Problem Solving

sanjoy18 wrote: |a-2|<4;|b+4|<8;|2c-3|<11. Find the difference between the maximum and minimum possible values of (a+b+c)².

A)35
B)289
C)324
D)244
E)none of the above

NOTE: I have a feeling that the question SHOULD feature less than OR EQUAL signs, as follows:

|a-2| < 4; |b+4| < 8; |2c-3| < 11. Find the difference between the maximum and minimum possible values of (a+b+c)².

A)35
B)289
C)324
D)244
E)none of the above

We'll use the following fact: If x < |a|, (where a > 0) then -a < x < a

|a-2| < 4
-4 < a-2 < 4
-2 < a < 6

|b+4| < 8
-8 < b+4 < 8
-12 < b < 4

|2c-3| < 11
-11 < 2c-3 < 11
-8 < 2c < 14
-4 < c < 7

(a+b+c)² is MINIMIZED when (a+b+c) = 0
Since it's possible for a+b+c to equal zero (a=0, b=0 and c=0), the MINIMUM value of (a+b+c)² is 0

(a+b+c)² is MAXIMIZED when (a+b+c) is the largest possible positive value or the smallest possible negative value.
If a = 6, b = 4 and c = 7, then a+b+c = 17 (which means (a+b+c)² = 17² = 289)
If a = -2, b = -12 and c = -4, then a+b+c = -18 (which means (a+b+c)² = (-18)² = 324
So, the MAXIMUM value of (a+b+c)² is 324

So, IF we change the question so that it has less than or equals signs, the correct answer is 324 - 0 [spoiler]= 324 = C[/spoiler]

HOWEVER, if we don't change the question, the correct answer is E

Cheers,
Brent