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A legal service bills p dollars for the first hour of service on a tas

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A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 19 Aug 2019, 00:17
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A
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C
D
E

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Question Stats:

60% (02:44) correct 40% (02:27) wrong based on 42 sessions

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A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q. If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

A. It increases by p - q dollars

B. It increases by h(p - q)dollars

C. It increases by (n - 1)(p - q) dollars

D. It decreases by (h - 1)(p - q) dollars

E. It decreases by n(p - q) dollars

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Re: A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 19 Aug 2019, 01:27
1
1 Task : p + (h-1)q amount shall be charged ........... (i)

N tasks & H hrs. of service: Each task will be of (h/n) hrs. of service -> n(p+((h/n) - 1)q) amount shall be charged ..... (ii)

(ii) - (i) = pn+hq-nq - p - hq + q = pn-qn - (p-q) = (p-q)(n-1) dollars => amount shall increase => C ans.
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Re: A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 19 Aug 2019, 06:12
i solved using values for p,q,h and n
p=2 $ , q = 1 $ , h = 4 hrs and n = 2 as its simple to divide 4 by 2

so nominal charge for 1 session would have been ; ( p+(h-1)*q) ; 2+(4-1)*1 ; 2+3 ;5$
but now we are having n sessions i.e 2 ;
so h/n ; 4/2 ; 2 so h would be 2 now
charges would be ; 2+(2-1)*1 ; 3 $ + 2+(2-1)*1 ; 3$ ; total cost 6$
effectively price of session would go up by 1 $
which is given as per expression
It increases by (n - 1)(p - q) dollars
i.e ( 2-1)*(2-1) ; 1*1 ; 1 $
IMO C



Bunuel wrote:
A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q. If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

A. It increases by p - q dollars

B. It increases by h(p - q)dollars

C. It increases by (n - 1)(p - q) dollars

D. It decreases by (h - 1)(p - q) dollars

E. It decreases by n(p - q) dollars

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Re: A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 20 Aug 2019, 01:32
Bunuel wrote:
A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q. If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

A. It increases by p - q dollars

B. It increases by h(p - q)dollars

C. It increases by (n - 1)(p - q) dollars

D. It decreases by (h - 1)(p - q) dollars

E. It decreases by n(p - q) dollars


Amount billed initially with just one task in h hours : p + (h-1)q

If the task is divided in n tasks, assuming each task will take h/n hours.
So, for one task, amount billed : p+ (h/n -1)q
Total amount billed for n tasks together : np + nq(h/n-1)
= np +q(h-n)

Extra billing which has to be paid : np + q(h-n) - p - (h-1)q
= (n-1)p + q(h-n-h+1)
= (n-1)p -q(n-1)
= (n-1)(p-q)
Hence C.
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Re: A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 20 Aug 2019, 05:38
Archit3110 wrote:
i solved using values for p,q,h and n
p=2 $ , q = 1 $ , h = 4 hrs and n = 2 as its simple to divide 4 by 2

so nominal charge for 1 session would have been ; ( p+(h-1)*q) ; 2+(4-1)*1 ; 2+3 ;5$
but now we are having n sessions i.e 2 ;
so h/n ; 4/2 ; 2 so h would be 2 now
charges would be ; 2+(2-1)*1 ; 3 $ + 2+(2-1)*1 ; 3$ ; total cost 6$
effectively price of session would go up by 1 $
which is given as per expression
It increases by (n - 1)(p - q) dollars
i.e ( 2-1)*(2-1) ; 1*1 ; 1 $
IMO C



Bunuel wrote:
A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q. If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

A. It increases by p - q dollars

B. It increases by h(p - q)dollars

C. It increases by (n - 1)(p - q) dollars

D. It decreases by (h - 1)(p - q) dollars

E. It decreases by n(p - q) dollars




Hey Archit3110

How reliable is this method

Lets say if i take p=10 q=5 and h=4 & n=2

after solving everything
10+5(3) = 25 ----- I

10+5(1) AND 10+5(1) = I.E 15+15 = 30 ----- II

difference between I and II is 5
both p-q
(n-1)(p-q)
will be equal to 5
and trying again with a different number will again consume a lot of time so how do we choose exact numbers so that we don't make such a mistake???
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Re: A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 20 Aug 2019, 06:39
Bunuel wrote:
A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q. If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

A. It increases by p - q dollars

B. It increases by h(p - q)dollars

C. It increases by (n - 1)(p - q) dollars

D. It decreases by (h - 1)(p - q) dollars

E. It decreases by n(p - q) dollars


Given: A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q.

