What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11
Can some one please explain what is the best way to solve statement 1?
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What is the value of y?
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eagleeye
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Hi PGMAT:
Let's look at 2) first.
We have |3-y| = 11 which implies either 3-y = +11 or 3-y = -11.
if 3-y=+11 then y = 3-11 = -8 ; if 3-y = -11 then y = 3+11 = 14
Now let's look at 1)
We have y - 2 = 3|x^2-4|, we don't actually need to solve the equation
we have y = 2 + 3|x^2-4|, now |x^2-4| is always non-negative because |anything| >=0, therefore y is 2 + something not negative hence y >=2. the only value of y which works from what we solved in 1) is y=14; hence from both the statements, y = 14 and the answer is C.
Let me know if that helps
Let's look at 2) first.
We have |3-y| = 11 which implies either 3-y = +11 or 3-y = -11.
if 3-y=+11 then y = 3-11 = -8 ; if 3-y = -11 then y = 3+11 = 14
Now let's look at 1)
We have y - 2 = 3|x^2-4|, we don't actually need to solve the equation
we have y = 2 + 3|x^2-4|, now |x^2-4| is always non-negative because |anything| >=0, therefore y is 2 + something not negative hence y >=2. the only value of y which works from what we solved in 1) is y=14; hence from both the statements, y = 14 and the answer is C.
Let me know if that helps
