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13 Jan 2022, 02:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:47) correct
31%
(02:23)
wrong
based on 68
sessions
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If n is a positive integer, Is n^2 + 4n + 3 divisible by 4?
(1) n is not divisible by 4
(2) n + 2 is divisible by 4
(1) n is not divisible by 4
(2) n + 2 is divisible by 4
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
13 Jan 2022, 02:57
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Pre-thinking: (n^2 + 4n + 3)/4 = n + (n^2 + 3)/4
The question "Is n^2 + 4n + 3 divisible by 4?" can be simplified to be
Is n^2 + 3 divisible by 4?
(1) Only.
If n = 1, n^2 + 3 = 4 is divisible by 4
If n = 2, n^2 + 3 = 7 is not divisible by 4
Not Sufficient.
(2) Only
Try n =2. 7 is not divisible by 4
Try n =6. 39 is not divisible by 4
Now, we realize that n has to be an even number (in order to satisfy the condition that n + 2 is divisible by 4)
So n^2 remains an even number
n^2 + 3 is an odd number
An odd number can never be divisible by 4.
Sufficient.
The answer is (B).
The question "Is n^2 + 4n + 3 divisible by 4?" can be simplified to be
Is n^2 + 3 divisible by 4?
(1) Only.
If n = 1, n^2 + 3 = 4 is divisible by 4
If n = 2, n^2 + 3 = 7 is not divisible by 4
Not Sufficient.
(2) Only
Try n =2. 7 is not divisible by 4
Try n =6. 39 is not divisible by 4
Now, we realize that n has to be an even number (in order to satisfy the condition that n + 2 is divisible by 4)
So n^2 remains an even number
n^2 + 3 is an odd number
An odd number can never be divisible by 4.
Sufficient.
The answer is (B).
13 Jan 2022, 11:20
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If n is a positive integer, Is n^2 + 4n + 3 divisible by 4?
Stat1: n is not divisible by 4,
n= 1 or 2, for n= 1, n^2 + 4n + 3 is divisible by 4. But for n= 2, n^2 + 4n + 3 is not divisible by 4. Not sufficient.
Stat2: n + 2 is divisible by 4
n= 2, 6, 10,....for all such value of n, n^2 + 4n + 3 is not divisible by 4. Sufficient.
So, I think B.
Stat1: n is not divisible by 4,
n= 1 or 2, for n= 1, n^2 + 4n + 3 is divisible by 4. But for n= 2, n^2 + 4n + 3 is not divisible by 4. Not sufficient.
Stat2: n + 2 is divisible by 4
n= 2, 6, 10,....for all such value of n, n^2 + 4n + 3 is not divisible by 4. Sufficient.
So, I think B.
