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If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?
(1) x - y is a multiple of 22
(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same
- 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;
- 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 are needed.
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If both x and y are positive integers less than 100 and greater than 1...
- If both x and y are multiples of 11, then both x + y and x - y will be multiples of 11. In other words, if two numbers have a common divisor, their sum and difference retain that divisor.
In case this is hard to conceptualize, consider the following examples:
42 - 18 {both numbers share a common factor of 6}
=(6 x 7) - (6 x 3)
=6(7 - 3)
=6(4)
=24 {which is a multiple of 6}
49 + 14 {both numbers share a common factor of 7}
=(7 x 7) + (7 x 2)
=7(7+2)
=7*9
=63 {which is a multiple of 7} - However, if x and y are not both multiples of 11, it is possible that x - y is a multiple of 11 while x + y is not a multiple of 11. For example:
68 - 46 = 22 but 68 + 46 = 114, which is not divisible by 11.
The reason x - y is a multiple of 11 but not x + y is that, in this case, x and y are not individually multiples of 11. - Evaluate Statement (1) alone.
- Since x-y is a multiple of 22, x-y is a multiple of 11 and of 2 because 22 = 11 x 2
- If both x and y are multiples of 11, the sum x + y will also be a multiple of 11. Consider the following examples:
44 - 22 = 22 {which is a multiple of 11 and of 22}
44 + 22 = 66 {which is a multiple of 11 and of 22}
88 - 66 = 22 {which is a multiple of 11 and of 22}
88 + 66 = 154 {which is a multiple of 11 and of 22} - However, if x and y are not individually divisible by 11, it is possible that x - y is a multiple of 22 (and 11) while x + y is not a multiple of 11. For example:
78 - 56 = 22 but 78 + 56 = 134 is not a multiple of 11. - Statement (1) alone is NOT SUFFICIENT.
- Evaluate Statement (2) alone.
- Since the tens digit and the units digit of x are the same, the range of possible values for x includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, x must be a multiple of 11. - Since the tens digit and the units digit of y are the same, the range of possible values for y includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, y must be a multiple of 11. - As demonstrated above, if both x and y are a multiple of 11, we know that both x + y and x - y will be a multiple of 11.
- Statement (2) alone is SUFFICIENT.
- Since the tens digit and the units digit of x are the same, the range of possible values for x includes:
- Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.
Most Upvoted Answer
If both x and y are positive integers less than 100 and greater than 1...
- If both x and y are multiples of 11, then both x + y and x - y will be multiples of 11. In other words, if two numbers have a common divisor, their sum and difference retain that divisor.
In case this is hard to conceptualize, consider the following examples:
42 - 18 {both numbers share a common factor of 6}
=(6 x 7) - (6 x 3)
=6(7 - 3)
=6(4)
=24 {which is a multiple of 6}
49 + 14 {both numbers share a common factor of 7}
=(7 x 7) + (7 x 2)
=7(7+2)
=7*9
=63 {which is a multiple of 7} - However, if x and y are not both multiples of 11, it is possible that x - y is a multiple of 11 while x + y is not a multiple of 11. For example:
68 - 46 = 22 but 68 + 46 = 114, which is not divisible by 11.
The reason x - y is a multiple of 11 but not x + y is that, in this case, x and y are not individually multiples of 11. - Evaluate Statement (1) alone.
- Since x-y is a multiple of 22, x-y is a multiple of 11 and of 2 because 22 = 11 x 2
- If both x and y are multiples of 11, the sum x + y will also be a multiple of 11. Consider the following examples:
44 - 22 = 22 {which is a multiple of 11 and of 22}
44 + 22 = 66 {which is a multiple of 11 and of 22}
88 - 66 = 22 {which is a multiple of 11 and of 22}
88 + 66 = 154 {which is a multiple of 11 and of 22} - However, if x and y are not individually divisible by 11, it is possible that x - y is a multiple of 22 (and 11) while x + y is not a multiple of 11. For example:
78 - 56 = 22 but 78 + 56 = 134 is not a multiple of 11. - Statement (1) alone is NOT SUFFICIENT.
- Evaluate Statement (2) alone.
- Since the tens digit and the units digit of x are the same, the range of possible values for x includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, x must be a multiple of 11. - Since the tens digit and the units digit of y are the same, the range of possible values for y includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, y must be a multiple of 11. - As demonstrated above, if both x and y are a multiple of 11, we know that both x + y and x - y will be a multiple of 11.
- Statement (2) alone is SUFFICIENT.
- Since the tens digit and the units digit of x are the same, the range of possible values for x includes:
- Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.
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Community Answer
If both x and y are positive integers less than 100 and greater than 1...
Statement (1): x - y is a multiple of 22
Statement (2): The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same
To determine if the sum x + y is a multiple of 11, we need to consider the divisibility rules of 11.
Divisibility rule of 11: A number is divisible by 11 if the difference between the sum of its odd-placed digits and the sum of its even-placed digits is either 0 or a multiple of 11.
Considering each statement individually:
Statement (1) x - y is a multiple of 22:
- If x - y is a multiple of 22, it implies that the difference between x and y is divisible by 22.
- However, this statement does not provide any information about whether the sum x + y is a multiple of 11.
- Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same:
- This statement provides information about the digits of x and y, but it does not provide any information about the difference or sum of x and y.
- Therefore, statement (2) alone is not sufficient to answer the question.
Considering both statements together:
- Combining the information from both statements, we know that x and y have the same tens digit and the same units digit.
- However, this information alone is still not sufficient to determine whether the sum x + y is a multiple of 11.
- Therefore, the combined statements (1) and (2) together are not sufficient to answer the question.
Since neither statement alone nor the combined statements are sufficient, the correct answer is option B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Statement (2): The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same
To determine if the sum x + y is a multiple of 11, we need to consider the divisibility rules of 11.
Divisibility rule of 11: A number is divisible by 11 if the difference between the sum of its odd-placed digits and the sum of its even-placed digits is either 0 or a multiple of 11.
Considering each statement individually:
Statement (1) x - y is a multiple of 22:
- If x - y is a multiple of 22, it implies that the difference between x and y is divisible by 22.
- However, this statement does not provide any information about whether the sum x + y is a multiple of 11.
- Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same:
- This statement provides information about the digits of x and y, but it does not provide any information about the difference or sum of x and y.
- Therefore, statement (2) alone is not sufficient to answer the question.
Considering both statements together:
- Combining the information from both statements, we know that x and y have the same tens digit and the same units digit.
- However, this information alone is still not sufficient to determine whether the sum x + y is a multiple of 11.
- Therefore, the combined statements (1) and (2) together are not sufficient to answer the question.
Since neither statement alone nor the combined statements are sufficient, the correct answer is option B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
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If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer?
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If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. 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 If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer?.
If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. 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 If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer?.
Solutions for If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?(1) x - y is a multiple of 22(2) The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the samea)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;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 are needed.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
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