February 23, 2019  February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT February 24, 2019 February 24, 2019 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 21 Oct 2017
Posts: 82
Location: France
Concentration: Entrepreneurship, Technology
GPA: 4
WE: Project Management (Internet and New Media)
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
 26 Nov 2017, 11:25
Can anyone please comment on the following strategy, given that I was able to write down the proper equations (i.e. rt= 336 and (r-2)(t+4) = 336). I almost immediately realized that I wouldn't be able to solve that in under 4-5 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 5-6 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)
|
|
|
|
|
|
VP
Joined: 09 Mar 2016
Posts: 1284
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 04:39
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 \((r-2)(t+4)=336\); So, \((r-2)(t+4)=rt\) --> \(rt+4r-2t-8=rt\) --> \(t=2r-4\). 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. Hello Bunuel, here is my solution let total number of hours be y let hourly rate be x Total amount payed x*y= 360 ---> Hourly rate x= y/336 to complete job it took 4 hours longer --> y+4 hourly rate reduced by 2 USD ---> x-2 (y+4)(x-2) = 336 plug in into above equation x= y/336 (y+4)(y/336 - 2) 336y/y - 2y+1344/y - 8 = 336 336 -2y+1344/y-8=336 -2y+1344/y= 336+8-336 -2y+1344/y =8 ok after this I got stuck and confused, where am I going what I am solving  can you please explain what have I done wrong ? I decoded the info correctly I mean expressed initially in numbers. thanks for your help.
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 53066
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 05:57
dave13 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 \((r-2)(t+4)=336\); So, \((r-2)(t+4)=rt\) --> \(rt+4r-2t-8=rt\) --> \(t=2r-4\). 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. Hello Bunuel, here is my solution let total number of hours be y let hourly rate be x Total amount payed x*y= 360 ---> Hourly rate x= y/336to complete job it took 4 hours longer --> y+4 hourly rate reduced by 2 USD ---> x-2 (y+4)(x-2) = 336 plug in into above equation x= y/336 (y+4)(y/336 - 2) 336y/y - 2y+1344/y - 8 = 336 336 -2y+1344/y-8=336 -2y+1344/y= 336+8-336 -2y+1344/y =8 ok after this I got stuck and confused, where am I going what I am solving can you please explain what have I done wrong ? I decoded the info correctly I mean expressed initially in numbers. thanks for your help. If \(xy = 336\), then \(x = \frac{336}{y}\), not x = y/336. \((y+4)(\frac{336}{y} - 2) = 336\); \(336 - 2y + 4*\frac{336}{y} - 8 = 336\); \(y^2 + 4y - 672 = 0\); \(y(y + 4) = 672\) Plug options: \(y = 24\) works. Hope it helps.
_________________
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?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
VP
Joined: 09 Mar 2016
Posts: 1284
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 07:50
here is my solution let total number of hours be y let hourly rate be x Total amount payed x*y= 360 ---> Hourly rate x= y/336to complete job it took 4 hours longer --> y+4 hourly rate reduced by 2 USD ---> x-2 (y+4)(x-2) = 336 plug in into above equation x= y/336 (y+4)(y/336 - 2) 336y/y - 2y+1344/y - 8 = 336 336 -2y+1344/y-8=336 -2y+1344/y= 336+8-336 -2y+1344/y =8 ok after this I got stuck and confused, where am I going what I am solving can you please explain what have I done wrong ? I decoded the info correctly I mean expressed initially in numbers. thanks for your help.[/quote] If \(xy = 336\), then \(x = \frac{336}{y}\), not x = y/336. \((y+4)(\frac{336}{y} - 2) = 336\); \(336 - 2y + 4*\frac{336}{y} - 8 = 336\); \(y^2 + 4y - 672 = 0\); \(y(y + 4) = 672\) Plug options: \(y = 24\) works. Hope it helps.[/quote] Bunuel - Many thanks ! Just two more question could you show in detail how you got this \(y^2 + 4y - 672 = 0\); and another question what is the point of factoring ? \(y(y + 4) = 672\)  I remember when we see such equation\(y^2 + 4y - 672 = 0\); we need to find discriminant ? like D = B^2-4AC
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 53066
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 07:58
|
|
|
|
|
|
VP
Joined: 09 Mar 2016
Posts: 1284
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 08:26
Bunuel wrote: dave13 wrote: Bunuel - Many thanks ! Just two more question could you show in detail how you got this \(y^2 + 4y - 672 = 0\); and another question what is the point of factoring ? \(y(y + 4) = 672\) I remember when we see such equation\(y^2 + 4y - 672 = 0\); we need to find discriminant ? like D = B^2-4AC \(336 - 2y + 4*\frac{336}{y} - 8 = 336\); Cancel 336: \(- 2y + 4*\frac{336}{y} - 8 = 0\); Reduce by 2: \(- y + 2*\frac{336}{y} - 4 = 0\); Multiply by y: \(-y^2+672-4y=0\) Re-arrange: \(y^2 + 4y - 672 = 0\); Here you can solve for y with discriminant formula but it's easier to factor the way shown and PLUG OPTIONS. Thank you Bunuel. When you reduce by 2, why didn't you reduce fraction by 2 as well 336/y Normally when we reduce and or multiply numbers in equation all numbers are subject to be changed accordingly - No ? please correct me if I am wrong.
