grandh01 wrote:Larry saves x dollars per month. Will
Larry's total savings one year from
now exceed his present savings by
at least $500 ? (Assume that there is
no interest.)
(1) In 6 months Larry's total savings
will be $900.
(2) In 3 months Larry's total savings
will exceed his present savings by
$150.

Statement 1: Insufficient because we don't know what is present savings level is compared with what it will be in the future. For example if his current savings level is 900, and after 6 months it is 0 dollars, no his total savings will not exceed his current level by 500. On the other hand, if he saves 0 now and in 6 months he saves 600, then yes it will. We have a yes and a no, insufficient.

Statement 2: Lets say his current level of savings is x. That means in 3 months he would have saved 3x, after 3 months he will save x+150. There are still 12-3= 9 months in the year. That means he will save 9(x+150) = 9x+1350 for the last 9 months. Plus the first three months we will have saved: 12x+1350, this is 1350 more than if he only saved x per month which is greater than 500. This is sufficient.