Asked: If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

Bill amount for the whole work (A)= p + (h-1)q
Bill amount for the broken up work (B)= np + (h-n)q

Difference (B-A) = np + (h-n)q - p - (h-1)q = (n-1)p - (n-1)q = (n-1)(p-q)

IMO C
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Re: A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 20 Aug 2019, 08:18
Nums99
well you got to use smart no. i.e use no which are easy to do calculation with .. on actual test you wont have the luxury of time as you have while now practising..
if you have understood the question well , then you can plugin/ substitute no which according to you would get you to correct answer.. one of the best way is to use the given answer choices and do plugin values to see whether your answer is correct or not ..

Nums99 wrote:
Archit3110 wrote:
i solved using values for p,q,h and n
p=2 $ , q = 1 $ , h = 4 hrs and n = 2 as its simple to divide 4 by 2

so nominal charge for 1 session would have been ; ( p+(h-1)*q) ; 2+(4-1)*1 ; 2+3 ;5$
but now we are having n sessions i.e 2 ;
so h/n ; 4/2 ; 2 so h would be 2 now
charges would be ; 2+(2-1)*1 ; 3 $ + 2+(2-1)*1 ; 3$ ; total cost 6$
effectively price of session would go up by 1 $
which is given as per expression
It increases by (n - 1)(p - q) dollars
i.e ( 2-1)*(2-1) ; 1*1 ; 1 $
IMO C



Bunuel wrote:
A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q. If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

A. It increases by p - q dollars

B. It increases by h(p - q)dollars

C. It increases by (n - 1)(p - q) dollars

D. It decreases by (h - 1)(p - q) dollars

E. It decreases by n(p - q) dollars




Hey Archit3110

How reliable is this method

Lets say if i take p=10 q=5 and h=4 & n=2

after solving everything
10+5(3) = 25 ----- I

10+5(1) AND 10+5(1) = I.E 15+15 = 30 ----- II

difference between I and II is 5
both p-q
(n-1)(p-q)
will be equal to 5
and trying again with a different number will again consume a lot of time so how do we choose exact numbers so that we don't make such a mistake???

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Re: A legal service bills p dollars for the first hour of service on a tas  [#permalink]

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New post 25 Aug 2019, 18:36
Bunuel wrote:
A legal service bills p dollars for the first hour of service on a task and q dollars for each additional hour, where p > q. If the client requires a specific number of hours h of service, how does the amount billed to the client change if the work is broken up into n tasks rather than one task?

A. It increases by p - q dollars

B. It increases by h(p - q)dollars

C. It increases by (n - 1)(p - q) dollars

D. It decreases by (h - 1)(p - q) dollars

E. It decreases by n(p - q) dollars


We can let p = 5, q = 2, h = 7 and n = 3. Furthermore, let’s say that the 3 tasks last 2, 2, and 3 hours, respectively.

Therefore, as one task, the total amount billed would be:

5 + 2(7 - 1) = 5 + 12 = 17 dollars

However, as three tasks, the total amount billed would be:

[5 + 2(2 - 1)] + [5 + 2(2 - 1)] + [5 + 2(3 - 1)] = 7 + 7 + 9 = 23 dollars.

We see that the total amount billed would increase by 6 dollars (and we can reject choices D and E). Let’s look at the other 3 choices.

A. p - q = 5 - 2 = 3 → This is not 6.

B. h(p - q) = 7(5 - 2) = 21 → This is not 6.

C. (n - 1)(p - q) = (3 - 1)(5 - 2) = 6 → This is 6.

Answer: C
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Re: A legal service bills p dollars for the first hour of service on a tas   [#permalink] 25 Aug 2019, 18:36
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