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

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At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 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.

Kudos [?]: 23 [0], given: 183

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Posts: 43296

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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 26 Dec 2017, 05:57
Expert's post
1
This post was
BOOKMARKED
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/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.
_________________

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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

Kudos [?]: 139200 [0], given: 12779

Manager
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Joined: 09 Mar 2016
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Kudos [?]: 23 [0], given: 183

At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 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

Kudos [?]: 23 [0], given: 183

Expert Post
Math Expert
User avatar
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Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 26 Dec 2017, 07:58
Expert's post
1
This post was
BOOKMARKED
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.
_________________

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

Kudos [?]: 139200 [0], given: 12779

Manager
Manager
User avatar
B
Joined: 09 Mar 2016
Posts: 133

Kudos [?]: 23 [0], given: 183

At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 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.

Kudos [?]: 23 [0], given: 183

Expert Post
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Math Expert
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V
Joined: 02 Sep 2009
Posts: 43296

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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 26 Dec 2017, 08:30
1
This post received
KUDOS
Expert's post
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

Kudos [?]: 139200 [1], given: 12779

Manager
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User avatar
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Joined: 09 Mar 2016
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Kudos [?]: 23 [0], given: 183

At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 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 ? :?

Kudos [?]: 23 [0], given: 183

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Joined: 02 Sep 2009
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Kudos [?]: 139200 [0], given: 12779

At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 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.
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Resources:
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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

Kudos [?]: 139200 [0], given: 12779

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At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 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 :)

Kudos [?]: 23 [0], given: 183

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Joined: 02 Sep 2009
Posts: 43296

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Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 26 Dec 2017, 09:14
Expert's post
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This post was
BOOKMARKED
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 \(\frac{1}{x}*(a*b) = \frac{a*b}{x}\)
_________________

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

Kudos [?]: 139200 [0], given: 12779

Manager
Manager
User avatar
B
Joined: 09 Mar 2016
Posts: 133

Kudos [?]: 23 [0], given: 183

Re: At his regular hourly rate, Don had estimated the labour cos [#permalink]

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New post 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!

Kudos [?]: 23 [0], given: 183

Re: At his regular hourly rate, Don had estimated the labour cos   [#permalink] 26 Dec 2017, 10:59

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