DS

[ketkoag]

What is the value of |x + 7|?
(1)|x + 3|= 14
(2) (x + 2)^2 = 169

Now here OA is : D but my answer is C coz if i take first, i get x=11, x = -17 insufficient.
By statement 2, x = 11, x = -13 insufficient.

By taking both the statements, x = 11 and hence we can calculate value of |x + 7|. hence Sufficient.
Please explain if i am missing something.....

[Jose Ferreira]

Hi,

First off, you are right. The answer is C.

Perhaps a more important point is that we should always be careful to note exactly what we have been asked to solve for. In this case, we need to find the value of |x + 7|. This is NOT the same as being asked to find x.

For example, let's say that one of the statements simplifies to x = -9 or x = -5. This statement does NOT allow us to find the value of x, but note that it DOES allow us to find the value of |x + 7|:
|-9 + 7| = |-2| = 2, and |-5 + 7| = |2| = 2. Both values of x (-9, -5) give us the same value of |x + 7| = 2.

So, the fact that a statement gives us two different values for x does not necessarily mean it will give us two different values for |x + 7|.

That said, the first statement gives us x = -17 or x = 11, as you said. This means that |x + 7| = |-17 + 7| = |-10| = 10, or |x + 7| = |11 + 7| = |18| = 18. So in this case, we do get two different values of |x + 7|.

The second statement gives us x = -15 or x = 11 (be careful with the negative value here). This means that |x + 7| = |-15 + 7| = |-8| = 8, or |x + 7| = |11 + 7| = |18| = 18. In this case, we also get two different values of |x + 7|.

When we combine the statements:
S1: |x + 7| = 10 or 18
S2: |x + 7| = 8 or 18
So |x + 7| must be 18, since that it the only value that meets the conditions in both statements.

[ketkoag]

thanks a lot for you reply.
Yes i messed up with the values in the explanation, but i think u get the concept of different values!
Thanks again..