.
Statement 1: rs is divisible by 9.
r=4 s=9
rs=36
r+s=13 ; remainder 1 when divided by 3
r=3 s=6 rs=18
r+s = 9; remiander 0 when divided by 3
Multiple possibilities. Not sufficient

Statement 2: s is divisible by 3
s=3 r=1
r+s=4; remainder 1 when divided by 3
s=3 r=2
r+s=5; remainder 2 when divided by 3
Again multiple possibilities. Not sufficient
If both statements are clubbed together:
rs is divisible by 9 and s is of the form 3k
r=3, s=6, rs=18=9*2, r+s=9; remainder 0
r=4, s=18, rs=72=9*8, r+s=22; remainder 1
So again doesn't give specific answer.
Not sufficient
So Neither of them individually or together is sufficient.
Hence, option E should be correct
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If r and s are positive integers, what is the remainder when r + s is divided by 3?(1) rs is divisible by 9(2) s is divisible by 3a)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 askd)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 'E'. Can you explain this answer?
Question Description
If r and s are positive integers, what is the remainder when r + s is divided by 3?(1) rs is divisible by 9(2) s is divisible by 3a)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 askd)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 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If r and s are positive integers, what is the remainder when r + s is divided by 3?(1) rs is divisible by 9(2) s is divisible by 3a)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 askd)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 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If r and s are positive integers, what is the remainder when r + s is divided by 3?(1) rs is divisible by 9(2) s is divisible by 3a)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 askd)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 'E'. Can you explain this answer?.
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