{x} denotes the smallest integer greater than or equal to x.

Question

\{x\}  denotes the smallest integer greater than or equal to  x . A video editing firm charges $140 for editing the first 15 minutes of a film or films up to 15 minutes in length. It then charges $20 for editing each additional 15 minutes of film or length of film up to 15 minutes. Which of the following would represent the charge in dollars for editing a film that has a length of  p  hours?

(A)  120 + 20\{4p\}

(B)  120 + 20 \{p\}

(C)  140 + 80 \{p\}

(D)  140 + 20\{4p\}

(E)  160 + 20\{4p\}

Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=rskGgtKWeTA

shashag · Answer

There must be some algebraic approach, sure, but I simply took p=1.

On doing that, the total cost comes out to be 140+20+20+20=200.

Only option A comes out to be 200. Hence, it is the answer. I would be happy to understand the algebraic solution too.

PurvaG · Answer

how did you get the 20+20+20?

shashag · Answer

We assume p to be 1 hour. An hour has 4 parts of 15 minutes. The first 15 minutes are 140. The remaining 3 parts of 15 minutes are priced at 20 each. Hence, 140+20+20+20.

I hope it's clear.

egmat · Answer

Hi PurvaG,

shashag picked  p = 1 hour  just to test the answers with a concrete number, so let's see where those three $20s come from.

The firm bills film in  15-minute  blocks:
- The  first15  minutes cost  $140 .
-  Every15 -minute block after that costs  $20 .

Now take  1  hour. One hour =  60 minutes , and  60  ÷  15  =  4 blocks  of  15  minutes each. Line them up:

- Block  1  ( 0 - 15  min) -  $140  (this is the first-block price)
- Block  2  ( 15 - 30  min) -  $20 
- Block  3  ( 30 - 45  min) -  $20 
- Block  4  ( 45 - 60  min) -  $20

So after the first block,  3  blocks are left, and each adds  $20 . That's the  20 + 20 + 20 . Total =  140  +  60  =  $200 .

The key idea: the  $140  already pays for the first block, so you only charge  $20  for the  remaining  blocks - here,  4  total minus  1  =  3  of them.

Quick check to lock it in:  try  p = 0.5 hour  ( 30  minutes).
-  30  ÷  15  =  2 blocks .
- First block =  $140 , then just  1  leftover block =  $20 .
- Total =  $160 .

Notice you always have (number of blocks -  1 ) of the  $20  charges. In algebra, the blocks are  {4p} , the leftovers are  {4p}  -  1 , and the cost is  140  +  20 ( {4p}  -  1 ) =  120 + 20{4p}  - which is exactly choice  A .

Answer: A

{x} denotes the smallest integer greater than or equal to x.

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{x} denotes the smallest integer greater than or equal to x.

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