Logic and Absolute Value Sign DS

[bretania]

Is lx-4l < 7?

(1) X < 3
(2) X > -11

Some say it's' D. Others say it's C. Could someone please put in his/her idea on this matter?

I think it's D because in both (1) and (2), we can always make sure of the validity of the given inequality (lX-4l < 7).

Please help.

[clock60]

i think the answer is E
that is my view
/x-4/<7 can be solved as -7<x-4<7. -7+4<x<7+4. so -3<x<11
so the question asks does x belong to the interval (-3, 11)
(1) x<3 but what about -5 for example it is less than 3 but doest fit ours
insufficient
(2) x>-11 insufficient for the same reasoning again -5 it is larger than -11 but does not fit condition
(1)+(2) together according we have interval (-11.3) if we put 0 for example
the answer is yes but for -5 the answer is no
so to my mind E
________ -11_______ -3__________3________11
our interval is (-3 11) any number in (-3 3) will be valid and in (-11 -3) will be invalid.

[bretania]

Sorry, there was a typo. This is the correct problem.

Is lx+4l < 7?

(1) X < 3
(2) X > -11

And clock60, you were right on your solution earlier. And using the same logic that you pointed out (when the term inside the abs value sign was x-y), the answer to the above corrected version is C

[sonikamadala]

Originally Posted by bretania

Sorry, there was a typo. This is the correct problem.

Is lx+4l < 7?

(1) X < 3
(2) X > -11

And clock60, you were right on your solution earlier. And using the same logic that you pointed out (when the term inside the abs value sign was x-y), the answer to the above corrected version is C

IMO answer is C

(1) : say x = 2 then lx+4l < 7 , if x = -12 then lx+4l > 7. so not suff.
(2) : say x = 2 then lx+4l < 7 , if x = 22 then lx+4l > 7. so not suff.
(1) & (2) : -11< x< 3 . say x = 2 then lx+4l < 7 , if x = -10 then lx+4l < 7. so suff.

so C wins

[iceman0]

From the question you have

x+4<7 which turns to x<3 and you have -x-4<7 which turns to x>-11

Statement 1 is not suff
Statement 2 is not suff
Statement 1 and Statement 2 together are suff.
Answer is C

[madhur_ahuja]

Agree with C