If j is a positive integer, is (j^3-27)^2(j^3+1)^3 odd?

Question

If j is a positive integer, is  (j^3-27)^2(j^3+1)^3  odd?

(1) j + 2 is even

(2) 2j is even

Kudos for a correct  solution .

gk3391 · Answer

(1) j + 2 is even   -- > This statement shows J is even. 
 From this we can split  (j^3-27)^2(j^3+1)^3   as 
  (j^3-27)^2  --> Any (even)^3 is even and also (j^3-27) is odd. Same way  (j^3-27)^2 is odd  (odd*odd is odd).
  (j^3+1)^3  ---> even^3 is even and also even +odd is odd. Also (j^3+1) is odd. Same way as odd*odd is odd,  (j^3+1)^3 is odd.  . 
Therefore, (j^3-27)^2(j^3+1)^3 is odd (odd*odd) --->  Statement 1 is sufficient.

(2) 2j is even   ----> 2j is even when J is odd or even. therefore we cant deduce if j is odd or even from it. Hence  Statement 2 is not sufficient.

Correct me if i am wrong.

GMATinsight · Answer

Question : Is  (j^3-27)^2(j^3+1)^3  odd?

To answer this question, all we need is to know whether j is even or Odd

Statement 1 : j + 2 is even 
i.e. j is even
i.e.  (j^3-27)^2(j^3+1)^3  =  (Even-27)^2(Even+1)^3  = Odd*Odd = Odd
SUFFICIENT

Statement 1 : 2j is even 
i.e. j may be Even or Odd
NOT SUFFICIENT

Answer: option A

Skywalker18 · Answer

1. j+2 is even => j is even suppose j=4 (j^3-27)(j^3+1)^3 =(64-27)(64+1)^3 =37(65)^3 =Odd x Odd = Odd 2. 2j is even J may be even or odd 2j=6 j=3 2j=8 j=4

Answer A

longfellow · Answer

IMO A is the answer.

We need to find if J is even or not.

Statement 1 states that j+2 is even so j is also even

Statement 2 states 2j is even where by j could be either even or odd.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If j is a positive integer, is (j^3-27)^2(j^3+1)^3 odd?
 
(1) j + 2 is even
(2) 2j is even

If we modify the original condition and the question according to the Variable Approach Method, we ultimately want to know whether j is an even number as odd x odd=odd, j^3 -27=odd, and j^3+1=odd?
For condition 1, j+2=even, j=even-2=even. So j is an even number. This condition is sufficient.
For condition 2, 2j=even=2m(m=integer), j=integer. So this does not tell whether j is even. This condition is insufficient, and the answer is (A).

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

bumpbot · Answer

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If j is a positive integer, is (j^3-27)^2(j^3+1)^3 odd?

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