Hey guys, I haven't seen this question anywhere else on the forum so thought I would share it, with my explanation.
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.
Original answer:
[spoiler]A[/spoiler]
Great DS question.
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- albatross86
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Explanation
Let's call the original, unreduced prices of the 3 contracts - x, y and z.
The reduction would then be: 0.1x, 0.1y and 0.15z.
The percentage reduction may then be expressed as:
100 * (0.1x + 0.1y + 0.15z) / (x + y + z)
This is the value we need to establish as being on either side of 11% to get a sufficient answer.
Let's play around with it a bit to reduce the expression. Splitting 0.15z into 0.1z + 0.05z, and factoring out 0.1 gives us:
100* [0.1(x+y+z) + 0.05z] / (x + y + z)
This further reduces to:
10 + [ 5z / (x+y+z)]
So if we are able to establish, that the second term in this equation is always less than 1 or always more than 1, we have an answer.
Let's look at statement 1. We have a value here for Z, which gives us a clear idea of the numerator of the term.
We also have a minimum value of x and y. We can further arrive at the inference that (x+y) is atleast 2400. Let's look at that value of the term:
(5 * 550) / (2400 + 550)
= 55 / 59
This is obviously less than 1, which means the total percent will be some value between 10% and 11%.
If we continue to increase x and y, over 1200, it should be clear that since the numerator only depends on the value of Z, an increase in the denominator (x + y + z) only further reduces the value of this term, bringing the total percent closer to 10%.
Thus statement (1) is sufficient to conclude that the percentage will always be less than 11%.
Let's look at statement (2). All we have is a value of x. Since nothing is indicated about y and more importantly z, we can not conclude whether the term is less than 1 or more than 1. INSUFFICIENT.
Hope that clears things up, and that you guys find weighted averages to be simpler now!
EXTRA NOTE:
When would 5z/(x+y+z) = 1?
This would be when x + y = 4z
i.e. when z = 20% of (x + y + z) or 25% of (x +y)
Let's call the original, unreduced prices of the 3 contracts - x, y and z.
The reduction would then be: 0.1x, 0.1y and 0.15z.
The percentage reduction may then be expressed as:
100 * (0.1x + 0.1y + 0.15z) / (x + y + z)
This is the value we need to establish as being on either side of 11% to get a sufficient answer.
Let's play around with it a bit to reduce the expression. Splitting 0.15z into 0.1z + 0.05z, and factoring out 0.1 gives us:
100* [0.1(x+y+z) + 0.05z] / (x + y + z)
This further reduces to:
10 + [ 5z / (x+y+z)]
So if we are able to establish, that the second term in this equation is always less than 1 or always more than 1, we have an answer.
Let's look at statement 1. We have a value here for Z, which gives us a clear idea of the numerator of the term.
We also have a minimum value of x and y. We can further arrive at the inference that (x+y) is atleast 2400. Let's look at that value of the term:
(5 * 550) / (2400 + 550)
= 55 / 59
This is obviously less than 1, which means the total percent will be some value between 10% and 11%.
If we continue to increase x and y, over 1200, it should be clear that since the numerator only depends on the value of Z, an increase in the denominator (x + y + z) only further reduces the value of this term, bringing the total percent closer to 10%.
Thus statement (1) is sufficient to conclude that the percentage will always be less than 11%.
Let's look at statement (2). All we have is a value of x. Since nothing is indicated about y and more importantly z, we can not conclude whether the term is less than 1 or more than 1. INSUFFICIENT.
Hope that clears things up, and that you guys find weighted averages to be simpler now!
EXTRA NOTE:
When would 5z/(x+y+z) = 1?
This would be when x + y = 4z
i.e. when z = 20% of (x + y + z) or 25% of (x +y)
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From 1
unreduced price of contract 1=1200+100x
unreduced price of contract 2=1200+100y
unreduced price of contract 3=550
total 2950+100x+100y=T
11% of T=324.50+11x+11y
reduction from contact 1=120+10x
reduction from contact 2=120+10y
reduction from contact 3=82.5
total reduction =322.50+10x+10y=Tr
for any value of x Tr<T..hence reduction from 3 contracts is not more than 11%..sufficient
From 2
no information about cost of contract 2 and 3...not sufficient
Ans option A
unreduced price of contract 1=1200+100x
unreduced price of contract 2=1200+100y
unreduced price of contract 3=550
total 2950+100x+100y=T
11% of T=324.50+11x+11y
reduction from contact 1=120+10x
reduction from contact 2=120+10y
reduction from contact 3=82.5
total reduction =322.50+10x+10y=Tr
for any value of x Tr<T..hence reduction from 3 contracts is not more than 11%..sufficient
From 2
no information about cost of contract 2 and 3...not sufficient
Ans option A
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- albatross86
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It is a typical DS Q where u do not need to do any calc.
K receives 10% less for the first two late contracts and 15% for the third. There were 3 late contracts.
Was the total reduction less than 11%. To answer this if we know the value of each contracts. Then, it will be possible to work out the total reduction and the %.
Options 2) is inadequate while option 1) clearly tells us the value of each contract. This is enough, calc the exact % or even whther it is < or > 11% is going to cost valuable time.
K receives 10% less for the first two late contracts and 15% for the third. There were 3 late contracts.
Was the total reduction less than 11%. To answer this if we know the value of each contracts. Then, it will be possible to work out the total reduction and the %.
