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If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?
(1) x = 18
(2) x + y = 30
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'D'. Can you explain this answer?
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If x and y are positive integers such that x > y and the least com...
Steps 1 & 2: Understand Question and Draw Inferences
We are given that for two positive integers x and y:
- x > y
- Least common multiple of x and y = 36
- Greatest common divisor of x and y = 6
Now, we know that for two numbers:
Least common multiple * greatest common divisor = Product of the numbers
So, x * y = 36 * 6 = 216 ………………. (1)
However, this information can’t directly help us to find the value of x and y. So let’s move on to the analysis of statement 1 and 2.
Step 3: Analyze Statement 1
Statement 1 says: x = 18
By plugging the value of x in equation (1), we get:
18 * y = 216
y =12
So, x - y =6
Hence, statement I is sufficient to answer the question: What is the value of x -y?
Step 4: Analyze Statement 2
Statement 2 says: x + y = 30 …………. (2)
We know that:
(x – y)2 = x2 + y2 – 2xy
By adding and subtracting 2xy in the right hand side, we get:
(x – y)2 = x2 + y2 – 2xy + 2xy -2xy
(x – y)2 = x2 + y2 + 2xy -4xy
(x – y)2 = (x + y)2 – 4xy
Plugging in the values from equation (1) and (2):
(x – y)2 = (30)2 – 4*216
= 900 – 864
= 36
So, x – y = 6
Hence, statement II alone is sufficient to answer the question: What is the value of x -y?
Step 5: Analyze Both Statements Together (if needed)
Since statement I and II alone are sufficient to answer the question, we don’t need to perform this step.
Answer: Option (D)
Most Upvoted Answer
If x and y are positive integers such that x > y and the least com...
Analysis:
To find the value of x - y, we need to determine the values of x and y. We are given that the least common multiple (LCM) of x and y is 36 and the greatest common divisor (GCD) is 6.
Statement 1:
x = 18
This statement alone is sufficient to find the values of x and y. Since the GCD is 6, y must be a multiple of 6. As x = 18, y = 6 satisfies the conditions. Therefore, x - y = 18 - 6 = 12.
Statement 2:
x - y = 30
This statement alone is not sufficient to determine the individual values of x and y. It only gives the difference between x and y, not allowing us to find the exact values of x and y.
Combined:
From statement 1, we found that x = 18 and y = 6, satisfying the conditions given in the question. Therefore, x - y = 18 - 6 = 12. Hence, both statements together are not necessary to find the value of x - y. Statement 1 alone is sufficient to determine the answer, making the correct choice option D.
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If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?(1) x = 18(2) x + y = 30a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?
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If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?(1) x = 18(2) x + y = 30a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.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 If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?(1) x = 18(2) x + y = 30a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.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 If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?(1) x = 18(2) x + y = 30a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?.
If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?(1) x = 18(2) x + y = 30a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.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 If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?(1) x = 18(2) x + y = 30a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.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 If x and y are positive integers such that x > y and the least common multiple and greatest common divisor of the two integers are 36 and 6 respectively, what is the value of x – y?(1) x = 18(2) x + y = 30a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?.
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