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What is the remainder of a positive integer N when it is divided by 2?
1. N contains odd numbers as factors
2. N is a multiple of 15
1. N contains odd numbers as factors
2. N is a multiple of 15
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer?
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Most Upvoted Answer
What is the remainder of a positive integer N when it is divided by 2?...
Any positive integer that is divided by 2 will have a remainder of 1 if it is odd. However, it will not have a remainder if it is even.
N/2 → Remainder = 0 if N is even
N/2 → Remainder = 1 if N is odd
Evaluate Statement (1) alone.
If a number contains only odd factors, it will be odd (and will have a remainder of 1 when divided by 2). If a number contains at least one even factor, it will be even (and divisible by 2).
15 = 3*5 {only odd factors; not divisible by 2; remainder of 1}
21 = 3*7 {only odd factors; not divisible by 2; remainder of 1}
63 = 3*3*7 {only odd factors; not divisible by 2; remainder of 1}
N/2 → Remainder = 0 if N is even
N/2 → Remainder = 1 if N is odd
Evaluate Statement (1) alone.
If a number contains only odd factors, it will be odd (and will have a remainder of 1 when divided by 2). If a number contains at least one even factor, it will be even (and divisible by 2).
15 = 3*5 {only odd factors; not divisible by 2; remainder of 1}
21 = 3*7 {only odd factors; not divisible by 2; remainder of 1}
63 = 3*3*7 {only odd factors; not divisible by 2; remainder of 1}
30 = 3*5*2 {contains an even factor; divisible by 2}
42 = 3*7*2 {contains an even factor; divisible by 2}
50 = 5*5*2 {contains an even factor; divisible by 2}
Simply because "N contains odd numbers as factors" does not mean that all of N's factors are odd. Consequently, it is entirely possible that N contains an even factor, in which case N is even and N is divisible by 2. Possible values for N:
18 = 2*3*3 {contains odd factors, but is divisible by 2; remainder = 0}
30 = 2*5*3 {contains odd factors, but is divisible by 2; remainder = 0}
But:
27 = 3*3*3 {contains odd factors, but is not divisible by 2; remainder = 1}
15 = 3*5 {contains odd factors, but is not divisible by 2; remainder = 1}
Since some values of N that meet the conditions of Statement (1) are divisible by 2 while other values that also meet the conditions of Statement (1) are not divisible by 2, Statement (1) does not provide sufficient information to definitively determine whether N is divisible by 2.
Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
Since "N is a multiple of 15", possible values for N include:
15, 30, 45, 60, 75, 90
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statement (2) is not sufficient for determining the remainder when N is divided by 2.
Statement (2) alone is NOT SUFFICIENT.
Evaluate Statements (1) and (2).
Since "N is a multiple of 15" and "N contains odd numbers as factors", possible values for N include:
15, 30, 45, 60, 75, 90
Adding Statement (1) to Statement (2) does not provide any additional information since any number that is a multiple of 15 must also have odd numbers as factors.
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statements (1) and (2) are not sufficient for determining the remainder when N is divided by 2.
Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer E is correct.
42 = 3*7*2 {contains an even factor; divisible by 2}
50 = 5*5*2 {contains an even factor; divisible by 2}
Simply because "N contains odd numbers as factors" does not mean that all of N's factors are odd. Consequently, it is entirely possible that N contains an even factor, in which case N is even and N is divisible by 2. Possible values for N:
18 = 2*3*3 {contains odd factors, but is divisible by 2; remainder = 0}
30 = 2*5*3 {contains odd factors, but is divisible by 2; remainder = 0}
But:
27 = 3*3*3 {contains odd factors, but is not divisible by 2; remainder = 1}
15 = 3*5 {contains odd factors, but is not divisible by 2; remainder = 1}
Since some values of N that meet the conditions of Statement (1) are divisible by 2 while other values that also meet the conditions of Statement (1) are not divisible by 2, Statement (1) does not provide sufficient information to definitively determine whether N is divisible by 2.
Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
Since "N is a multiple of 15", possible values for N include:
15, 30, 45, 60, 75, 90
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statement (2) is not sufficient for determining the remainder when N is divided by 2.
Statement (2) alone is NOT SUFFICIENT.
Evaluate Statements (1) and (2).
Since "N is a multiple of 15" and "N contains odd numbers as factors", possible values for N include:
15, 30, 45, 60, 75, 90
Adding Statement (1) to Statement (2) does not provide any additional information since any number that is a multiple of 15 must also have odd numbers as factors.
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statements (1) and (2) are not sufficient for determining the remainder when N is divided by 2.
Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer E is correct.
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Community Answer
What is the remainder of a positive integer N when it is divided by 2?...
Any positive integer that is divided by 2 will have a remainder of 1 if it is odd. However, it will not have a remainder if it is even.
