Manhattan Question Bank Word

[Jimmy]

What is the average of x and |y| ?

(1) x + y = 20

(2) |x + y| = 20

Stacey/Ron I wanted to go over this problem with the board....You guys solve this problem by picking #s...But is it fair to rephrase it as...

If y > 0 ...(x+y)/2 =

If y < 0 ...(x-y)/2 =

So the question could be rephrased is y positive or negative to start?

[Jimmy]

anyone?

[RonPurewal]

first off, even if you have NO CLUE how to solve this problem, you can still notice that statement (1) implies statement (2); in other words, if statement 1 is true, then statement 2 MUST be true.
this observation alone eliminates 2 answer choices: "B" (because, if 2 is sufficient, then so is 1 because it implies 2), and "C" (because the two statements together are equivalent to statement 1 by itself; statement 2 doesn't provide any new information if statement 1 is true)

so we're down to a/d/e.

try statement (1) alone:
x + y = 20

this problem has to do with POSITIVES AND NEGATIVES, because ALL problems having to do with absolute value are, at heart, about positives and negatives. therefore, you need to try both positive and negative values of y.

sample values with y positive: y = 10, x = 10
average of x and |y| = 10

sample values with y negative: y = -10, x = 30
average of x and |y| = 20

10 and 20 are different, so, insufficient
a/d are gone
answer = e