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

Question

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

Ilishar · Answer

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.

Archit3110 · Answer

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

amarsinha · Answer

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.

Nums99 · Answer

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???

Kinshook · Answer

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

Archit3110 · Answer

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 ..

ScottTargetTestPrep · Answer

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:

+   +   = 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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards