Lesson: Tips for the Input-Output Approach

Comment on Tips for the Input-Output Approach

Hey, I had fun using an approach that you taught in a different vid. Total purchase price was 90 cents, so if you set b = 30, then zero nuts were purchased. Makes it faster to evaluate, but I don't know if there's more than one answer choice that works for it. (at 3:44)
greenlight-admin's picture

Try plugging in a = 0 and b = 30 and see which answer choices yield the required output of 90 cents. PRO TIP: Using super convenient numbers like this will often yield more than one answer choice that works (the test-makers often penalize you from using easy numbers like 0), which means you'll have take the remaining answer choices and plug in different values.

Sir i took my investment to be $100
from Wednesday to Thursday = 5% increase
From Thursday to Friday = 7% increase
I randomly selected 5% and 7%

Therefore
Thursday => 5% increase means = 105% or 1.05
=> 1.05*100 = 105$
Friday => 7% increase means 107% or 1.07
=> 1.07*105 = $112.35

percentage change is 112.35 - 100 = 12.35.

none of my options yield the result 12.35

Option A gives 12%/100
Option B gives 0.120035 or 12.0035%
Option c gives 12%
option D gives 12.0035%
option E gives 0.0011985 or 0.11%

what am i doing wrong?

ohhh okay i got.... My mistake in the previous comment was that i was taking values of X and Y in terms of percentage. After i plugged the the values of X and Y as 5 and 7 in option B, i got the correct value..so B is correct option :)

Please can you also share the algebraic solution. I have tried multiple times but not able to get the format in answer choice B.
greenlight-admin's picture

I believe you're referring to the question that starts around 6:25 in the video.

It's a killer!!!

Let W = value of portfolio on Wednesday
So (1 + x/100)W = value of portfolio on Thursday
And (1 + y/100)(1 + x/100)W = value of portfolio on Friday

Percent increase = 100(new - old)/old

So, percent increase = 100[(1 + y/100)(1 + x/100)W - W]/W

This expression does not match any of the answer choices.
So, we need to rewrite the expression.

Take: 100[(1 + y/100)(1 + x/100)W - W]/W
Divide top and bottom by W to get: 100[(1 + y/100)(1 + x/100) - 1]/1
Expand to get: (100)(1 + y/100)(1 + x/100) - 100]/1

Aside: (100)(1 + y/100)= 100 + y
So, we can write: [(100 + y)(1 + x/100) - 100]/1

Multiply top and bottom of the fraction by 100 to get: [(100 + y)(100 + x) - 100²]/100
Rewrite as: (100 + y)(100 + x)/100 - 100²/100
Simplify: (100 + y)(100 + x)/100 - 100

Answer: B

Does that help?

Cheers,
Brent

Isn't the percent increase (180-150/150)*100
greenlight-admin's picture

I'm not sure what question you're referring to, but your calculations are correct.

If some value increases from 150 to 180, then the...
...percent increase = [(180-150)/150](100)
= [30/150](100)
= [1/5](100)
= 100/5
= 20%

For more on percent increase, watch: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1083

Cheers,
Brent

No answer was given for the nuts and bolts example, but I believe it's B.
greenlight-admin's picture

The correct answer (B) is displayed at 5:15 in the above video.

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