In the fractions and , where a, b, c and d are positive integers, both b and d have two prime factors each. What is the number of prime factors in the product of b and d?(1) The least common denominator of a/b and c/d is half the product of b and d(2) The highest integer that divides both b and d completely is 2a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)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 'D'. Can you explain this answer?

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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?

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Test: LCM And GCD- 2

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In the fractions and , where a, b, c and d are positive integers, both...

Step 1 & 2: Understand Question and Draw Inference

and d = , where P , P , P and P are prime number and q, r, s, and t are integers > 0

To Find : Number of prime factors of b*d

b* d =
If P , P , P and P are distinct prime numbers, then b*d will have 4 prime factors, else b *d will have less than 4 prime factors
- If b and d have 1 shared prime factor, then b *d will have 3 prime factors
- If b and d have 2 shared prime factors, then b*d will have 2 prime factors

Step 3 : Analyze Statement 1 independent

The least common denominator of a/b and c/d is half the product of b and d

Least common denominator of a fraction means the LCM of the denominators.
LCM(b, d) =
- 2* LCM(b, d) = bd ...(A)
Now, from the property of GCD and LCM, we know that GCD(b, d) *LCM(b, d) = b*d . . . (B)
- So, using equations (A) and (B) together, we can write:
  - GCD(b, d) * LCM(b, d) = 2*LCM(b, d)
  - GCD(b, d) = 2

So, 2 divides both b and d. Hence, 2 has to be the only common prime factor of both b and d. Had there been any other common prime factor, it would have come in the GCD(b, d)
- Let’s assume P = P = 2
As b and d have 1 common prime factors, therefore the number of prime factors of b*d = 2, P and P , i.e. a total of 3 prime factors.

Sufficient to answer.

Step 4 : Analyze Statement 2 independent

2. The highest integer that divides both b and d completely is 2

That is, GCD(b, d) = 2
So, 2 divides both b and d. Hence, 2 has to be the only common prime factor of both b and d. Had there been any other common prime factor, it would have come in the GCD(b, d)
- Let’s assume P = P = 2
As b and d have 1 common prime factor, therefore the number of prime factors of b*d = 2, P and P , i.e. a total of 3 prime factors.

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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In the fractions and , where a, b, c and d are positive integers, both b and d have two prime factors each. What is the number of prime factors in the product of b and d?(1) The least common denominator of a/b and c/d is half the product of b and d(2) The highest integer that divides both b and d completely is 2a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)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 'D'. Can you explain this answer?

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In the fractions and , where a, b, c and d are positive integers, both b and d have two prime factors each. What is the number of prime factors in the product of b and d?(1) The least common denominator of a/b and c/d is half the product of b and d(2) The highest integer that divides both b and d completely is 2a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)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 'D'. 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 In the fractions and , where a, b, c and d are positive integers, both b and d have two prime factors each. What is the number of prime factors in the product of b and d?(1) The least common denominator of a/b and c/d is half the product of b and d(2) The highest integer that divides both b and d completely is 2a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)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 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the fractions and , where a, b, c and d are positive integers, both b and d have two prime factors each. What is the number of prime factors in the product of b and d?(1) The least common denominator of a/b and c/d is half the product of b and d(2) The highest integer that divides both b and d completely is 2a)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)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 'D'. Can you explain this answer?.

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