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Late contracts - Please help

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Late contracts - Please help

by rahulvsd » Sat Oct 29, 2011 6:55 am
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 received $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 received $1500 for the first of the three late contracts.

OA: A
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Source: — Data Sufficiency |
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by GmatMathPro » Sat Oct 29, 2011 7:43 am
Let's say the 1st, 2nd, and 3rd contracts pay out at x, y, and z, respectively. When she delivers them late, the amount of her reduction is .1x+.1y+.15z. Let T be her total compensation before reductions. That is, T=x+y+z. To calculate the percentage reduction, divide the reduction by her total original compensation and multiply by 100 to make it a percentage: 100*(.1x+.1y+.15z)/T=(10x+10y+15z)/T. Note that if the third one were also reduced by only ten percent, the overall reduction would just be ten percent, regardless of the values of x, y, and z. Whether the overall percentage climbs to more than 11 depends entirely on how big z is compared to the other values.

(10x+10y+15z)/T=

(10x+10y+10z+5z)/T=

(10x+10y+10z)/T+5z/T=

10(x+y+z)/T + 5z/T

But remember x+y+z=T, so the left part just becomes 10...

10+5z/T=percentage reduction.

We want it to be greater than 11%, so

10+5z/T>11

5z/T>1

z/T>1/5

Note that z/T is the fraction of the total compensation that is made up of z, so the question depends entirely on what that fraction is. Specifically, for the percentage to be greater than 11, z must make up MORE than 1/5 of the total compensation. This makes sense because 11 is 1/5 of the way from 10 to 15.

Statement 1: This says that x+y>=2400 and z=550. Let's first check what happens when x+y=2400. In that case, z/T=550/(2950)=55/295=11/59. 11/59 is less than 11/55, so this says z/T is definitely less than 1/5. If we made x or y bigger, the fraction would be even less. SUFFICIENT.

Statement 2: This says that x=1500, but tells us nothing about y or z, so we have no way of determining the fraction of the total that is made up by z. INSUFFICIENT.

A
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