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y dollars from the rental venture

by sanju09 » Sat Dec 28, 2013 12:12 am
Jason collects x dollars by renting out his family's house while they are on vacation. He also receives a 2-dollar tip from the renters. Jason's family has five members including Jason, and all of the money Jason receives from the renters including the tip is divided evenly among the five family members. Jason spends six dollars of his share leaving him with y dollars from the rental venture. Which of the following represents the amount, x, that Jason charged for the house rental?
(A) 5 "¢ (y + 6) / 2
(B) ((y + 6) / 5) - 2
(C) 5y + 28
(D) 5y + 8
(E) 2 "¢ (y + 6) / 5


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by Brent@GMATPrepNow » Sat Dec 28, 2013 6:56 am
sanju09 wrote:Jason collects x dollars by renting out his family's house while they are on vacation. He also receives a 2-dollar tip from the renters. Jason's family has five members including Jason, and all of the money Jason receives from the renters including the tip is divided evenly among the five family members. Jason spends six dollars of his share leaving him with y dollars from the rental venture. Which of the following represents the amount, x, that Jason charged for the house rental?
(A) 5 "¢ (y + 6) / 2
(B) ((y + 6) / 5) - 2
(C) 5y + 28
(D) 5y + 8
(E) 2 "¢ (y + 6) / 5
Here's an algebraic approach:

$ from rental: x
$ from tip: 2
TOTAL revenue = x + 2

All of the money Jason receives from the renters including the tip is divided evenly among the five family members.
So, Jason's share = (x+2)/5

Jason spends six dollars of his share leaving him with y dollars from the rental venture.
So, (x+2)/5 - 6 = y

Which of the following represents the amount, x, that Jason charged for the house rental?
Solve the equation for x
(x+2)/5 - 6 = y
Add 6 to both sides to get: (x+2)/5 = y+6
Multiply both sides by 5 to get: x+2 = 5(y+6)
Subtract 2 from both sides to get: x = 5(y+6) - 2
Simplify to get: x = [spoiler]5y + 28 = C[/spoiler]

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by Brent@GMATPrepNow » Sat Dec 28, 2013 7:08 am
sanju09 wrote:Jason collects x dollars by renting out his family's house while they are on vacation. He also receives a 2-dollar tip from the renters. Jason's family has five members including Jason, and all of the money Jason receives from the renters including the tip is divided evenly among the five family members. Jason spends six dollars of his share leaving him with y dollars from the rental venture. Which of the following represents the amount, x, that Jason charged for the house rental?
(A) 5 "¢ (y + 6) / 2
(B) ((y + 6) / 5) - 2
(C) 5y + 28
(D) 5y + 8
(E) 2 "¢ (y + 6) / 5
Here's a solution using the input-output approach:

Let's choose a nice value of x (rental price) that yields a nice y-value (Jason's remaining money).
Let's say x = 28
If x = $28, then the TOTAL revenue (after the tip) = $30, which means Jason's share is $6
Once Jason spends $6, he has $0 remaining.
In other words, y = 0

So, when y = 0, x = 28
Now we'll check the answer choices to see which one yields an output of 28 when y = 0

(A) 5 "¢ (y + 6) / 2 = 5 "¢ (0 + 6) / 2 = 15 (NOPE)
(B) ((y + 6) / 5) - 2 = ((0 + 6) / 5) - 2 = negative something (NOPE)
(C) 5y + 28 = 5(0) + 28 = 28 BINGO!!
(D) 5y + 8 = 5(0) + 8 = 8 (NOPE)
(E) 2 "¢ (y + 6) / 5 = 2 "¢ (0 + 6) / 5 = 12/5 (NOPE)

Answer: C

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by theCodeToGMAT » Sat Dec 28, 2013 8:30 am
Rent = x
Total Amount = x + 2
Share per person = (x+2)/5

(x+2)/5 - 6 = y
x + 2 = 5 (y+6)
x = 5(y+6) - 2
x = 5y + 28
[spoiler]{C}[/spoiler]
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by sanju09 » Sat Dec 28, 2013 10:32 pm
Brent's second approach is wonderful. It makes life easy for those who are not very comfortable at Algebra. Hope Brent or Rahul pay their two bits at the following thread too:

https://www.beatthegmat.com/on-this-chri ... tml#706570
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by Amrabdelnaby » Mon Nov 30, 2015 3:11 am
Hello Brent,

I actually solved this question using the algebra; however i see that u used it using plug ins method.

I am a bit of good in both; however I want to ask you, in general, when should I use plug ins and when should i use algebra? what signs should i look for that would guide me to a faster solving approach.

I don't want to for example start using algebra and find it time consuming then switch to plug ins during the exam. I will waste a lot of time :)

Please advise

Thanks
Brent@GMATPrepNow wrote:
sanju09 wrote:Jason collects x dollars by renting out his family's house while they are on vacation. He also receives a 2-dollar tip from the renters. Jason's family has five members including Jason, and all of the money Jason receives from the renters including the tip is divided evenly among the five family members. Jason spends six dollars of his share leaving him with y dollars from the rental venture. Which of the following represents the amount, x, that Jason charged for the house rental?
(A) 5 "¢ (y + 6) / 2
(B) ((y + 6) / 5) - 2
(C) 5y + 28
(D) 5y + 8
(E) 2 "¢ (y + 6) / 5
Here's an algebraic approach:

$ from rental: x
$ from tip: 2
TOTAL revenue = x + 2

All of the money Jason receives from the renters including the tip is divided evenly among the five family members.
So, Jason's share = (x+2)/5

Jason spends six dollars of his share leaving him with y dollars from the rental venture.
So, (x+2)/5 - 6 = y

Which of the following represents the amount, x, that Jason charged for the house rental?
Solve the equation for x
(x+2)/5 - 6 = y
Add 6 to both sides to get: (x+2)/5 = y+6
Multiply both sides by 5 to get: x+2 = 5(y+6)
Subtract 2 from both sides to get: x = 5(y+6) - 2
Simplify to get: x = [spoiler]5y + 28 = C[/spoiler]

Cheers,
Brent
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by Brent@GMATPrepNow » Mon Nov 30, 2015 9:56 am
Amrabdelnaby wrote:Hello Brent,

I actually solved this question using the algebra; however i see that u used it using plug ins method.

I am a bit of good in both; however I want to ask you, in general, when should I use plug ins and when should i use algebra? what signs should i look for that would guide me to a faster solving approach.

I don't want to for example start using algebra and find it time consuming then switch to plug ins during the exam. I will waste a lot of time :)

Please advise

Thanks
Great question.
Here's my not-so-great response: It really depends on each test-taker's strengths and weaknesses.
In general, I like to look for an algebraic response first, but if it looks it will be a tedious process, I might go to the plug-in approach.
The plug-in approach USUALLY takes longer (since you have to check EVERY answer choice), but it's a great option if you don't know how to solve it algebraically.
I suggest that people try to solve these kinds of questions using BOTH approaches as they practice to help them see which one works best for them.

If you'd like more information on these two approaches, we have some free videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent
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