GMATinsight wrote:

How many distinct integer values of n satisfy the inequality ||n-3| + 4| ≤ 12 ?

A. 15

B. 16

C. 17

D. 18

E. 19

METHOD-1||n-3| + 4| ≤ 12 can be re-written as

i.e. -12 ≤ |n-3| + 4 ≤ 12

i.e. -12-4 ≤ |n-3| ≤ 12-4

i.e.

-16 ≤ |n-3| ≤ 8

Here the corrective action needs to be taken.-16 ≤ |n-3| in the above Inequation is REDUNTANT because we know that absolute value of any expression can't be less than zero. So an absolute value is greater than -16 doesn't contribute to our information at alli.e. The Inequation can be sufficiently defined by the expression |n-3| ≤ 8

i.e. -8 ≤ n-3 ≤ 8

i.e. -8+3 ≤ n ≤ 8+3

i.e. -5 ≤ n ≤ 11The Number of Integer values from -5 to 11 (Inclusive) is 17

Answer: Option CMETHOD-2The primary expression is

||n-3| + 4| ≤ 12 i.e. The Absolute value of the expression on Left Hand Side (LHS) can go upto 12

i.e. The value of |n-3| can go upto 8

i.e. the Extreme absolute Value of n-3 can be

+8

i.e. when n-3 = +8, The extreme value of n = +11

and when n-3 = -8, The extreme value of n = -5

i.e. The Value of n can range from -5 to +11 i.e. 17 Integer values

Answer: Option CI have solved some problems of this kind previously, without any corrective action taken as such. I think the double absolute modulus has made this difference. Do you think, however, we are better off turning the double modulus into one, before setting the final inequality....? For example ...

OR, if there is any guiding principle to follow when solving questions as such, please say to me ...