Hi All,
When it comes to "layered" questions, you have to be careful about the approach that you take. The more complex an approach is, the more likely you are to make a mistake, miss a detail or do a calculation that is incorrect.
Here, we have:
|X+4|^2 - 10|X+4| = 24
This is certainly a complex looking calculation, but it IS based on some simple ideas and rules. Rather than take a calculation-heavy approach, let's break this into 'pieces' and talk through what each piece means...
First, I'm going to rewrite the equation:
|X+4|^2 = 24 + 10|X+4|
This tell us that....
|X+4|^2 is exactly 24 "bigger" than 10|X+4|
Next, let's compare pieces...
|X+4|^2 = (|X+4|)(|X+4|)
(|X+4|)(|X+4|) is 24 "bigger" than (10)(|X+4|)
Compare the two products....they each have a (|X+4|) a term. The difference of 24 must be based on the OTHER terms...
|X+4| MUST be > 10
....but probably not that much bigger, since the difference in the overall calculation is just 24.
So.....what happens in this equation: |X+4|^2 = 24 + 10|X+4|
When.....X = 7......
121 = 24 + 110???? This is not correct (121 does NOT = 134)
When....X = 8.....
144 = 24 + 120? This IS correct (144 = 144)
When....X = 9....
169 = 24 + 130??? This is not correct (169 does NOT = 154)
As X gets bigger, we can see that the calculation will NOT be equal. This means that |X+4| MUST = 12 and that ONE of the solutions is X=8. Since we're dealing with an absolute value, we have 2 equations to solve:
X+4 = 12
X = 8
X+4 = -12
X = -16
So the 2 solutions are X=8 and X = -16. There are NO other options.
The prompt asks for the sum of the solutions: -16 + 8 = -8
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★