What is the value of integer n ? (1) n(n + 1)(n + 2) = 120 (2) n! = 24

Question

What is the value of positive integer n ?
 
(1) n(n + 1)(n + 2) = 120
(2) n! = 24

kumarparitosh123 · Answer

Statement 1 : n=4.
Sufficient.

Statement 2: n=4
Each alone is sufficient.

Answer is D.

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Nikkb · Answer

Find : n <- integer given

(1) n(n + 1)(n + 2) = 120
=> 120 = 4*5*6 ( we don't have to worry about negative numbers as product of 3 -ve numbers is -ve but given number is +ve)
=> n=4
Sufficient

(2) n! = 24 
1*2*3*4 = 24
Therefore n=4 , 4! =24
Sufficient

Answer: D

IanStewart · Answer

The question needs to tell you n is a positive integer, or else test takers might wonder if they need to understand what n! means when n is negative (there's no consensus in math about how to define factorials for negatives, but i've seen at least one paper that proposes (-4)! should equal 24, though that's a non-standard view). Any real GMAT question with "n!" in it will tell you in advance that n is a positive integer, to ensure the expression is properly defined.

If we know n is a positive integer, then the larger n is, the larger (n)(n+1)(n+2) is. So there can only be one conceivable positive value of n that makes (n)(n+1)(n+2) precisely equal to 120, and Statement 1 is sufficient. Similarly, the larger n is, the larger n! is, so only one value of n can make Statement 2 true. It's DS, so there's no reason to actually solve for n, and the answer is D.

AnirudhaS · Answer

(1) n(n + 1)(n + 2) = 120
We dont need to solve it, since n is a positive integer and the expression means product of 3 consecutive integers, then n must be ONE number
Sufficient

(2) n! = 24
In gmat we only consider positive factorials, so n must be 4
Sufficient

**Just checking n=4 in (1) 4*5*6=120, aha!! We saved some time not bothering with the solution of the equation!

Answer:  D

hiranmay · Answer

What is the value of positive integer n ?
 
(1) n(n + 1)(n + 2) = 120-->  suff: n(n + 1)(n + 2) = 120=2^3*3*5=2*3*4*5=4*5*6, so n=4 
(2) n! = 24 -->  suff: n! = 24 = 2^3*3=1*2*3*4=4!, so n=4
 Answer: D

hardikjain · Answer

n is a positive integer.

statement 1: multiplication of three positive consecutive integer is 120.

put, n=4. sufficient

statement 2: again 4!=24, n=4
sufficient

What is the value of integer n ? (1) n(n + 1)(n + 2) = 120 (2) n! = 24

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GMAT Data Sufficiency (DS) Questions

What is the value of integer n ? (1) n(n + 1)(n + 2) = 120 (2) n! = 24

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