Question

Is x a natural number?

(1) |x + 3| = 4x - 3
(2) |x + 1| = 2x - 1

• A. IF statement (1) alone is sufficient, but statement (2) is not
• B. If Statement (2) alone is sufficient but statement (1) is not
• C. If Each statement ALONE is sufficient
• D. Statements (1) and (2) TOGETHER are not sufficient

Answer 1

The correct option is C If Each statement ALONE is sufficient

From Statement 1

x + 3 = 4x - 3
6 = 3x
x=2
When x + 3 is positive,x= 2, a positive value. X=2 satisfies the original equation

And

-1(x + 3) = 4x - 3
-x - 3 = 4x - 3
0 = 5x
0 = x

But x=0 does not satisfy the original equation

Therefore, there is no solution when x + 3 is negative and we know that 2 is the only solution possible and we can say that x is definitely positive.

Statement 2

|x + 1| = 2x - 1
x + 1 = 2x - 1
x = 2.

Here again, x = 2 satisfies the original equation.

And

|x + 1| = 2x - 1 $\Rightarrow$-x - 1 = 2x - 1 $\Rightarrow$ x = 0
x = 0 does not satisfy the original equation.

We can determine using each statement alone, that the answer can be obtained as x=2 . Answer is option (C)