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705-805 (Hard)|   Algebra|   Exponents|      
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Bunuel
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What is the value of the integer n? (1) n^2+ 3n = 4 (2) (n + 3)^n = 1 02 Feb 2023, 06:00
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Difficulty:

75% (hard)

Question Stats:

38% (01:32) correct 62% (01:27) wrong based on 55 sessions

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What is the value of the integer n?

(1) \(n^2+ 3n = 4\)
(2) \((n + 3)^n = 1\)
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C
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gmatophobia
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What is the value of the integer n? (1) n^2+ 3n = 4 (2) (n + 3)^n = 1 02 Feb 2023, 07:18
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What is the value of the integer n?

(1) \(n^2+ 3n = 4\)
(2) \((n + 3)^n = 1\)
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Statement 1

(1) \(n^2+ 3n = 4\)

\(n^2+ 3n - 4 = 0\)

\(n^2+ 4n - n - 4 = 0\)

\((n-1)(n+4) = 0\)

n = 1 or n = -4

As we have two possible values of n, the statement is not sufficient. We can eliminate A and D.

Statement 2

(2) \((n + 3)^n = 1\)

\(n = 0; (0 + 3)^0 = 1\)

\(n = -2; (-2 + 3)^{-2} = 1^{-2} = 1\)

The statement is not sufficient. Hence eliminate B.

Combined

The statements combined give n = -4

Hence sufficient.

Option C
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What is the value of the integer n? (1) n^2+ 3n = 4 (2) (n + 3)^n = 1 02 Feb 2023, 07:20
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Bunuel
What is the value of the integer n?

(1) \(n^2+ 3n = 4\)
(2) \((n + 3)^n = 1\)

Statement 1

(1) \(n^2+ 3n = 4\)

\(n^2+ 3n - 4 = 0\)

\(n^2+ 4n - n - 4 = 0\)

\((n-1)(n+4) = 0\)

n = 1 or n = -4

As we have two possible values of n, the statement is not sufficient. We can eliminate A and D.

Statement 2

(2) \((n + 3)^n = 1\)

\(n = 0; (0 + 3)^0 = 1\)

\(n = -2; (-2 + 3)^{-2} = 1^{-2} = 1\)

The statement is not sufficient. Hence eliminate B.

Combined

The statements combined give n = -4

Hence sufficient.

Option C
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Combined statements give n=1

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What is the value of the integer n? (1) n^2+ 3n = 4 (2) (n + 3)^n = 1 02 Feb 2023, 07:27
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ChanSu


Combined statements give n=1

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ChanSu - Can you please elaborate on the reasoning?

IMO, If n = 1, Statement 2 gets violated

\((1+3)^1 \neq 1\)

Let me know if I am missing anything.
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What is the value of the integer n? (1) n^2+ 3n = 4 (2) (n + 3)^n = 1 02 Feb 2023, 07:46
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ChanSu


Combined statements give n=1

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ChanSu - Can you please elaborate on the reasoning?

IMO, If n = 1, Statement 2 gets violated

\((1+3)^1 \neq 1\)

Let me know if I am missing anything.
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Sry . My bad . N=-4 is correct

But your statement 2 should written as (-4+3) ^-4 = 1 which translates to n=-4
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What is the value of the integer n? (1) n^2+ 3n = 4 (2) (n + 3)^n = 1 02 Feb 2023, 07:59
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ChanSu


Sry . My bad . N=-4 is correct

But your statement 2 should written as (-4+3) ^-4 = 1 which translates to n=-4
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n = -4 is a valid value for Statement 2, so is n = -2 and n = 0.

In DS question, each statement needs to be evaluated in isolation. It is not necessary to find out / conclude all possible values that a variable can hold in a particular statement. For ex. In this question, the moment we conclude that n can have multiple values in Statment 2, we can reject that statement and move to the subsequent step. One may take n = -4 as a possible value in Statement 2 to conclude insufficiency, which is perfectly fine, but it's not necessary to do so.

Only when the statements are combined, any additional values from Statement 1 can be evaluated in light of Statement 2 (or vice versa).
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What is the value of the integer n? (1) n^2+ 3n = 4 (2) (n + 3)^n = 1 02 Feb 2023, 09:21
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ChanSu


Sry . My bad . N=-4 is correct

But your statement 2 should written as (-4+3) ^-4 = 1 which translates to n=-4

n = -4 is a valid value for Statement 2, so is n = -2 and n = 0.

In DS question, each statement needs to be evaluated in isolation. It is not necessary to find out / conclude all possible values that a variable can hold in a particular statement. For ex. In this question, the moment we conclude that n can have multiple values in Statment 2, we can reject that statement and move to the subsequent step. One may take n = -4 as a possible value in Statement 2 to conclude insufficiency, which is perfectly fine, but it's not necessary to do so.

Only when the statements are combined, any additional values from Statement 1 can be evaluated in light of Statement 2 (or vice versa).
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Got it. But n=-4 needs to be considered in this case because when you combine statements 1 and 2 (after you’re done evaluating statement 2) , n=-4 will be common to both

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