Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 862
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
22 Oct 2015, 12:44
So you have two equations from the question stem. Let x be the hourly rate and y the time in hours: \(x*y=336\) and \((y+4)*(x2) = 336\) which expands to: \(xy2y+4x8=336\) plug in \(x*y=336\) in the above formula: \(3362y+4x8=336\), simplify to: \(2xy2=0\) Now pick numbers which fit, start with C, then go up to B: 2x244=0, if y=24, then x=14 and 2x=28. So this fits.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Intern
Joined: 18 Aug 2012
Posts: 10

At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
29 Nov 2015, 12:43
Given Info: The total hours estimated by Don differs from the actual number of hours required to finish the job. He had to work 4 more hours to finish the job. For this reason, he received $2 less than was estimated to be given per hour for his job. He received a total amount of $336 to complete his job.
Interpreting the Problem: We have to find the time Don had initially estimated to complete his job. This can be worked out by forming two equations from 2 different conditions given to us. One can be worked out on the number of hours initially estimated and his hourly rate to complete the job, and the other could be worked out on the actual hours worked nd actual hourly rate he received for the job. After that, we will equate both the equations to the total payment received and find the hours estimated for the job.
Solution: Let us assume the time estimated by Don for the job be n hours and let the cost Don charges per hour for the job be $x per hour.
From the information in the question
n Hours (estimated) * x(Don charge for job per hour) = $336 Equation 1: \(nx=336\)
Also, from the information in the question
n+4(Hours actualltaken to complete the job)*x2(Don actual payment per hour)=$336 Equation 2: \((n+4)(x2)=336\)
Solving equations 1 and 2 for n and x Putting nx from equation 1 in equation 2
\(336+4x2n8=336\) \(4x2n=8\)
Putting value of x in terms of n from Equation 1
\(4(336/n)2n=8\) \(672/nn=4\) \(n^2+4n672=0\) \(n^2+28n24n672=0\) \((n+28)(n24)=0\) \(n=24\)(Ignoring n=28 as number of hours cannot be negative)
So time Don had estimated to finish the job is 24 hours. Hence, the Answer is B



Current Student
Joined: 08 Feb 2016
Posts: 3
Location: United States
GPA: 3.61
WE: Brand Management (Health Care)

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
25 Feb 2016, 20:06
Reverse Plug in!
1) Start with the middle number and determine in you should go up or down: 336/16= $21/hr 16 is choice C Next add 4 hours > 336/20 = 16.8. hour Difference is not 2. Move up in hours
2) 336/24 = 14 24 is choice B Next add 4 hours > 336/28=12 Difference is 2 so this is the answer



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2649

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
09 Mar 2016, 21:39
Hey Anyone Looking for a more algebraic approach? here is what i actually did let it took x hours to complete the Job So wage per hour = 336/x now as per question => it took x+4 hours to do the job and he was paid => 336/x  2 /hour now total wage must remain constant hence 336 = (336/x  2 ) * (x+4) => x^2 +8x  672 = 0 x=8+52/2 (neglecting the negative value as hours are non negative ) x= 28 Hence A is sufficient ... Would Love your Thoughts on this approach .. MathRevolution
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 664
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
26 May 2016, 17:33
This is one of the toughest questions in the OG: 85% incorrect on GMAT Club! I have found that this one is much easier if you just draw a factor tree and use a little bit of trial and error with the various factors (and combinations thereof). Look for one set of numbers that is 4 apart, and the other 2 apart, and you have your answer. You know that the rate and the time are going to be relatively close to one another, because a difference of $2 in Don's hourly rate results in a difference of 4 hours in the time spent on the job. These numbers are not exactly the same, but they are close, suggesting that r and t are relatively close to one another in value. Attached is a visual that should help.
Attachments
Screen Shot 20160526 at 5.33.02 PM.png [ 108.82 KiB  Viewed 1662 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring
Contact: mcelroy@post.harvard.edu



