Hi,

This question is from GMATPrep Practicse Test -2.

If |x+2| = 4. What is the value of x?

1) X^2 is not equal to 4.

2) x^2 = 36.

Evaluating |x+2| = 4 gives two values x= 2 when x is positive and x = -6 when x is negative.

The OA is D. But I marked A as the answer cuz According to me the second option gives two values -6 and 6.

My doubt is how does the second statement also give the solution for x.

Thanks

your evaluation of question statement is correct

|X+2| = 4 gives the following:

X+2 = + 4 >> X = 2 and X+2 = - 4 >> X = -6

1) X^2 is not equal to 4 >> X not equal to + 2 & -2, using with question statement gives X = -6 (unique soln)

2) x^2 = 36 >> X = + 6 and X = -6, using with question statement gives X = - 6 (unique soln)

The question gives 2 values of X and so does each of the statements 1 and 2, but look at the common solution of the Question and individual statements, which gives a single solution. (this may not seem natural approach, but questions like these might require to find if there is a unique value in both question and solution statements)

Hope it helps

Statement 2 works because x=6 and x=-6, it means that answer is 'no' No x in not equal to either 2 or -2. In data sufficiency the answer 'no' is something enough.
I hope it helped

Capthan

Statement 2 works because x=6 and x=-6, it means that answer is 'no' No x in not equal to either 2 or -2. In data sufficiency the answer 'no' is something enough.
I hope it helped

Capthan
correction:
Sorry about misspelling of 'sometime'(something=sometimes. :)

whoa, no.
this isn't even a yes/no question.

the correct way to rephrase the prompt is this: you have to realize that whatever follows "if" is a GIVEN CONDITION that must ALWAYS be true. so, in this problem, it is a fact, which can be taken essentially as gospel, that |x + 2| = 4.
therefore, they are telling you, flat out, that x is either 2 or -6.

notice that this is NOT a yes/no question; it's a value question. still, we can rephrase it, because x can't be any number; it can only be one of 2 or -6. therefore, here's the best rephrase of this question:

** WHICH of 2 or -6 is x? **

there's your rephrase.

statement (1):
rephrase: x is neither 2 nor -2.
therefore, x must be -6.
sufficient.

statement (2):
rephrase: x is either 6 or -6.
between these two, the only one on the proverbial VIP guest list is -6 (remember that the only numbers on the guest list are 2 and -6), so x must be -6.
sufficient.

answer = (d).

--

epilogue:
your workup rejects statement (2) because "it gives two values -6 and 6". by this logic (which is incorrect), you should have also rejected statement (1), because it gives infinitely many values (i.e., ALL numbers except 2 or -2).