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a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positive
integer c is divided by the lowest number that has both a and b as its factors?
(1) c has the same number of factors as that of the least common multiple of a and b.
(2) When c is divided by 4 times the product of a and b, the remainder is 0.
integer c is divided by the lowest number that has both a and b as its factors?
(1) c has the same number of factors as that of the least common multiple of a and b.
(2) When c is divided by 4 times the product of a and b, the remainder is 0.
- 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 'B'. Can you explain this answer?
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Verified Answer
a and b are positive integers such that they do not have any common pr...
Step 1 & 2: Understand Question and Draw Inference
- a is a positive integer
where P1 , P2 are prime numbers and q, r are integers > 0
- b is a positive integer
where P3 , P4 are prime numbers and s, t are integers > 0
- c is a positive integer
- Lowest number that has both a and b as its factors = LCM(a, b)
To Find: the value of y in c = LCM (a, b)x + y, where x and y are non-negative integers and 0 ≤ y < x
- As a and b do not have any common factor, LCM (a, b) = a* b
- Alternatively, since a and b do not have any common prime factor, GCD(a, b) = 1
- As a * b = LCM(a, b) * GCD(a, b), we have LCM(a, b) =
- c = (ab)x + y
- Following cases can occur:
- If c is a multiple of LCM(a, b) or ab, y = 0
- If c is not a multiple of LCM (a, b) or ab, y ≠ 0 and y < ab
Step 3 : Analyze Statement 1 independent
- c has the same number of factors as that of the least common multiple of a and b.
- Number of factors(c) = Number of factors (LCM(a, b)) = Number of factors (ab)
- Let
where P5 and P6 are prime numbers and u, v are integers > 0 - So, (q+1)(r+1)..*(s+1)(t+1)… = (u +1) (v+1)….
- This, does not tell us for sure if c is a multiple of LCM(a, b) or not.
- For example, 2 * 3 has the same number of factors as 5 * 7.
However, 2 * 3 is a not a multiple of 5 * 7
- For example, 2 * 3 has the same number of factors as 5 * 7.
Insufficient to answer.
Step 4 : Analyze Statement 2 independent
2. When c is divided by 4 times the product of a and b, the remainder is 0.
- c = 4ab
- c is a multiple of ab, so y = 0
Sufficient to answer
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step-4, this step is not required.
Answer: B
Answer: B
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a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer?
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a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. 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 a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer?.
a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. 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 a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer?.
Solutions for a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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Here you can find the meaning of a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice a and b are positive integers such that they do not have any common prime factor. What is the remainder when the positiveinteger c is divided by the lowest number that has both a and b as its factors?(1) c has the same number of factors as that of the least common multiple of a and b.(2) When c is divided by 4 times the product of a and b, the remainder is 0.a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
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