GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Sep 2019, 20:16

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

At his regular hourly rate, Don had estimated the labor cos

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
Joined: 12 Aug 2019
Posts: 1
Re: At his regular hourly rate, Don had estimated the labor cos  [#permalink]

Show Tags

New post 25 Aug 2019, 13:57
converge wrote:
Let t be the hourly rate and p the price: t * p = $336

Additional 4 hours and $2 less per hour would yield: (t+4) * (p-2) = $336

Since both equations are equal:

336 : p = (336 : (p-2))-4

Solving for p yields 14 (the other solution is negative, so we do not consider it)

At this point probably we are very pressed on time, so the shortcut is to find the answer the last digit of which multiplied by 4 yields 6. 14 squared is not 336 so by elimination it is 24

Answer: B



As the quotation above, many people handle the information from the question then end with the same quadratic equation which gives us hard time to solve. Some people solve it by mechanical work while others use the answers to plug in the equation or make guess then hit the correct choice.

I did the same way when facing this equation. However, I try to find an easier way to solve this ugly equation. After few days, I find one and want to share with you. Hope you find it useful and let me know if you find any error.

In general, the quadratic equation will be from these equations

x * y = A (1)
(x - a) * (y + b) = A (2)

(2) <=> x*y + x*b - a*y - a*b = A
<=> x*b - y*a = a*b (we have x*y=A)
<=> x/a - y/b = 1 (divide both side by ab)

Set M = x/a and N = y/b
(1) <=> M * N = A/(a*b)
(2) <=> M - N = 1

These equations are much easier to solve than the original ones. Now we come back the equations above.

t * p = $336 (1)
(p-2) * (t+4) = $336 (2)

Set M = p/2 and N = t/4

(1) <=> M * N = 336/(2*4)
M * N = 42
(2) M - N = 1

From these equations, we can solve M = 7 and N = 6

With N = 6 => t = 24

=========================

I want to expand a little bit. If we have quite similar equations such as

x * y = A
(x + a) * (y +b) = A

We can use the same way to break them down then solve them

x * y = A
x/a + y/b = -1

M * N = A/(a*b)
M + N = -1
with M = x/a and N = y/b
GMAT Club Bot
Re: At his regular hourly rate, Don had estimated the labor cos   [#permalink] 25 Aug 2019, 13:57

Go to page   Previous    1   2   3   4   [ 61 posts ] 

Display posts from previous: Sort by

At his regular hourly rate, Don had estimated the labor cos

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne