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Word problem - rates

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RobertP: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Fri Jan 22, 2016 11:59 am

by RobertP » Thu Feb 04, 2016 5:03 pm

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Hello everyone!

Ok, this question is actually from the GMAT review book 2016. I am only posting this here because I tried the method demonstrated on the videos, but it is just not working so I would like to grasp what I am doing wrong. Could someone help me, please? Thank you!

Working simultaneously at their respective constate rates, Machines A and B produce 800 nails in X hours. Wokring alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y how many hours does it take Machine B working alone at its constant rate, to produce 800 nails?

A) x/x+y
B) y/x+y
C) xy/x+y
D) xy/x-y
E)xy/y-x

Answer: E

I was trying to do the substition method, as such: x = 20, y = 10. Plugged the formula in: 1/80+ Rb = 1/40. Eventually RB lead me to 1/80. When checking the answers, nothing would match.

Thank you very much for your help!

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Source: Beat The GMAT — Problem Solving | Thu Feb 04, 2016 5:03 pm

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by Brent@GMATPrepNow » Thu Feb 04, 2016 5:05 pm

Working simultaneously at their respective constant rates, Machine A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?

(A) x/(x+y)
(B) y/x+y
(C) xy/(x+y)
(D) xy/(x-y)
(E) xy/(y-x)

I was stuck when I tried to pick numbers.

The picking numbers approach

Let's pick some nice numbers for x and y

We'll say that, working together, machines A and B can produce 800 nails in 2 hours.
This means that, in one hour, they can produce a total of 400 nails.

We'll also say that, working alone, machine A can produce 800 nails in 8 hours.
This means that, in one hour, machine A can produce 100 nails.

So, working together A and B produce 400 nails in one hour, and, working alone, A can produce 100 nails in one hour. This means that machine B can make 300 nails in one hour.

If machine B can make 300 nails in one hour, how long will it take to produce 800 nails? It will take 8/3 hours.

In other words, when x=2 and y=8, the result is that it takes machine B 8/3 hours to make 800 nails.

Now we check the answer choices to see which one yields a result of 8/3 when x=2 and y=8.

(A) x/(x+y) --> 2/(2+8) = 1/5 NOPE
(B) y/x+y --> 8/2+8 = 12 NOPE
(C) xy/(x+y) --> (2)(8)/(2+8) = 8/5 NOPE
(D) xy/(x-y) --> (2)(8)/(2-8) = -8/3 NOPE
(E) xy/(y-x) --> (2)(8)/(8-2) = 8/3 YES!!

So, the answer is E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Brent@GMATPrepNow » Thu Feb 04, 2016 5:06 pm

Working simultaneously at their respective constant rates, Machine A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?

(A) x/(x+y)
(B) y/x+y
(C) xy/(x+y)
(D) xy/(x-y)
(E) xy/(y-x)

Here's the algebraic approach.

It requires us to use two rules:

Rule #1: If it takes k hours to complete a job then, after 1 hour, the job will be 1/k completed.
Example: If it takes Val 5 hours to paint the house, then after 1 hour, she will have painted 1/5 of the house

Rule #2: If, after one hour, a job is x/y completed, the entire job will take y/x hours to complete.
Example: After 1 hour, Pump A has removed 2/7 of the water from the pool. Therefore, it will take a total of 7/2 hours to remove all of the water.

Okay, now to the question.

Given: Working together, Machines A and B produce 800 nails in x hours.
By rule #1, we can say that, after 1 hour, the machines will have completed 1/x of the job (the job being the production of 800 nails)

Given: Working alone, Machine A produces 800 in y hours
By rule #1, we can say that, after 1 hour, Machine A will have completed 1/y of the job (the job being the production of 800 nails)

Important: After one hour, Machine A's contribution + Machine B's contribution = 1/x

We can now write: 1/y + Machine B's contribution = 1/x
So, after one hour, Machine B's contribution = 1/x - 1/y
Combine the fractions to get: Machine B's contribution = y/xy - x/xy = (y-x)/xy
So, in one hour, Machine B can complete (y-x)/xy of the job.

By rule #2, it will take machine B xy/(y-x) hours to complete the job (the job being the production of 800 nails)

So, the answer is E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Thu Feb 04, 2016 8:04 pm

Hi RobertP,

What videos are you referring to?

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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RobertP: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Fri Jan 22, 2016 11:59 am

by RobertP » Fri Feb 05, 2016 7:03 am

Hi Rich,

To the videos posted on the link bellow:

https://www.gmatprepnow.com/module/gmat-word-problems.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Feb 05, 2016 7:06 am

RobertP wrote:Hi Rich,

To the videos posted on the link bellow:

https://www.gmatprepnow.com/module/gmat-word-problems.

Are you referring to our lessons on Variables in the Answer Choices?
- https://www.gmatprepnow.com/module/gmat- ... /video/933
- https://www.gmatprepnow.com/module/gmat- ... /video/934
- https://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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RobertP: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Fri Jan 22, 2016 11:59 am

by RobertP » Fri Feb 05, 2016 7:51 am

Yep!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Feb 05, 2016 11:47 am

RobertP wrote:Hello everyone!

Ok, this question is actually from the GMAT review book 2016. I am only posting this here because I tried the method demonstrated on the videos, but it is just not working so I would like to grasp what I am doing wrong. Could someone help me, please? Thank you!

Working simultaneously at their respective constate rates, Machines A and B produce 800 nails in X hours. Wokring alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y how many hours does it take Machine B working alone at its constant rate, to produce 800 nails?

A) x/x+y
B) y/x+y
C) xy/x+y
D) xy/x-y
E)xy/y-x

Answer: E

I was trying to do the substitution method, as such: x = 20, y = 10. Plugged the formula in: 1/80+ Rb = 1/40. Eventually RB lead me to 1/80. When checking the answers, nothing would match.

Thank you very much for your help!

Let's be careful that we use your input values ( x = 20, y = 10) correctly.

If x = 20, then, TOGETHER, A and B can make 800 nails in 20 hours. This means their COMBINED rate is 40 nails PER HOUR

If y = 10, then, MACHINE A can make 800 nails in 10 hours. This means MACHINE A's rate is 80 nails PER HOUR

Stop right there! This scenario is impossible.
This means that, working ALONE, Machine A makes more nails per hour than Machines A and B working TOGETHER.

------------------------------------------
Let's try some different numbers.
How about x = 10 and y = 20

If x = 10, then, TOGETHER, A and B can make 800 nails in 10 hours. This means their COMBINED rate is 80 nails PER HOUR

If y = 20, then, MACHINE A can make 800 nails in 20 hours. This means MACHINE A's rate is 40 nails PER HOUR

If their COMBINED rate is 80 nails PER HOUR, and MACHINE A's rate is 40 nails PER HOUR, then MACHINE B's rate is 40 nails PER HOUR
If MACHINE B's rate is 40 nails PER HOUR, then it will take machine B 20 hours to make 800 nails.
So, when we INPUT x = 10 and y = 20, the OUTPUT (answer to the question) must be 20

When we check each answer choice, only E outputs the correct value of 20

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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