For all positive integers x,when x is even and when x is odd. What is the value of positive integer x?(1) The highest power of 2 that divides (4x)completely is 36(2) The highest power of 2 that divides (4)*xcompletely is 8a)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 needeCorrect answer is option 'A'. Can you explain this answer?

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For all positive integers x,

when x is even and

when x is odd. What is the value of positive integer x?

(1) The highest power of 2 that divides &(4x) completely is 36

(2) The highest power of 2 that divides (&4)*x completely is 8

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 neede

Correct answer is option 'A'. Can you explain this answer?

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For all positive integers x,when x is even and when x is odd. What is ...

Steps 1 & 2: Understand Question and Draw Inferences

Given:

Integer x > 0

Step 3: Analyze Statement 1 independently

(1) The highest power of 2 that divides &(4x) completely is 36

This means, &(4x) contains 2³⁶ but not any higher power of 2
4x is definitely an even integer.

In this case, the power of 2 will only come from the term 2^4x+2
Since the highest power of 2 in &(4x) is 36, we can write:
- 4x + 2 = 36
That is, 4x = 34
This doesn’t give an integral value of x. So, this case is rejected.

Case 2: x is even
- In this case, x contains at least 2¹ but may also contain higher powers of 2.
- So, we will have to consider these possibilities:

So, the only possible value of x = 2² = 4

Thus, Statement 1 is sufficient to determine a unique value of x.

Step 4: Analyze Statement 2 independently

(2) The highest power of 2 that divides (&4)*x completely is 8

Statement 2 tells us that the highest power of 2 that divides 2⁶x is 8
- 2⁶ is a constant. The power of 2 in this number is 6
So, from Statement 2, we infer that the highest power of 2 contained in x is 2
- So, x is divisible by 2² (that is, 4) but not be 2³, 2⁴ etc.
- Thus, x must be of the form 4 * odd number
So, x = 4(2k+1) where k is a positive integer
Values such as 4*1, 4*3, 4*5 etc. will all satisfy Statement 2

Thus, Statement 2 is not sufficient to determine a unique value of x.

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in Step 3, this step is not required

Answer: Option A

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For all positive integers x,when x is even and when x is odd. What is the value of positive integer x?(1) The highest power of 2 that divides &(4x)completely is 36(2) The highest power of 2 that divides (&4)*xcompletely is 8a)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 needeCorrect answer is option 'A'. Can you explain this answer?

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For all positive integers x,when x is even and when x is odd. What is the value of positive integer x?(1) The highest power of 2 that divides &(4x)completely is 36(2) The highest power of 2 that divides (&4)*xcompletely is 8a)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 needeCorrect answer is option 'A'. 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 all positive integers x,when x is even and when x is odd. What is the value of positive integer x?(1) The highest power of 2 that divides &(4x)completely is 36(2) The highest power of 2 that divides (&4)*xcompletely is 8a)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 needeCorrect answer is option 'A'. 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 all positive integers x,when x is even and when x is odd. What is the value of positive integer x?(1) The highest power of 2 that divides &(4x)completely is 36(2) The highest power of 2 that divides (&4)*xcompletely is 8a)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 needeCorrect answer is option 'A'. Can you explain this answer?.

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