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Bunuel
What is the value of integer n ?

(1) n(n + 1) = 12
(2) 3^(n+1) = 81

Target question: What is the value of n?

Statement 1: n(n + 1) = 12
Expand: n² + n = 12
Rewrite as: n² + n - 12 = 0
Factor: (n + 4)(n - 3) = 0
So, EITHER n = -4 OR n = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3^(n+1) = 81
Rewrite 81 as 3^4 to get: 3^(n+1) = 3^4
So, we can conclude that n+1 = 4
Solve: n = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:
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What is the value of integer n ?

(1) n(n + 1) = 12
(2) 3^(n+1) = 81

Solution:

Statement 1: Tricky indeed. n can be 3 or n can be -4. So it is insufficient.
Statement 2: Only possible value of n is 3 as 3^(n+1)=3^(3+1)=81. Sufficient.

Therefore, the answer is Option B.
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Imo B
Statement 1 is insufficient as it gives the values of n as 3,-4
Statement 2 is sufficient as value of n is 3
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Bunuel
What is the value of integer n ?

(1) n(n + 1) = 12
(2) 3^(n+1) = 81

1) n = -4,3
Insufficient

2) 3^n = 3^3
=> n=3
Sufficient.

B
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Bunuel
What is the value of integer n ?

(1) n(n + 1) = 12
(2) 3^(n+1) = 81

Read the question carefully , it is asking whether we can find the value of integer n

Given : nothing
DS : Value of n

Option 1: n(n+1) = 12 = 3*4 (possible )=4*3(not possible ) = 12*1 (not possible) = 1*12 (not possible)
We must also check -ve values
n (n+1) = -4*-3 (possible)= -3*-4 , -12*-1, -1*-12 (not possible)

So n = -4, 3 .................NOT SUFFICIENT



Option 2: 3^(n+1) = 81
-> 3^(n+1) = 3^4
n = 3..........................SUFFICIENT

Answer B
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