DS on Absolute value

[getso]

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


Ans is D...but I feel it should be C

[iamseer]

can't see the characters correctly. please do the needful

[thephoenix]

agreed it has to be C
wats the source

[getso]

Source I'm not really sure..

I have a doc file which says questions are from previous OG and GMAT.

Thanks,
Shobha

[iamseer]

from 1:
x= 11 or -17, not sufficient

from 2:
x= 11 or -15, not sufficient

combining 1and 2
x=11

Answer C

[harshavardhanc]

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


Ans is D...but I feel it should be C

It has to be C.

The question asks us to find the distance of x from -7.

St1 says : distance of x from -3 is 14.

so, x can be on the either side of -3 at a distance 14, which will give us different values of distance from -7. Not sufficient.

St2 says : (x+2)^2 = 169 which can be re-written as |x+2|^2 = 169 or |x+2| = 13

or distance of x from -2 is 13 units.

Not sufficient, as the point can be on the either side of -2 at a distance 13, which will give us different values of distance from -7 .

Combining we get, that X is at a distance 14 from -3 and 13 from -2, which indicates that x is on right side of these two points and therefore on the right of -7 as well and at a distance of 18 units from -7.

[Testluv]

The correct answer is definitely choice C, and both harsha and iamseer's approaches are great.

_______

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

In a value DS question, a statement needs to provide one and only one value to be sufficient.

Because (1) gives an absolute value equation, (1) will lead to two possible values. Insufficient. Eliminate A and D.

Because (2) gives a square, (2) will also lead to two possible values. Eliminate B....the answer will be C or E.

(1) + (2):

From (1), x can be either 11 or -17.

In (2) we see that the right hand side is 13^2 or (-13)^2. So, as harsha points out, either x + 2 = 13 or else x + 2 = -13. So, either x = 11 or else x = -15. Because, together, there is only one shared value (11), the statements are sufficient when combined.

Choose C.