Senior Manager
Joined: 18 Jan 2010
Posts: 254

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
27 May 2016, 02:47
Suppose Don estimated that the job will be completed in t hours.
Then his hourly rate becomes \(\frac{336}{t}\) $ per hour.
Now when works for 4 hours longer, his hourly rate is $2 less. so
\(\frac{336}{t+4}\) will be the hourly rate
\(\frac{336}{t}\)  2 = \(\frac{336}{t+4}\)
t(t+4) = 2 *21*16 = 24 * 28
We get t = 24
Answer is B



VP
Joined: 07 Dec 2014
Posts: 1064

At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
27 May 2016, 14:35
algebraic approach with one variable 336/t*(t+4)2(t+4)=336 t^2+4t672=0 t=24 hours



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3161
Location: United States (CA)

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
16 Jun 2016, 06:02
macjas wrote: At his regular hourly rate, Don had estimated the labour cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
(A) 28 (B) 24 (C) 16 (D) 14 (E) 12 To solve this problem we can translate the problem with the given information into an equation. Since we don’t know Don's hourly rate nor the time he had estimated for the job, we use two variables: w = Don’s hourly rate t = number of hours he estimated for the job We are given that Don was paid $336, based on his original estimate, so we can say: w x t = 336 Next we are given that the job took 4 hours longer and that, as a result, he earned 2 dollars less than his regular rate. This leads us to say: (w – 2)(t + 4) = 336 We rewrite the equation w x t = 336 as w = 336/t. Now we substitute 336/t for w in the equation (w – 2)(t + 4) = 336. Thus, we have: [(336/t) – 2](t + 4) = 336 After FOILing we have: 336 + (4x336)/t – 2t – 8 = 336 (4x336)/t – 2t – 8 = 0 Multiplying the entire equation by t, we get: 4 x 336 – 2t^2 – 8t = 0 Dividing the entire equation by 2, we get: 2 x 336 – t^2 – 4t = 0 or 672 – t^2 – 4t = 0 We can also rewrite this as: t^2 + 4t – 672 = 0 Now this is where we should be strategic with our answer choices. To solve this quadratic we are looking for two numbers that sum to a positive 4 and multiply to a negative 672. Our answer choices are: (A) 28 (B) 24 (C) 16 (D) 14 (E) 12 There are only two pairs of answer choices that are 4 units apart: 16 and 12, and 28 and 24. Since 24 multiplied by 28 is 672, we know that the numbers that are needed for the factoring are 24 and 28. Thus, we can say: (t – 24)(t + 28) = 0 We can see that t = 24 or t = 28. However, since we can’t have a negative number of hours, only t = 24 is the correct answer. Answer B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 28 Jun 2016
Posts: 207
Location: Canada
Concentration: Operations, Entrepreneurship

Re: At his regular hourly rate, Don had estimated the labour cost
[#permalink]
Show Tags
29 Oct 2016, 17:06
336/(t+4) = 336/t 2 (336+2t+8)*t = 336t +1344 2t^2+8t1344=0 t^2+4t672=0 (t+28)(t24)=0 t = 24 or 28 Time cannot be negative. So t=24. Sent from my iPhone using GMAT Club Forum mobile app



Manager
Joined: 13 Mar 2013
Posts: 173
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
10 May 2017, 23:11
Hi Bunuel , Could you please explain , where it given in the question that w – 2)(t + 4) = 336 Regards
_________________
Regards ,



Math Expert
Joined: 02 Sep 2009
Posts: 47918

At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
11 May 2017, 02:48



Director
Joined: 13 Mar 2017
Posts: 616
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
11 May 2017, 03:31
macjas wrote: At his regular hourly rate, Don had estimated the labour cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
(A) 28 (B) 24 (C) 16 (D) 14 (E) 12 Let the regular hourly rate of Don is x. And the estimated time is y. > xy =336 Since he took 4 hours longer than the estimated time & was paid the $2 per hour less than his regular hourly rate. (x2)(y+4) = 336 > xy  2y + 4x  8 = 336 > 336 + 4x  2y  8 = 336 > 4x 2y = 8 > 2x  y = 4 > 2x  336/x = 4 > x  168/x = 2 > x^2  168  2x = 0 > x^2  14x + 12x  168 = 0 > x(x14) + 12(x14) = 0 > (x+12)(x14) = 0 > x = 14 Estimated time y = 336/14 = 24.
_________________
CAT 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1394
Location: Viet Nam

