capsicumgirl wrote:
Is b<50
(1) The square of (b+x) is less than 2500
(2) The square of (b-x) is less than 1500
Here's an approach testing specific cases:
(1) This one simplifies to -50 < b + x < 50.
Case 1: b = 0, x = 0, answer is "yes"
Case 2: b = 100, x = -100, answer is "no"
Not sufficient.
(2) Well, 1500 is a little less than 1600, so the square root should be a little less than 40. If I need to get it more precisely, I can do that later, but for now I'll say '~40' (approximately 40).
~-40 < b - x < ~40
Case 1: b = 0, x = 0, answer is "yes"
Case 2: b = 100, x = -100, answer is "no" (Try to notice chances to reuse cases! That can speed things up.)
Not sufficient.
(1 + 2)
Now I have two inequalities:
~-40 < b - x < ~40
-50 < b + x < 50
Notice that the x and -x will cancel if I add these inequalities together. You can always add any two inequalities whose inequality signs are pointing in the same direction. So, we get this:
~-90 < 2b < ~90
~-45 < b < ~45
We already decided that '~45' is
less than 45, since 1500 is less than 1600. So, b is definitely less than 45, and the two statements combined are sufficient.
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