Options 2) is inadequate while option 1) clearly tells us the value of each contract. This is enough, calc the exact % or even whther it is < or > 11% is going to cost valuable time.
- albatross86
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KSTV:
Option 1 does not give us the value of each contract, but only a lower limit. I'm not sure how one would jump to the conclusion that that is sufficient to get one side of 11% without first analyzing it.
Option 1 does not give us the value of each contract, but only a lower limit. I'm not sure how one would jump to the conclusion that that is sufficient to get one side of 11% without first analyzing it.
I start a fresh on this.
If the 3 contracts are say, X, Y and Z , then the question basically asks whether
10%X + 10%Y +15%Z > 11%X +11%Y + 11%Z ?
This is also the same as 15%Z - 11%Z > 11%X +11%Y - 10%X - 10%Y ?
4%Z > 1%X + 1%Y OR 4Z > X + Y?
From Stmt 1... Z = 550 , and both X and Y are > 1200.
So substituting for x , y and z ( with the minimum values)
4Z > X + Y ...... 4*550 > 1200+1200 . So , Is 2200 > 2400? and thats a resounding NO, meaning that at no time will the reduction of comp be greater than 11%.... and that sufficient to answer the question.
As for Stmt 2. No info is available for contracts 2 and 3 and thus insufficient.
Hope that helps
If the 3 contracts are say, X, Y and Z , then the question basically asks whether
10%X + 10%Y +15%Z > 11%X +11%Y + 11%Z ?
This is also the same as 15%Z - 11%Z > 11%X +11%Y - 10%X - 10%Y ?
4%Z > 1%X + 1%Y OR 4Z > X + Y?
From Stmt 1... Z = 550 , and both X and Y are > 1200.
So substituting for x , y and z ( with the minimum values)
4Z > X + Y ...... 4*550 > 1200+1200 . So , Is 2200 > 2400? and thats a resounding NO, meaning that at no time will the reduction of comp be greater than 11%.... and that sufficient to answer the question.
As for Stmt 2. No info is available for contracts 2 and 3 and thus insufficient.
Hope that helps
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Suppose rates for 3 contracts are x y and zalbatross86 wrote:Hey guys, I haven't seen this question anywhere else on the forum so thought I would share it, with my explanation.
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.
Original answer:
[spoiler]A[/spoiler]
Is 10x + 10y + 15z > 11(x + y + z) i.e.4z > x + y ?
(1) 4z = 2200 x + y >=2400 SUFF
(2) NOT SUFF
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Careful! (1) gives the exact amount of one contract and lower bounds for the other two. What would be the answer if (1) said at least $1000 for the others?kstv wrote:It is a typical DS Q where u do not need to do any calc.
K receives 10% less for the first two late contracts and 15% for the third. There were 3 late contracts.
Was the total reduction less than 11%. To answer this if we know the value of each contracts. Then, it will be possible to work out the total reduction and the %.
Options 2) is inadequate while option 1) clearly tells us the value of each contract. This is enough, calc the exact % or even whther it is < or > 11% is going to cost valuable time.
Kevin Armstrong
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Gmatclasses
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1st contract priced $ 550 is reduced by 10%
2nd and 3 contract priced > $1200 reduced by 15%
the resultant reduction will be between 10% to 15%
the 2nd and 3rd contract ($2400) > 4 times the 1st contract (550)
so a 15% reduction of $ 2400 will be definitely > 12.5% of the total
the 2rd & 3rd contract has a > influence than the 3 rd contract on the final outcome
but if the lower limit of 2nd and 3 contract = 1000*2 = 2000
15% reduction = 300& 10% reduction on 550 = 55
this may need a more careful calc.
but 355 is still > 11% of 2550
2nd and 3 contract priced > $1200 reduced by 15%
the resultant reduction will be between 10% to 15%
the 2nd and 3rd contract ($2400) > 4 times the 1st contract (550)
so a 15% reduction of $ 2400 will be definitely > 12.5% of the total
the 2rd & 3rd contract has a > influence than the 3 rd contract on the final outcome
but if the lower limit of 2nd and 3 contract = 1000*2 = 2000
15% reduction = 300& 10% reduction on 550 = 55
this may need a more careful calc.
but 355 is still > 11% of 2550
- albatross86
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The THIRD contract is 550$, which is reduced by 15%, and the first 2 which were atleast 1200$ were reduced by 10%. So this is incorrect.kstv wrote:1st contract priced $ 550 is reduced by 10%
2nd and 3 contract priced > $1200 reduced by 15%
the resultant reduction will be between 10% to 15%
the 2nd and 3rd contract ($2400) > 4 times the 1st contract (550)
so a 15% reduction of $ 2400 will be definitely > 12.5% of the total
the 2rd & 3rd contract has a > influence than the 3 rd contract on the final outcome
but if the lower limit of 2nd and 3 contract = 1000*2 = 2000
15% reduction = 300& 10% reduction on 550 = 55
this may need a more careful calc.
but 355 is still > 11% of 2550
Do read the other solutions.
- albatross86
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That is just AWESOME. How did I miss that!!!kevincanspain wrote:Suppose rates for 3 contracts are x y and zalbatross86 wrote:Hey guys, I haven't seen this question anywhere else on the forum so thought I would share it, with my explanation.
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.
Original answer:
[spoiler]A[/spoiler]
Is 10x + 10y + 15z > 11(x + y + z) i.e.4z > x + y ?
(1) 4z = 2200 x + y >=2400 SUFF
(2) NOT SUFF
Thanks a bunch!