GMAT Exam > GMAT Questions > The positive integer y is at a distance of 2 ...
Start Learning for Free
The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?
(1) y is x/2 units more than the square of x, where x/2 is even
(2) y – 3 is a multiple of 5
- 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 'A'. Can you explain this answer?
Verified Answer
The positive integer y is at a distance of 2 units from the nearest mu...
Steps 1 & 2: Understand Question and Draw Inferences
- x is an integer such that 0 < x < 10
- y is an integer > 0
- Let the multiple of x be mx.
- So, two values are possible for values of y:
- y = mx + 2 or
- y = mx – 2
- Possible values of x: {1….9}
- However, as y is 2 units away from a multiple of x,
- x ≠ 1(because then y will be a multiple of x)
- x ≠ 2(because then y will be at a maximum distance of 1 unit from a multiple of x)
- x ≠ 3(because then y will be at a maximum distance of 1 unit from the nearest multiple of x)
- So, x = {4, 5, ….9}………………(1)
- However, as y is 2 units away from a multiple of x,
To Find: How much should be added to y so that it is divisible by x?
- Case-I: If y = mx – 2, then 2 should be added to y to get to make it divisible by x. The resulting number will be mx
- Case-II:If y = mx + 2, then to represent y as the next multiple of x i.e. (m+1)x, we should add, (m+1)x – (mx +2) = mx + x – mx – 2= x-2. So, x-2 should be added to y= mx + 2 to make y divisible by x.
- So, the statement will be sufficient if:
- Both the cases give us the same answer OR
- We are able to reject 1 case and the other case gives us a unique answer.
Step 3: Analyze Statement 1 independently
(1) y is x/2 units more than the square of x, where x/2 is even
- Case-I: y = mx + 2.
- As per Statement 1, y=x2+(x/2)
- So, we need to add to y to make it divisible by x.
- As x/2 is an even integer, x/2={2,4} . Any value of x/2, would result in value of x ≥ 10. Since 0 < x < 10, these values cannot be accepted.
- So, x = {4, 8}
- For x = 4, we have y =
), which is of the form 4x + 2. So, x = 4 is a possible value of x - For x = 8, we have y =
. However, 68 is of the form 8x + 4 and not of the form 8x + 2. So, x = 8 is not a possible value of x. - So, we have x/2=2
- Hence 2 needs to be added to y to make it divisible by x
- Case-II: y = mx – 2
- 2 should be added to y so that it is divisible by x
As we have a unique answer from both the cases, the statement is sufficient to answer.
Step 4: Analyze Statement 2 independently
(2) y – 3 is a multiple of 5
- Case-I: y = mx + 2
- As per statement 2, y -3 = 5k, where k is an integer > 0
- So, mx + 2 -3 = 5k
- For m to be an integer, 5k + 1 should be a multiple of x. Let’s observe a few cases and see if this constraint gives us a unique value of x-2:
- This case does not give us a unique value of x -2.
Case-II: y = mx – 2
- 2 should be added to y so that it is divisible by x.
As the cases do not give us a unique value of the number that should be added to make y divisible by x, this statement is not sufficient to answer.
Step 5: Analyze Both Statements Together (if needed)
As we have a unique answer from step-3, this step is not required.
Answer: A
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer?
Question Description
The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer?.
The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer?.
Solutions for The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer?, a detailed solution for The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? has been provided alongside types of The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The positive integer y is at a distance of 2 units from the nearest multiple of a single digit positive integer x. What is the minimum positive value that should be added to y, so that it becomes divisible by x?(1) y is x/2 units more than the square of x, wherex/2 is even(2) y – 3 is a multiple of 5a)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 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup