For each landscaping job that takes more than 4 hours, a certain contr

Given: \(r>100\)
Question: is \(t>10\)?

(1) \(r+0.2r(t-4)=288\) --> \(t=\frac{1440-r}{r}\) --> if \(r=101\), then \(t>10\) but if \(r=200\), then \(t<10\). Not sufficient.

(2) \(r+0.2r(t-4)=2.4r\) --> \(t=11\). Sufficient.

Answer: B.
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Say total number of hours the job took = x

(1) \(r + 0.2r*(X-4) = 288\)

The prompt is for a constraint on X. Without knowing the value of r, you cannot determine any possible value for x.
Eg. If r = 288, X = 4
If r = 100, X is more than 13.
--> INSUFF

(2) \(r + 0.2r*(X-4) = 2.4r\)

Cancel out r throughout:

\(1 + 0.2X - 0.8 = 2.4\)

\(0.2X = 2.2\)

\(X = 11\) Answer to the prompt is YES

--> SUFFICIENT

Pick B.

Hello All,

On this question, can we manipulate the question stem to say:

Is the total amount paid = r + 0.2r * 6 ----> r +1.2r ----> 2.2r ( so the question is asking if the money paid was 2.2r)
This was derived from breaking down the 10hrs into portions of 4 and 6hrs respectively

Stmt 1 just gives a figure and does not consider r - hence insufficient

So Stmt 2 gives us a direct correlation between 2.2r and 2.4r - and is sufficient

Could you please explain how you got (t-4)?

We are told that "For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2r dollars for each additional hour..."

So, if the job takes 6 hours first 4 hours cost $r and each of the remaining (6 - 4) = 2 hours cost $0.2r.
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hi experts,
I am confused about statement #1, here is my approach, please point out my fault

Suppose H represents the total working time
r + 0.2r(H -4 ) = 228
228 = 0.2r(6+H)
0.2r = 228/(6+H)

because r>100, so 0.2r>20,
we can get
228/(6+H) > 20
because 6+H > 0
so 228> 20*(6+H)
57*4 > 4*5*(6+H)
57>6+H
H< 5.4
that must not be greater than 10
so I think statement #1 is sufficient

Please help

thanks in advance
have a nice day
>_~
57>5*(6+H)

The red part is not correct:

r + 0.2r(H - 4) = 228
r + 0.2rH - 0.8r = 228
0.2r + 0.2rH = 228
0.2r(1+H) = 228
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Hi Bunuel,

I am unable to understand the wordings of the question:

I understood that the question is saying: for 1st four hours of work, the rate is 1r and after 4 hours it is 1.2r, and if let say R is 101, then for 1st 4 hours the rate has to be minimum 404, thus:
"statement I:- if total charge is 288, then, T <10.

Can you help clarify is really the question asking ? I tried pretty hard to understand.
I understood you answer, but unable to understand what really the question is asking
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Hello

I will try. The question says that for 1st four hours of work, IN TOTAL the rate is 'r', and not per hour. So first 4 hours total is 'r', After that its 0.2r per hour, and Not 1.2r.

So lets say the work takes 6 hours - contractor will charge 'r' for first 4 hours, and 0.2r each for the next 2 hours. So total would be = r + 0.2r*2 = r + 0.4r = 1.4r.

In case work takes 11 hours - contractor will charge 'r' for first 4 hours, and 0.2r each for the next 7 hours. So total would be = r + 0.2r*7 = r + 1.4r = 2.4r.

Hey amanvermagmat
Thanks a lot, very poor reading from my side.
Appreciate
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For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2*r dollars for each additional hour or fraction of an hour where r > 100, Did a particular landscaping job took more than 10 hours.

The important thing to note is r > 100.

(1) The contractor charges a total of $288 for the job.

If r = 100, then the landscaping job took more than 10 hours. If r = 200, then the landscaping job took less than 10 hours. INSUFFICIENT.

(2) The contractor charges a total of 2.4r dollars for the job.

r = first 4 hours

We have 1.4r remaining. We can conclude the landscaping job took more than 10 hours. SUFFICIENT.

Answer is B.
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Is t > 10?

Statement 1:
Test whether it's possible that t=10.
Case 1: t = 10 hours
Since $r dollars is charged for the first 4 hours and $0.2r is charged for each of the 6 additional hours, we get:
r + 0.2r(6) = 288
2.2r = 288
\(r = \frac{288}{2.2}\) ≈ 130
In this case, t=10. so the answer to the question stem is NO.

Test whether it's possible that t>10.
Case 2: t = 11 hours
Since $r dollars is charged for the first 4 hours and $0.2r is charged for each of the 7 additional hours, we get:
r + 0.2r(7) = 288
2.4r = 288
\(r = \frac{288}{2.4} = 120\)
In this case, t>10, so the answer to the question stem is YES.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Statement 2:
The blue equation in Case 2 indicates that the total charge = 2.4r when t=11.
Thus, the answer to the question stem is YES.
SUFFICIENT.


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Lets remake this question to make things a little funnier:

For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2*r dollars for each additional hour, where r is an integer > 100. If the contractor charged 288$ for a particular job. How many hours did that job take?

a) 5
b) 6
c) 7
d) 8
e) 9

Bunuel VeritasKarishma I guess there is some gap in my logic. I used the following Logic for statement 1. I decided to rephrase the question stem as follows
r+0.2r(6)<288? i.e is the amount paid for atleast 10 hours?
2.2r<288?
So the question becomes is r<13.9?
Which is given i.e.r>100
So Sufficient
I guess am missing something. Please help

2.2r<288
gives r < 130.9
We are given that r > 100 but is it less or more than 130.9, we don't know.

Note that if work needed more than 10 hrs, the total charge would be r + 0.2r * 7 or higher.
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