Can the total number of integers that divide x be expressed in the form of 2k + 1, where k is a positive integer?(1) andradic;12x is an integer(2) The product of andradic;x and andradic;y is an integer, where the total number of factors of y/3 is odd.a)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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Can the total number of integers that divide x be expressed in the for...

Step 1 & 2: Understand Question and Draw Inference

We know that a number in the form of 2k + 1 leaves a remainder of 1 when divided by 2, (that is, a number that leaves a remainder of 1 when divided by 2) is odd.
So, we are asked to find if the number of factors of x is odd.

To Find: Is the number of factors of x odd?

We know that if a number has odd number of factors, it has to be a perfect square. So, we are (indirectly) asked to find if x is a perfect square?

Step 3 : Analyze Statement 1 independent

√12 x is an integer

is an integer. For √3x to be an integer,
x should contain an odd power of 3.
Now, if 3 occurs odd number of times in x, x can’t be a perfect square.
Hence statement-1 is sufficient to answer the question.

Step 4 : Analyze Statement 2 independent

2. The product of √x and √y is an integer, where the total number of factors of y/3 is odd.
Statement-2 tells us that the total number of factors of y/3 is odd i.e. y/3 is a perfect square. Let’s assume y/3 = 3z². Since z² is always non-negative, y will also be a non-negative integer

So, we know that

is an integer i.e. z√3x is an integer.

For √3x to be an integer, x should contain an odd power of 3. If 3 occurs odd
number of times in x, x can’t be a perfect square
Hence statement-2 is sufficient to answer the question.

Step 5: Analyze Both Statements Together (if needed)

Since we have a unique answer from steps 3 and 4, this step is not required.
Answer: D

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Most Upvoted Answer

Can the total number of integers that divide x be expressed in the for...

Statement (1): √12x is an integer
This statement tells us that √12x is an integer, which implies that x has at least one factor of 12. However, it doesn't give us enough information to determine the total number of integers that divide x.

Statement (2): The product of √x and √y is an integer, where the total number of factors of y/3 is odd
This statement provides us with information about the product of √x and √y, as well as the total number of factors of y/3 being odd. However, it still doesn't directly give us the total number of integers that divide x.

Combined statements:
By combining both statements, we can gather more information about x and y. Statement (1) tells us that x has at least one factor of 12, and statement (2) gives us information about y having an odd number of factors. With this combined information, we can determine the total number of integers that divide x.

Therefore, each statement alone is not sufficient to answer the question, but together they provide enough information to determine the total number of integers that divide x. Hence, the correct answer is option 'D'.

Answered by Talent Skill Learning · View profile

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Can the total number of integers that divide x be expressed in the form of 2k + 1, where k is a positive integer?(1) √12x is an integer(2) The product of √x and √y is an integer, where the total number of factors of y/3 is odd.a)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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Can the total number of integers that divide x be expressed in the form of 2k + 1, where k is a positive integer?(1) √12x is an integer(2) The product of √x and √y is an integer, where the total number of factors of y/3 is odd.a)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 Can the total number of integers that divide x be expressed in the form of 2k + 1, where k is a positive integer?(1) √12x is an integer(2) The product of √x and √y is an integer, where the total number of factors of y/3 is odd.a)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 Can the total number of integers that divide x be expressed in the form of 2k + 1, where k is a positive integer?(1) √12x is an integer(2) The product of √x and √y is an integer, where the total number of factors of y/3 is odd.a)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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