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

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

Cheers,
Brent

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