N/2 → Remainder = 0 if N is even
N/2 → Remainder = 1 if N is odd
Evaluate Statement (1) alone.
If a number contains only odd factors, it will be odd (and will have a remainder of 1 when divided by 2). If a number contains at least one even factor, it will be even (and divisible by 2).
15 = 3*5 {only odd factors; not divisible by 2; remainder of 1}
21 = 3*7 {only odd factors; not divisible by 2; remainder of 1}
63 = 3*3*7 {only odd factors; not divisible by 2; remainder of 1}
N/2 → Remainder = 0 if N is even
N/2 → Remainder = 1 if N is odd
Evaluate Statement (1) alone.
If a number contains only odd factors, it will be odd (and will have a remainder of 1 when divided by 2). If a number contains at least one even factor, it will be even (and divisible by 2).
15 = 3*5 {only odd factors; not divisible by 2; remainder of 1}
21 = 3*7 {only odd factors; not divisible by 2; remainder of 1}
63 = 3*3*7 {only odd factors; not divisible by 2; remainder of 1}
30 = 3*5*2 {contains an even factor; divisible by 2}
42 = 3*7*2 {contains an even factor; divisible by 2}
50 = 5*5*2 {contains an even factor; divisible by 2}
Simply because "N contains odd numbers as factors" does not mean that all of N's factors are odd. Consequently, it is entirely possible that N contains an even factor, in which case N is even and N is divisible by 2. Possible values for N:
18 = 2*3*3 {contains odd factors, but is divisible by 2; remainder = 0}
30 = 2*5*3 {contains odd factors, but is divisible by 2; remainder = 0}
But:
27 = 3*3*3 {contains odd factors, but is not divisible by 2; remainder = 1}
15 = 3*5 {contains odd factors, but is not divisible by 2; remainder = 1}
Since some values of N that meet the conditions of Statement (1) are divisible by 2 while other values that also meet the conditions of Statement (1) are not divisible by 2, Statement (1) does not provide sufficient information to definitively determine whether N is divisible by 2.
Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
Since "N is a multiple of 15", possible values for N include:
15, 30, 45, 60, 75, 90
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statement (2) is not sufficient for determining the remainder when N is divided by 2.
Statement (2) alone is NOT SUFFICIENT.
Evaluate Statements (1) and (2).
Since "N is a multiple of 15" and "N contains odd numbers as factors", possible values for N include:
15, 30, 45, 60, 75, 90
Adding Statement (1) to Statement (2) does not provide any additional information since any number that is a multiple of 15 must also have odd numbers as factors.
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statements (1) and (2) are not sufficient for determining the remainder when N is divided by 2.
Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer E is correct.
42 = 3*7*2 {contains an even factor; divisible by 2}
50 = 5*5*2 {contains an even factor; divisible by 2}
Simply because "N contains odd numbers as factors" does not mean that all of N's factors are odd. Consequently, it is entirely possible that N contains an even factor, in which case N is even and N is divisible by 2. Possible values for N:
18 = 2*3*3 {contains odd factors, but is divisible by 2; remainder = 0}
30 = 2*5*3 {contains odd factors, but is divisible by 2; remainder = 0}
But:
27 = 3*3*3 {contains odd factors, but is not divisible by 2; remainder = 1}
15 = 3*5 {contains odd factors, but is not divisible by 2; remainder = 1}
Since some values of N that meet the conditions of Statement (1) are divisible by 2 while other values that also meet the conditions of Statement (1) are not divisible by 2, Statement (1) does not provide sufficient information to definitively determine whether N is divisible by 2.
Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
Since "N is a multiple of 15", possible values for N include:
15, 30, 45, 60, 75, 90
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statement (2) is not sufficient for determining the remainder when N is divided by 2.
Statement (2) alone is NOT SUFFICIENT.
Evaluate Statements (1) and (2).
Since "N is a multiple of 15" and "N contains odd numbers as factors", possible values for N include:
15, 30, 45, 60, 75, 90
Adding Statement (1) to Statement (2) does not provide any additional information since any number that is a multiple of 15 must also have odd numbers as factors.
Possible values for N give different remainders when divided by 2:
15/2 → Remainder = 1
30/2 → Remainder = 0
45/2 → Remainder = 1
60/2 → Remainder = 0
75/2 → Remainder = 1
90/2 → Remainder = 0
Since different legitimate values of N give different remainders when divided by 2, Statements (1) and (2) are not sufficient for determining the remainder when N is divided by 2.
Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer E is correct.
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What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer?
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What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. 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 What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer?.
What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. 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 What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer?.
Solutions for What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer?, a detailed solution for What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer? has been provided alongside types of What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the remainder of a positive integer N when it is divided by 2?1. N contains odd numbers as factors2. N is a multiple of 15a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer thequestion asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer thequestion 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 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.
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