Is the integer n ODD?
1. (n^2) - n is NOT a multiple of 4
2. n is a multiple of 3
Doubt: [spoiler]Is 0 a multiple of n?[/spoiler]
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is the integer n ODD?
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vk_vinayak
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adthedaddy
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Zero is the multiple of all numbers.
Check Stuart's reply in a similar discussion: https://www.beatthegmat.com/is-zero-to-b ... t4268.html
To the above problem, in my opinion, the answer should be (E)
Case-1:
For n=2, n^2-n=2 which is not a multiple of 4 ; n is even
For n=3, n^2-n=6 which is not a multiple of 4 ; n is odd
NOT SUFFICIENT
Case-2:
n is a multiple of 3
Zero being a multiple of 3 and it is even so this condition is NOT SUFFICIENT
Together:
'n' is a multiple of 3 & n^2-n is not a multiple of 4
For n= -6 ; n^2-n = 36-(-6)=36+6=42 which not a multiple of 4 ; Integer 'n' is Even
For n= 3; n^2-n = 6 which is not a multiple of 4 ; Integer 'n' is Odd
NOT SUFFICIENT
Thus, ans is (E)
Check Stuart's reply in a similar discussion: https://www.beatthegmat.com/is-zero-to-b ... t4268.html
To the above problem, in my opinion, the answer should be (E)
Case-1:
For n=2, n^2-n=2 which is not a multiple of 4 ; n is even
For n=3, n^2-n=6 which is not a multiple of 4 ; n is odd
NOT SUFFICIENT
Case-2:
n is a multiple of 3
Zero being a multiple of 3 and it is even so this condition is NOT SUFFICIENT
Together:
'n' is a multiple of 3 & n^2-n is not a multiple of 4
For n= -6 ; n^2-n = 36-(-6)=36+6=42 which not a multiple of 4 ; Integer 'n' is Even
For n= 3; n^2-n = 6 which is not a multiple of 4 ; Integer 'n' is Odd
NOT SUFFICIENT
Thus, ans is (E)
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E
Went about it by plugging numbers in the equations
Statement no 1
N^2-n is not divisible by 4
Plug in different numbers
In case of 2 it is even but n^2-n yields 2 which is not a multiple of 4
Similarly plug in 4 and n^2-n yields 13 which is a multiple of 4
Therefore n can/cannot be even
Whereas -3 is odd but n^2-n yields 12 which is a multiple of 4
Similarly 3 is odd but n^2-n yields 6 which is not a multiple of 4
Therefore n can/cannot be odd
Hence statement 1 alone must not be sufficient as conflict
Statement 2
Multiples of 3: 3,6,9,12..... Which are odd as well as even
Therefore statement 2 is also insufficient
Combining the two statements
Plug in 3,6,9,12 in n^2-n we he get that none of the multiples of 3 (both even and odd) result in answers that are multiples of 4. Hence both statements together are insufficient. Answer must be E
Went about it by plugging numbers in the equations
Statement no 1
N^2-n is not divisible by 4
Plug in different numbers
In case of 2 it is even but n^2-n yields 2 which is not a multiple of 4
Similarly plug in 4 and n^2-n yields 13 which is a multiple of 4
Therefore n can/cannot be even
Whereas -3 is odd but n^2-n yields 12 which is a multiple of 4
Similarly 3 is odd but n^2-n yields 6 which is not a multiple of 4
Therefore n can/cannot be odd
Hence statement 1 alone must not be sufficient as conflict
Statement 2
Multiples of 3: 3,6,9,12..... Which are odd as well as even
Therefore statement 2 is also insufficient
Combining the two statements
Plug in 3,6,9,12 in n^2-n we he get that none of the multiples of 3 (both even and odd) result in answers that are multiples of 4. Hence both statements together are insufficient. Answer must be E
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Brent@GMATPrepNow
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Target question: Is the integer n ODD?vk_vinayak wrote:Is the integer n ODD?
1. (n^2) - n is NOT a multiple of 4
2. n is a multiple of 3
Statement 1: (n^2) - n is NOT a multiple of 4
Important: When it comes to integer properties questions such as this, it's useful to know that expressions like n^2 - n are a tricky way of hiding some helpful information about the variable.
In this case, we can rewrite n^2 - n as n(n-1) or (n-1)(n)
Now notice that n-1 and n are two consecutive integers.
So, statement 1 is telling us that the product of two consecutive integers is not divisible by 4.
Given this, we can consider two cases (among many)
case a: n-1 = 2 and n = 3, in which case n is odd.
case b: n-1 = 5 and n = 6, in which case n is not odd.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is a multiple of 3
Given this information, we can consider two cases (among many)
case a: n-1 = 2 and n = 3, in which case n is odd.
case b: n-1 = 5 and n = 6, in which case n is not odd.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 & 2:
Even when we combine the two statements, we can still have conflicting answers to the target question. Here are two possible cases (among many)
case a: n-1 = 2 and n = 3, in which case n is odd.
case b: n-1 = 5 and n = 6, in which case n is not odd.
Since we cannot answer the target question with certainty, statements 1 & 2 combined are NOT SUFFICIENT
Answer = E
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
