Hi askaichin,
I solved this in about 1min 15secs through the reasoning below:
3 late contracts. The first 2 are reduced by 10%. the last is reduced by 15%. Is the reduction for all three more than 11%?
The reduction for all 3 is a weighted average of the first 2 taken together and the 3rd. If the first 2 were initially worth $1 million total and the last was worth just $1, then the overall reduction would be very close to the reduction of the first 2 (10%). On the other hand, if the first 2 were worth $1 total and the last were worth $1 million, then the overall reduction would be very close to the reduction of the last (15%)
In general, in weighted average questions between 2 things, the ratio of the distances between each datapoint and the weighted average is the inverse of the ratio of the two quantities being averaged (quantity refers to how large/important each thing is). In this case the two datapoints (values of each 'thing') are 10% and 15%. If the weighted average were 11%, the ratio of distances between datapoints and average would be 1:4. This means that the ratio of quantities (the dollar amounts) would be 4:1. In other words, for the overall reduction to be 11%, the first 2 contracts together would be 4 times as large as the 3rd contract alone.
so a possible rephrase would be "Are the first 2 contracts worth 4 times as much as the 3rd?"
Note however that we are not asked whether the weighted average is exactly 11. Instead we're asked whether it's more than 11. For the weighted average to move from 11 toward 15, the value of the 3rd contract should increase.
Rephrase: "Are the first 2 contracts (total) worth less than 4 times the 3rd?"
(1) First 2 taken together are worth at least 2400. 3rd contract is worth 550. 4 times the 3rd would be 2200, so we know for a fact that the first 2 are NOT less than 4 times the 3rd. SUFFICIENT
(2) gives us no info on the ratio of first 2 contracts to last contract. NOT SUFFICIENT.
Pick A.
To practice weighted avg questions in timed drills, set topic='Weighted Averages' and difficulty='600-700 & 700+' in the Drill Generator
-Patrick
