Is the positive integer n a multiple of 3?

Question

(1) (n – 1) is a multiple of 2
(2) (n + 1) is a multiple of 4

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GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • n is a positive integer.
• We need to find if n is a multiple of 3.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  (n – 1) is a multiple of 2
 • According to this statement, n = 2k + 1, where k is non-negative integer.
• So, n can be: 1, 3, 5, 7, 9, 11, 13, 15…. And so on.
 o We can see that n may or may not be a multiple of 3.  
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  (n + 1) is a multiple of 4
 • It means, n = 4p - 1, where p is a positive integer.
• So, n can be: 3, 7, 11,15, 19…. And so on 
 o If n = 3 or 15 etc. it is a multiple of 3, however if n = 7, 11 or 19 etc., it is not a multiple of 3.  
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining 
From statement 1: n can be 1, 3, 5, 7, 9, 11, 13, 15…. And so on.
From statement 2: n can be 3, 7, 11,15, 19…. And so on
On combining we get, n can be 3, 7, 11, 15…. And so on.
 • Still n can be or cannot be a multiple of 3. 
Thus, the correct answer is  Option E.

dimri10 · Answer

Statement 1: picking numbers. Not sufficient.
Statement 2: the same
Both: n-1, n, n+1 are consecutive. 
N-1 is even and n+1 is even . Thus N is odd. 
2,3,4 => n is divisible , 8, 9,10 N is divisble
4,5,6 or 6,7,8 => n is not.

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IanStewart · Answer

There's simply no relationship between divisibility by 2 (or by 4) and divisibility by 3, so there's no reason either Statement would even be useful here. Of course we can check numbers to confirm: using both Statements, n can be 3, which is divisible by 3, or n can be 7, which is not divisible by 3. So the answer is E.

CrackverbalGMAT · Answer

This is a question based on the concept of consecutive integers. 
Any set of 3 consecutive integers will always have a multiple of 3. As such, from the data given, we need to determine if the set of integers is in such a way that ‘n’ is a multiple of 3.

From statement I alone, (n-1) is a multiple of 2. In other words, (n-1) is even. 
If (n-1) = 2, n = 3. Is n a multiple of 3? YES.
If (n-1) = 4, n = 5. Is n a multiple of 3? NO.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, (n+1) is a multiple of 4. 
If (n+1) = 4, n = 3. Is n a multiple of 3? YES.
If (n+1) = 12, n = 11. Is n a multiple of 3? NO.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, we have the following:
From statement I, (n-1) is even. From statement II, (n+1) is a multiple of 4. 
If (n-1) = 2, n = 3 and (n+1) = 4. Both conditions are met. Is n a multiple of 3? YES.
If (n-1) = 10, n = 11 and (n+1) = 12. Both conditions are met. Is n a multiple of 3? NO.

The combination of statements is insufficient to give us a definite YES or NO. Answer option C can be eliminated. 
 The correct answer option is E .

Hope that helps!

sambitspm · Answer

Statement 1 => n-1 = 2k
n= 2k+1

But we need to check if n = 3p
Insufficient

Statement 2 => n+1 = 4m
n= 4m-1

But we need to check if n = 3p
Insufficient

Combining
n = 2k+1 = 3,5,7,9,11,13,15
n = 4m-1 = 3,7,11,15

Taking common set
3,7,11,15
Some are, some aren't multiples of 3

Insufficient.
E

Is the positive integer n a multiple of 3?

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