was wondering if 0 is an even interger for a question like this:
If n is an integer, is n even?
(1) n2 −1 is an odd integer.
(2) 3n + 4 is an even integer.
is 0 an even integer?
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This is one of the problem from the "tough math problems set" floating around on this site......Ian Stewart wrote:Yes, 0 is always an even integer.
51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A.14 B.15. C.16 D.17 E.18
Soln: if we arrange this in AP, we get
4+7+10+.......+49
so 4+(n-1)3=49: n=16
C is my pick
They have not considered 1 as one of the options......is this incorrect?
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1 has to be a part of it since it leaves a remainder of 1 when divided by 3aniruddhkashyap wrote:This is one of the problem from the "tough math problems set" floating around on this site......Ian Stewart wrote:Yes, 0 is always an even integer.
51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A.14 B.15. C.16 D.17 E.18
Soln: if we arrange this in AP, we get
4+7+10+.......+49
so 4+(n-1)3=49: n=16
C is my pick
They have not considered 1 as one of the options......is this incorrect?
so the solution quoted is incorrect, in my opinion
n=17 is the correct answer
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CITI29 wrote:was wondering if 0 is an even interger for a question like this:
If n is an integer, is n even?
(1) n2 −1 is an odd integer.
(2) 3n + 4 is an even integer.
(1)
Implies n^2 is even which means n is even
Hence Suff.
(2)
Since 3n+4 is even
and even + even = even
Hence 3n must be even, that means n is even
Hence Suff
Answer D
And to reiterate what Ian said, 0 zero is a non-positive, non -negative even integer.
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A positive integer divisor n has exactly n number of possible remainders to succumb. In case the dividend is smaller than the divisor, the remainder happens to be same in value as the dividend. In the presented example, 1 is a member of list so the account is erroneous.aniruddhkashyap wrote:This is one of the problem from the "tough math problems set" floating around on this site......Ian Stewart wrote:Yes, 0 is always an even integer.
51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A.14 B.15. C.16 D.17 E.18
Soln: if we arrange this in AP, we get
4+7+10+.......+49
so 4+(n-1)3=49: n=16
C is my pick
They have not considered 1 as one of the options......is this incorrect?
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Claudia,
0 is a non negative even integer.
Regards
Anup
0 is a non negative even integer.
Regards
Anup
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(A) 0 is an even integer.[email protected] wrote:Is zero positive?
(B) 0 is a neutral integer too, hence 0 is neither positive nor negative.
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Target question: Is n even?CITI29 wrote: If n is an integer, is n even?
(1) n^2 −1 is an odd integer.
(2) 3n + 4 is an even integer.
Statement 1: n^2 −1 is an odd integer.
If n^2 −1 is an odd integer, then n^2 must be an even integer.
If n^2 is an even integer, then n must be even.
Rationale: (odd)^2 - odd, but (even)^2 = even
As such, statement 1 is SUFFICIENT
Statement 2: 3n + 4 is an even integer.
If 3n + 4 is an even integer, then 3n must be an even integer (since Even + Even = Even).
If 3n must be an even integer, then n must be even.
Rationale: (odd)(even) = even and
As such, statement 2 is SUFFICIENT
Answer = D
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If anyone wants to practice more Data Sufficiency questions involving odd and even integers, here are a few more:
https://www.beatthegmat.com/what-about- ... 17014.html
https://www.beatthegmat.com/is-the-inte ... 19182.html
https://www.beatthegmat.com/og-13th-ds- ... 22138.html
https://www.beatthegmat.com/even-or-not ... nt=Chicago
Cheers,
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https://www.beatthegmat.com/what-about- ... 17014.html
https://www.beatthegmat.com/is-the-inte ... 19182.html
https://www.beatthegmat.com/og-13th-ds- ... 22138.html
https://www.beatthegmat.com/even-or-not ... nt=Chicago
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Type of Question: Yes or NoCITI29 wrote:was wondering if 0 is an even interger for a question like this:
If n is an integer, is n even?
(1) n2 −1 is an odd integer.
(2) 3n + 4 is an even integer.
We need to find out whether n is even.
ST 1: n^2 - 1 is odd. Therefore n^2 and 1 should have opposite parity. 1 is odd. hence n^2 should be even. n is even. Is n even? We have a definite YES! SUFFICIENT.
ST 2: 3n + 4 is even. In this case too both the numbers should have the same parity. 4 is even. 3n should be even. 3 is odd. Hence n should be even. Is n even? We have a definite YES! SUFFICIENT.
OA: D
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Hi All,
We're told that N is an INTEGER. We're asked if N is EVEN. This is a YES/NO question (and to answer the initial question posted - YES, zero is an EVEN integer). This question can be answered by TESTing VALUES or with Number Property rules.
1) N^2 -1 is an ODD integer.
Since N^2 - 1 = Odd
N^2 = Odd + 1
N^2 = Even
We're told that N is an INTEGER, and the only types of integers that end up EVEN when SQUARED are EVEN integers. Thus, N MUST be Even and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
2) 3N + 4 is an EVEN integer.
Since 3N + 4 = Even
3N = Even - 4
3N = Even
(Odd)(N) = Even
Since the product of the two integers is EVEN, at least one of the two integers MUST be even. Since 3 is Odd, N must be Even - and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: D
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Rich
We're told that N is an INTEGER. We're asked if N is EVEN. This is a YES/NO question (and to answer the initial question posted - YES, zero is an EVEN integer). This question can be answered by TESTing VALUES or with Number Property rules.
1) N^2 -1 is an ODD integer.
Since N^2 - 1 = Odd
N^2 = Odd + 1
N^2 = Even
We're told that N is an INTEGER, and the only types of integers that end up EVEN when SQUARED are EVEN integers. Thus, N MUST be Even and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
2) 3N + 4 is an EVEN integer.
Since 3N + 4 = Even
3N = Even - 4
3N = Even
(Odd)(N) = Even
Since the product of the two integers is EVEN, at least one of the two integers MUST be even. Since 3 is Odd, N must be Even - and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
Final Answer: D
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Rich
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We need to determine whether integer n is even.CITI29 wrote:was wondering if 0 is an even interger for a question like this:
If n is an integer, is n even?
(1) n2 −1 is an odd integer.
(2) 3n + 4 is an even integer.
Statement One Alone:
n^2 - 1 is an odd integer.
Since n^2 - 1 is an odd integer, we know that n^2 must be even and thus n must be even.
Statement one is sufficient to answer the question.
Statement Two Alone:
3n + 4 is an even integer.
Since 3n + even = even integer, we know that 3n must be even, and since 3 is odd, n must be even. Statement two is sufficient to answer the question.
Answer: D
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