Bunuel
A bag contains red balls that weigh 100 grams each and green balls that weigh 50 grams each. If the number of green balls is 9 more than the number of red balls, how many balls are there in the bag?
(1) If two red balls are added to the bag, the number of red balls will be half the number of green balls
(2) The total weight of the balls in the bag is between 1.05 kilogram and 1.35 kilogram
From the question stem, we have G=R+9. We are asked for G+R.
Evaluating statement (1) alone:
R+2=G/2 --> 2R+4=G
We already had R+9+G.
Two non-equivalent equations with two variables, so we can solve for each.
Do we have enough information to find the total number of balls? Yes. AD
Evaluating statement (2) alone:
We have two options here. We could either set up inequalities or we can test a few numbers. I prefer the latter. The total weight is 1200g and there are 9 more G than R.
Let's try R=4 and G=13. That would be 400+650=1050g. That doesn't work.
Let's try R=5 and G=14. That would be 500+700=1200g. That works.
Let's try R=6 and G=15. That would be 600+750=1050g. That doesn't work.
There is only one possibility.
Do we have enough information to find the total number of balls? Yes. D
Answer choice D