Lesson: Tips for the Input-Output Approach

Comment on Tips for the Input-Output Approach

Great tips

Hi! If you were to solve this algebraically, how would you do it? I get to (1 + y/100 + x/100 + xy/100^2) - 1 and that's basically the right answer... but how do you simplify that to match the answer format? I mean, once I know the answer (100+y)(100+x) then multiplying gives me the above expression inside parenthesis.. but if I didn't know that factorization was there, how do you reach to it?
gmat-admin's picture

You're referring to the question that appear at 6:23 in the above video.

You have: (1 + y/100 + x/100 + xy/100²) - 1

Rewrite first part with denominator 100²
We get: (100²/100² + 100y/100² + 100x/100² + xy/100²) - 1
Combine the first 4 terms: (100² + 100y + 100x + xy)/100² - 1
Factor top part to get: (100 + x)(100 + y)/100² - 1

Hmmm, I have a feeling your first expression, (1 + y/100 + x/100 + xy/100²) - 1, is incorrect.

Can you tell me how you got to (1 + y/100 + x/100 + xy/100²) - 1?


At his regular hourly rate, Don had estimated the labor
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
sir how to solve this question?
gmat-admin's picture

sir please explain.
gmat-admin's picture

At the risk of appearing super lazy, I've seen Mitch (GMATGuruNY) post this great solution several times, and I think it's perfect: https://www.beatthegmat.com/og-13-ps-218-is-this-prob-really-doable-with... (Mitch's solution is the 4th post)

He also provides some great advice about the potential to skip (guess) and move on!

If you need any clarification regarding Mitch's solution, please let me know.


Hi Brent,

Is there an easy way to solve the below question:

gmat-admin's picture

As you mentioned, an *algebraic* solution is usually quicker than the *input-output* approach. For the *nuts and bolts* question, the equation is: 2n + 3b = 90; then n (number of nuts) = 45 - 3b/2 => which is correct, right?

If so, I assume you're just using it as an example to demo the *input-output* technique, even though there is an algebraic solution, correct?

gmat-admin's picture

Yes, I'm using the input-output for this question so I can demonstrate the strategy.

Regarding the second question, I am so confused with the way you plug 0 into x.
Given the fact of question, "x percent greater than it's value on Wednesday", if we plug 0 into x which does not make sense at all ?
Please help !
gmat-admin's picture

I believe you're referring to the question that starts at 6:22 in the video above.

It's perfectly fine to have an "increase" of 0%. This Just means there was no increase.

For example, if Townville had a population of 10,000 in 2018, and a population of 10,000 in 2019, then we can say that the population "increased" 0% from 2018 to 2019. In other words, the population in 2019 is 0% greater than the population in 2018.

Does that help?

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