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
11 May 2017, 08:37
macjas wrote: At his regular hourly rate, Don had estimated the labour cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
(A) 28 (B) 24 (C) 16 (D) 14 (E) 12 \(x\) is the hours that Don had estimated, so \(\frac{336}{x}\) is the money per hour he earned. We have \((x+4)\times (\frac{336}{x}2)=336\) \(\implies (x+4)(3362x)=336x \\ \implies 336x  2x^2 + 4\times 336  8x = 336x \\ \implies 2x^2 +8x = 4 \times 336 \\ \implies x^2 +4x = 2\times 336 = 672 \\ \implies x^2 + 4x + 4 = 676 \\ \implies (x+2)^2 = 676\) Note that \(676 = 2\times 338 =2 \times 2 \times 169 = 2^2 \times 13^2 = 26^2\) Hence \((x+2)^2=26^2 \implies x+2=26\) since \(x > 0\) \(\implies x=24\). The answer is B.
_________________
Actual LSAT CR bank by Broall
How to solve quadratic equations  Factor quadratic equations Factor table with sign: The useful tool to solve polynomial inequalities Applying AMGM inequality into finding extreme/absolute value
New Error Log with Timer



Intern
Joined: 20 May 2017
Posts: 4

At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
22 May 2017, 13:30
Hi guys,
I have two questions:
1) I understand every part of the solution, but I need a lot of time for factoring (last step):
(t^2)+4t672=0 > factor (t24)(t+28)=0
How do you do that? What is your approach? What I would do is, split 672 up into its factors, which are 2^5*3*7 ... and then I try every single calculation to find the right figures.
2) How can questions like this be done within 2 minutes? Even after I knew this question by heart, it took me 5 1/2 minutes to get it done, by writing all the important steps down, without taking a break to think. There are worse questions than this one, but still ...
Thanks, Tom



CEO
Joined: 12 Sep 2015
Posts: 2702
Location: Canada

At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
28 Aug 2017, 14:26
macjas wrote: At his regular hourly rate, Don had estimated the labour cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
(A) 28 (B) 24 (C) 16 (D) 14 (E) 12 Here's an algebraic solution: Let h = # of hours that Don ESTIMATED for the job. So, h + 4 = ACTUAL # of hours it took Don to complete the job. So, IF Don, had completed the job in h hours, his RATE would have = $336/hHowever, since Don completed the job in h+4 hours, his RATE was actually = $336/(h + 4)...consequently, he earned 2$ per hour less than his regular hourly rate.In other words, (John's estimated rate)  2 = (John's actual rate) So, $336/h  2 = $336/(h + 4)ASIDE: since the above equation is a bit of a pain to solve, you might consider plugging in the answer choices to see which one works. Okay, let's solve this: $336/h  2 = $336/(h + 4)To eliminate the fractions, multiply both sides by (h)(h+4) to get: 336(h+4)  2(h)(h+4) = 336h Expand: 336h + 1344  2h²  8h = 336h Simplify: 2h²  8h + 1344 = 0 Multiply both sides by 1 to get: 2h² + 8h  1344 = 0 Divide both sides by 2 to get: h² + 4h  672 = 0 Factor (yeeesh!) to get: (h  24)(h + 28) = 0 Solve to get: h = 24 or h = 28 Since h cannot be negative (in the real world), h must equal 24. Answer:
_________________
Brent Hanneson – Founder of gmatprepnow.com



Manager
Joined: 07 Jun 2017
Posts: 175
Location: India
Concentration: Technology, General Management
GPA: 3.6
WE: Information Technology (Computer Software)

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
01 Sep 2017, 00:29
Plug the Answer choice always take from middle (C) here 336/16 = 21, so 19*20 not equal to 336 and also it is 380 so go lesser value (B) 336 /24 = 14, S0 12* 26 = 336 fits so answer is B
_________________
Regards, Naveen email: nkmungila@gmail.com Please press kudos if you like this post



