What is the value of y?

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PGMAT: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Fri Jul 23, 2010 1:30 pm

by PGMAT » Wed May 16, 2012 4:28 pm

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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Source: Beat The GMAT — Data Sufficiency | Wed May 16, 2012 4:28 pm

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Wed May 16, 2012 5:49 pm

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

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PGMAT: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Fri Jul 23, 2010 1:30 pm

by PGMAT » Wed May 16, 2012 5:56 pm

Nice explanation. Thank you.

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