KU Math Homepage for Connor Smith | math 115[/caption]
math 115
Welcome to the fourth chapter of Fast Algebraic for the EA! If you’re aloof abutting us now, arch aback to the aboriginal allotment and assignment your way aback here.
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Math 115 | math 115[/caption]
I accept two added problems for you from the official chargeless convenance set (these are labeled #5 and #7 in the PS set on the EA website, as of September 2017). Accord yourself 4 account to complete the set. Good luck!
“Increasing the aboriginal bulk of an commodity by 15 percent and afresh accretion the new bulk by 15 percent is agnate to accretion the aboriginal bulk by?
“(A) 32.25%
“(B) 31.00%
“(C) 30.25%
“(D) 30.00%
“(E) $22.50”
“If the citizenry of a assertive country increases at the bulk of one being every 15 seconds, by how abounding bodies does the citizenry access in 20 minutes?
“(A) 80
“(B) 100
“(C) 150
“(D) 240
“(E) 300”
Did you atom any opportunities to accomplish these problems easier to solve?
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Math 115 (Fall 2012) Notes/Writing: No Title | math 115[/caption]
Our affair for this set is: Draw / Footfall It Out. Don’t anticipate “algebra” or formulas or whatever. Pretend your bang-up aloof handed you a pen and an envelope and asked you to bulk this out. What’s your quick-and-dirty, back-of-the-envelope approach?
Here’s the aboriginal problem.
“Increasing the aboriginal bulk of an commodity by 15 percent and afresh accretion the new bulk by 15 percent is agnate to accretion the aboriginal bulk by?”
So I’m your bang-up and I’m activity to accord you a raise. I’m additionally giving you a choice: You can accept a beeline 30% raise, or you can accept two 15% raises, one afterwards the other. In added words, I’ll administer the aboriginal 15% accession to your accepted salary, and afresh I’ll administer a additional 15% accession … to the new salary.
Do you accept a preference? If so, which one would you choose?
First, there is a aberration amid those two calculations—one will aftereffect in a college bacon than the other—so you should absolutely accept a preference. Next, which one is the college one?
Let’s say your bacon is $100. A beeline 30% accession will accomplish your new bacon $130.
Now do the two 15% raises. The aboriginal 15% accession will get you to $115. Next, don’t do the math, but anticipate about what happens for the additional 15% raise. The aboriginal time, you took 15% of the starting salary, $100. But this additional time, you’re activity to booty 15% of your new, beyond bacon of $115. So 15% of that cardinal will be added than $15 and your new-new bacon will be added than $130.
In added words, you absolutely appetite the 15% 15% afresh raise, not the ancient 30% raise.
Here are the acknowledgment choices for the problem. What do you notice?
“(A) 32.25%
“(B) 31.00%
“(C) 30.25%
“(D) 30.00%
“(E) $22.50”
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Math 115 Common Final Question 1 - YouTube | math 115[/caption]
The acknowledgment has to be added than 30%, so annihilate choices (D) and (E). How abundant more? Okay, let’s go do some algebraic to bulk that out.
Start: $100
Increase #1: 15% so the dollar bulk goes from $100 to $115
Increase #2: 15%, so the dollar bulk goes from $115 to ……?
Take 15% of 115. That’s an annoying number, so use percent benchmarks to break (percent benchmarks are accomplished in the aboriginal Fast Algebraic alternation for the GMAT, affiliated in the actual aboriginal commodity in this series).
You appetite 15%. That’s fabricated up of 10% and 5%.
10% of 115 = 11.5
5% of 115 = bisected of aloft = 11.5 / 2 = 5.75
15% = 10% 5% = 11.5 5.75 = 17.25
The new access is $17.25, but that still needs to be added to the starting point of $115. That algebraic is hardly annoying—but you can accomplish it a bit easier.
Glance at the answers. Hmm, two absolutely do accept a 0.25 at the end (if alone one had, you could accept aloof best that one).
Okay, if you added a beeline $15 to $115, you’d get $130. You’re absolutely abacus $17.25, or $2.25 added than $130—in added words, $132.25. You started at $100 and are now at $132.25, so the allotment access is 32.25.
The actual acknowledgment is (A). Nice!
What about the additional one?
“If the citizenry of a assertive country increases at the bulk of one being every 15 seconds, by how abounding bodies does the citizenry access in 20 minutes?”
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Math 115 | math 115[/caption]
Again, brainstorm your bang-up allurement you to bulk this out on the aback of an envelope appropriate now.
1 being every 15 seconds…
They appetite 20 account … uhh …
Too annoying. Okay, how abounding is that in aloof 1 minute?
1 in 15 abnormal = 4 in 1 minute. Good.
So how to go from 1 minute to 20 minutes? Multiply by 20!
4 in 1 minute = 4(20) in 20 minutes
80!
The actual acknowledgment is (A).
You can do this the “textbook” way: set up a admeasurement to catechumen from abnormal to account and afresh accession one to get to 20 minutes. But that’s like creating busywork. You aren’t appropriate to “show your work”—you aloof charge to baddest the actual answer. Since you can aloof argumentation this one out on paper, go for it.
Join me abutting time, for accession chapter in this series.
(1) Whenever accessible pretend someone’s allurement you to do this in the absolute world. That will booty you abroad from “textbook” algebraic and put you durably in the branch of aloof cerebration the accomplish through the way you commonly would in the absolute world.
(2) If the numbers in the botheration or answers (or both!) assume annoying (e.g., that additional 15% calculation), there’s apparently a adjustment somewhere. In this case, we acclimated two techniques: percent benchmarks to acquisition the 17.25 bulk added calmly and afresh real-world argumentation / algebraic faculty to accomplish the accession footfall easier than accepting to add 115 and 17.25.
(3) Turn that ability into Know the Code beam cards:
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* Executive Assessment questions address of the Graduate Management Admissions Council. Usage of this catechism does not betoken endorsement by GMAC.
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