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

 It is currently 22 Feb 2019, 21:08

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

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
• ### FREE Quant Workshop by e-GMAT!

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.

# 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

Manager
Joined: 21 Oct 2017
Posts: 82
Location: France
Concentration: Entrepreneurship, Technology
GMAT 1: 750 Q48 V44
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 $$r=14$$ --> $$rt=14*24=336$$.

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.

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.
_________________
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/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.[/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
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.
_________________
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 $$\frac{1}{2}*4*\frac{336}{y}=2*\frac{336}{y}$$.
_________________
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 $$\frac{1}{2}*4*\frac{336}{y}=2*\frac{336}{y}$$.

Bunuel - 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
Quote:
Quote:
dave13 wrote:
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 $$\frac{1}{2}*4*\frac{336}{y}=2*\frac{336}{y}$$.

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 practicing questions.
_________________
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
dave13 wrote:
@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

Generally $$\frac{1}{x}*(a + b) = \frac{a}{x} + \frac{b}{x}$$ but $$\frac{1}{x}*(a*b) = \frac{a*b}{x}$$
_________________
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.

Bunuel 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
Top Contributor
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 $$r=14$$ --> $$rt=14*24=336$$.

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 ]

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 Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.