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by Atekihcan » Tue Jun 11, 2013 3:11 am
If x is an integer, y = 15 - 3x will also be an integer.

Now, |y| < 30
So, |15 - 3x| < 30
So, 3*|5 - x| < 30
So, |5 - x| < 10

This means distance between x and 5 is less than 10.
So, x must be greater than (5 - 10) = -5 but less than (5 + 10) = 15

So, -5 < x < 15

So, possible number of such points = possible number of integral values of x = (15 - (-5)) - 1 = 20 - 1 = 19

Answer : B
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by Brent@GMATPrepNow » Tue Jun 11, 2013 6:11 am
I just wanted to point out a technique we can use once we get to |5 - x| < 10 in Atekihcan's excellent solution.

If |5 - x| < 10, then we can write -10 < 5 - x < 10

Aside:
To generalize, if |something| < positive k, then negative k < something < positive k

Okay, so we have: -10 < 5 - x < 10
Subtract 5 from all 3 parts: -15 < -x < 5
Divide all 3 parts by -1: 15 > x > -5 [and reverse the inequalities]

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Brent
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