For an integer n greater than 1, n! denotes the product of all integers from 1 to n, inclusive. If x and y are two distinct positive integers such that y x, what are the values of x and y?(1) The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.(2) The lowest common multiple and the highest common factor of y! and x! have 3 and 2 prime factors respectivelya)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 'C'. 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 'C'. Can you explain this answer?

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Test: LCM And GCD- 2

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For an integer n greater than 1, n! denotes the product of all integer...

Step 1 & 2: Understand Question and Draw Inference

n! = 1*2*3……*n
x, y are distinct integers > o
y > x

To Find: Values of x and y

Step 3 : Analyze Statement 1 independent

The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.

x! = 1*2*3…..*x
y! = 1*2*3….x*(x+1)…….* y ( as y > x)
- So, we can write: y! = x! * a, where a is a positive integer
As y! is a multiple of x!, LCM( x!, y!) = y!
Similarly, as x! is a factor of y!, GCD(x!, y!) = x!

So,

Hence, 20 needs to be expressed as a product of 1 or more consecutive positive
integers. Following cases are possible:

As 20 = 2² * 5, following cases are possible:
20 = 4 * 5
- So, (x+1) * y = 20. Therefore, x + 1 = 4, i.e. x = 3 and y = 5
The other possible case is when (x+1) = y = 20, i.e. y = 20 and x = 19. So,

As we do not have unique values of x and y, the statement is insufficient to answer

Step 4 : Analyze Statement 2 independent

2. The lowest common multiple and the highest common factor of y! and x!
have 3 and 2 prime factors respectively.

we know that LCM(x!, y!) = y! = 1*2*3*4*5…y (we deduced this in the analysis of statement-1)
- As y! has 3 prime factors only, they have to be the smallest 3 prime factors, i.e. {2, 3 , 5}. So, 5! ≤ y! < 7! as 7! will have 4 prime factors {2, 3, 5, 7}
- 5 ≤ y < 7. So, y = 5 or 6
We also know that GCD(x!, y!) = x! = 1*2*3… x (we deduced this in the analysis of statement-1)
- As x! has 2 prime factors only, they have to be the smallest 2 prime factors , i.e. {2, 3}. So, 3!≤ x! < 5!, as 5! will have 3 prime factors {2, 3, 5}
- 3≤ x < 5 So, x = {3, 4}

As we do not have unique values of x and y, insufficient to answer

Step 5: Analyze Both Statements Together (if needed)

1. From statement-1, we inferred that y = {20, 5} and x = {19, 3}
2. From statement-2, we inferred that y = { 5, 6} and x = { 3,4 }
Combining both the statements, we have y = 5 and x = 3.
Sufficient to answer.
Answer: C

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For an integer n greater than 1, n! denotes the product of all integers from 1 to n, inclusive. If x and y are two distinct positive integers such that y > x, what are the values of x and y?(1) The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.(2) The lowest common multiple and the highest common factor of y! and x! have 3 and 2 prime factors respectivelya)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 'C'. Can you explain this answer?

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For an integer n greater than 1, n! denotes the product of all integers from 1 to n, inclusive. If x and y are two distinct positive integers such that y > x, what are the values of x and y?(1) The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.(2) The lowest common multiple and the highest common factor of y! and x! have 3 and 2 prime factors respectivelya)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 'C'. 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 For an integer n greater than 1, n! denotes the product of all integers from 1 to n, inclusive. If x and y are two distinct positive integers such that y > x, what are the values of x and y?(1) The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.(2) The lowest common multiple and the highest common factor of y! and x! have 3 and 2 prime factors respectivelya)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 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For an integer n greater than 1, n! denotes the product of all integers from 1 to n, inclusive. If x and y are two distinct positive integers such that y > x, what are the values of x and y?(1) The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.(2) The lowest common multiple and the highest common factor of y! and x! have 3 and 2 prime factors respectivelya)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 'C'. Can you explain this answer?.

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If x and y are two distinct positive integers such that y > x, what are the values of x and y?(1) The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.(2) The lowest common multiple and the highest common factor of y! and x! have 3 and 2 prime factors respectivelya)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 'C'. 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If x and y are two distinct positive integers such that y > x, what are the values of x and y?(1) The ratio of the lowest common multiple and the highest common factor of y! and x! is 20:1.(2) The lowest common multiple and the highest common factor of y! and x! have 3 and 2 prime factors respectivelya)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 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.

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