If x and y are integers and y=|x+3| + |4-x|, does y equals 7?
(1) x < 4
(2) x > -3
Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks.
At first i tried to apply the approach given in the gmatclub math guide regarding dealing with absolute value questions. But than i remembered that approach is for finding the solutions of an equation.
After further thought i looked at the question and than at
1) x < 4. Their can be infinite values of x less than 4. Some of which gives y= 4(3,2..etc) and some don't x = -10. INSUFFICIENT.
2)x > -3. Same as above. Some values give y=7(-2,-1..etc). Some don't x= 10. INSUFFICIENT.
Combining 1 and 2, we can see that all values -2,-1,0,1,2,3 given y=7. Hence SUFFICIENT.