Intern
Joined: 12 Nov 2015
Posts: 31

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
04 Oct 2017, 02:42
Bunuel wrote: macjas wrote: At his regular hourly rate, Don had estimated the labour cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
(A) 28 (B) 24 (C) 16 (D) 14 (E) 12 Say the regular hourly rate was \(r\)$ and estimated time was \(t\) hours, then we would have: \(rt=336\) and \((r2)(t+4)=336\); So, \((r2)(t+4)=rt\) > \(rt+4r2t8=rt\) > \(t=2r4\). Now, plug answer choices for \(t\) and get \(r\). The pair which will give the product of 336 will be the correct answer. Answer B fits: if \(t=24\) then \(r=14\) > \(rt=14*24=336\). Answer: B. Hope it's clear. I'm a bit confused here. I see that once I get to t=2r4 that I can plug in the answers to see which one fits, but If I try answer a, 28, I get 28=2r4, r=12, 12*28 = 336 which is the same as I get when I plug in answer choice B. I'm sure I'm missing a step here but I can't figure it out. Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 47918

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
04 Oct 2017, 03:00
jboog wrote: Bunuel wrote: macjas wrote: At his regular hourly rate, Don had estimated the labour cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?
(A) 28 (B) 24 (C) 16 (D) 14 (E) 12 Say the regular hourly rate was \(r\)$ and estimated time was \(t\) hours, then we would have: \(rt=336\) and \((r2)(t+4)=336\); So, \((r2)(t+4)=rt\) > \(rt+4r2t8=rt\) > \(t=2r4\). Now, plug answer choices for \(t\) and get \(r\). The pair which will give the product of 336 will be the correct answer. Answer B fits: if \(t=24\) then \(r=14\) > \(rt=14*24=336\). Answer: B. Hope it's clear. I'm a bit confused here. I see that once I get to t=2r4 that I can plug in the answers to see which one fits, but If I try answer a, 28, I get 28=2r4, r=12, 12*28 = 336 which is the same as I get when I plug in answer choice B. I'm sure I'm missing a step here but I can't figure it out. Thanks! If t = 28, then \(28=2r4\) > \(32=2r\)and \(r = 16\), not 12.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 21 Oct 2017
Posts: 70
Location: Canada
Concentration: Entrepreneurship, Technology
WE: Project Management (Internet and New Media)

Re: At his regular hourly rate, Don had estimated the labour cos
[#permalink]
Show Tags
26 Nov 2017, 12:25
Can anyone please comment on the following strategy, given that I was able to write down the proper equations (i.e. rt= 336 and (r2)(t+4) = 336). I almost immediately realized that I wouldn't be able to solve that in under 45 minutes with my current ability in algebra, so I went for pairing... Considering one of the answers will give me the time "t", and considering the GMAT loves traps, I looked for a combination of r*t that would give me 336, which wasn't too hard looking at the unit digits... I fully understand I should practice on getting this solved in about 2 minutes, but this is not where I'm at currently. So on test day I would be left with the option of tanking the test by spending 56 minutes or randomly guessing. Please let me know your thoughts. Thanks!
_________________
Please Press +1 Kudos if it helps!
October 9th, 2017: Diagnostic Exam  Admit Master (GoGMAT)  640 November 11th, 2017: CAT 1  Admit Master (GoGMAT)  700 November 20th, 2017: CAT 2  GMATPrep  700 (Q: 47, V: 40) November 25th, 2017: CAT 3  Admit Master (GoGMAT)  710 (Q: 48, V: 40) November 27th, 2017: CAT 4  GMATPrep  720 (Q: 49, V: 40)
December 4th, 2017: GMAT Exam  750 (Q: 48, V: 44, IR: 8, AWA: 6)




Re: At his regular hourly rate, Don had estimated the labour cos &nbs
[#permalink]
26 Nov 2017, 12:25



Go to page
Previous
1 2 3
Next
[ 52 posts ]