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 53066
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 08:30
dave13 wrote: Bunuel wrote: dave13 wrote: Bunuel - Many thanks ! Just two more question could you show in detail how you got this \(y^2 + 4y - 672 = 0\); and another question what is the point of factoring ? \(y(y + 4) = 672\) I remember when we see such equation\(y^2 + 4y - 672 = 0\); we need to find discriminant ? like D = B^2-4AC \(336 - 2y + 4*\frac{336}{y} - 8 = 336\); Cancel 336: \(- 2y + 4*\frac{336}{y} - 8 = 0\); Reduce by 2: \(- y + 2*\frac{336}{y} - 4 = 0\); Multiply by y: \(-y^2+672-4y=0\) Re-arrange: \(y^2 + 4y - 672 = 0\); Here you can solve for y with discriminant formula but it's easier to factor the way shown and PLUG OPTIONS. Thank you Bunuel. When you reduce by 2, why didn't you reduce fraction by 2 as well 336/y Normally when we reduce and or multiply numbers in equation all numbers are subject to be changed accordingly - No ? please correct me if I am wrong. No. When you divide \(4*\frac{336}{y}\) you get \(\frac{1}{2}*4*\frac{336}{y}=2*\frac{336}{y}\).
_________________
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?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
VP
Joined: 09 Mar 2016
Posts: 1284
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 08:50
Quote: Quote: Thank you Bunuel. When you reduce by 2, why didn't you reduce fraction by 2 as well 336/y Normally when we reduce and or multiply numbers in equation all numbers are subject to be changed accordingly - No ? please correct me if I am wrong. No. When you divide \(4*\frac{336}{y}\) you get \(\frac{1}{2}*4*\frac{336}{y}=2*\frac{336}{y}\). - But isn't 336/y a separate number ? Shouldn't we have done so 1/2 *4 and 1/2 * 336/y ?
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 53066
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 08:55
|
|
|
|
|
|
VP
Joined: 09 Mar 2016
Posts: 1284
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 09:06
Quote: Quote: Bunuel wrote:
No. When you divide \(4*\frac{336}{y}\) you get \(\frac{1}{2}*4*\frac{336}{y}=2*\frac{336}{y}\).
Bunuel - But isn't 336/y a separate number ? Shouldn't we have done so 1/2 *4 and 1/2 * 336/y ? No. Let me ask you: what is the value of 4*6 when reduced by 2? Is it 2*6 = 12 or 2*3 = 6? I think you'll benefit if you brush up fundamentals before practising questions. @Bunuel- thanks for asking me this question I think if we reduce 4*6 by 2 the answer will be 12 because 4*6 is one number. I have brushed up fundamentals but sometimes in some PS questions i encounter some technical details i have a vague idea about or simply cant use theory in practice. Thanks a lot for explanation
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 53066
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 09:14
|
|
|
|
|
|
VP
Joined: 09 Mar 2016
Posts: 1284
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Dec 2017, 10:59
Bunuel wrote: dave13 wrote: Bunuel - Many thanks ! Just two more question could you show in detail how you got this \(y^2 + 4y - 672 = 0\); and another question what is the point of factoring ? \(y(y + 4) = 672\) I remember when we see such equation\(y^2 + 4y - 672 = 0\); we need to find discriminant ? like D = B^2-4AC \(336 - 2y + 4*\frac{336}{y} - 8 = 336\); Cancel 336: \(- 2y + 4*\frac{336}{y} - 8 = 0\); Reduce by 2: \(- y + 2*\frac{336}{y} - 4 = 0\); Multiply by y: \(-y^2+672-4y=0\) Re-arrange: \(y^2 + 4y - 672 = 0\); Here you can solve for y with discriminant formula but it's easier to factor the way shown and PLUG OPTIONS. could you please tell me in which case should I use factoring and in which case conventional method of finding discriminant ? Thanks a lot answering my questions. Highly appreciated!
|
|
|
|
|
|
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 504
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
21 Jul 2018, 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 \((r-2)(t+4)=336\); So, \((r-2)(t+4)=rt\) --> \(rt+4r-2t-8=rt\) --> \(t=2r-4\). 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. Solving Quadric equation is taking too much time. So What we take back solving approach. RT = 336 and, (R-2)(T+4)=336-----(ii) If we start back solving from C then we get Time 16 and Rate 21, these values don't satisfy equation (ii) the given answer choices are increasing so we don't have to try D and E options. Trying B, Time is 24 and Rate is (334/24)= 14 Thus, Puting the values in equation ii, (14-2)(24+4) = 12 x 28 = 336 Ans B.
_________________
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html
|
|
|
|
|
|
Director
Joined: 19 Oct 2013
Posts: 508
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
Show Tags
26 Sep 2018, 05:00
Well what I did was basically to prime factorize \(336 = \frac{2^4 * 3 * 7}{x}\)
I then tried \(x = 24 = 2^3 * 3\) back in the equation and ended up with \(2 * 7 = 14\)
Now if we add \(x+4 = 24 + 4 = 28\)
\(28 = 2^2 * 7 = 28\) and that would leave \(2^2 * 3 = 12\)
|
|
|
|
|
|
|
Re: At his regular hourly rate, Don had estimated the labor cos
[#permalink]
26 Sep 2018, 05:00
|
|
|
|
|
Go to page
Previous
1 2 3
[ 54 posts ]
|
|
|
|
|
|
close
