Percentages

[askaichin]

Mrs K is paid at a reduced rate for contracts completed late, and the contract prices may vary. Her compensation for the first two late contracts in any month is reduced by 10% and her compensation for any subsequent late contracts in the same month, was her total compensation for those three contracts reduced by more than 11%?

1. Without any reduction, she would have recieved $ 550 for the last of the three late contracts, and at least $ 1200 for each of the others.

2. Without any reduction, she would have recieved $ 1500 for the first of the three late contracts.

[Patrick_GMATFix]

Hi askaichin,

Where is this question from please? The grammar in the question stem is incorrect and this makes the question difficult to understand: "compensation for 1st 2 late contracts is reduced by 10% and her compensation for any subsequent late contracts in the same month" ??? That's not even the end of the sentence; this is followed by a comma (,) and then the question. The question itself seems to suggest that there are just 3 contracts, contradicting the suggestion made in the rest of the stem.

Please share the source of the question
-Patrick

[askaichin]

Yes Patrick You are right.
I am afraid it was my mistake, the line after the comma got mistakenly deleted..Here is the complete question.

Mrs K is paid at a reduced rate for contracts completed late, and the contract prices may vary. Her compensation for the first two late contracts in any month is reduced by 10%, and her compensation for any subsequent late contracts in the same month is reduced by 15%. If Mrs K completed three contracts late, in the same month, was her total compensation for those three contracts reduced by more than 11%?

1. Without any reduction, she would have recieved $ 550 for the last of the three late contracts, and at least $1200 for each of the others.

2. Without any reduction, she would have recieved $ 1500 for the first of the three late contracts.

[Patrick_GMATFix]

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

[gmatmachoman]

Let P1,P2,P3 denote the payments. T denote the Total Payments

P1+P2+P3 = T

Stem ask if 0.11 (T) < 0.1P1+ 0.1P2 + .15P3 ??

St 1 :

P1>=1200
P2>=1200
P3=550

Find LHS & RHS of the stem and equate. Sufficient

St 2:

P1 =1500
No data about P2 &P3

Insufficient

Pick A