## SAT Math – Percents | Part 2

Hopefully, you have finished the first blog post I wrote about percentages because this directly follows that one. If you haven’t, it describes how to write percentages in the form of multiplication which is very useful when working with a complicated problem. Here we will discuss the more complicated percentage questions and how to go about solving them. The test likely won’t ask you to solve a simple question like “Decrease Y by X percentage” but is more likely to ask something that involves multiple steps. The two most common are “successive percentages” and “reversing percentages.” Keep reading below to find strategies for solving both of them.

# Part 1: Successive Percentages

These questions involve multiple percentages to be taken of the same value to find the answer.

Ex: A book has a retail price P, it is on sale with a 20% discount. Dave uses a super coupon to get an extra 40% off the sale price. What percent of the retail price does Dave pay?

The most common incorrect response I see is P – 20% – 40% = P – 60%, so Dave received a 60% discount. This is wrong because the 40% is a reduction of the sale price, not of the original retail price.Thinking of percentages using the technique in the first blog post will save you here and make it very simple.

P reduced by 20% is P(0.8) and reduced by a further 40% is P(0.8)(0.6) = P(0.48)

So Dave pays 48% of the original retail price.

If you see a problem with a value changed by multiple percentages do not add or subtract the percentages but rewrite them so they can be multiplied!

# Part 2: Reversing Percentages

These problems involve receiving the result of a percentage being taken and you need to solve for the original value.

Ex: A population decreased by 30% from 2010 to 2015. The population in 2015 is 150,000, what was the population in 2010?

The most common mistake for this question is simply increasing the population in 2015 by 30%. 150,000*(1.3) = 195,000. This may get you close to the right answer, but it will never be the right answer. Percentages are not reversible in this way. An easy example to think about is below:

100 decreased by 90% is 10. 10 increased by 90% is NOT 100, it’s 19.

Why does it work like this? The simple answer is that 90% of 100 is not equivalent to 90% of 10. The same way 30% of 150,000 is not equal to 30% of the population in 2010.

To solve this properly you should write it as an algebra equation. Let’s call the population in 2010 P. That gives us:

P * (0.7) = 150,000 solving gives us P = 214,285

Rewriting the equations or at least thinking about the algebraically should help a lot when you need to reverse percentages and will save you from making simple mistakes!

Practice: Put the techniques to use and solve these more complicated percentage problems!

## SAT Math - Quiz

Put the techniques to use and solve these more complicated percentage problems!

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## SAT Math – Percents | Part 1

So you want to take the SAT? This is quite the challenge for nonnative English speakers as it’s even a challenge for native speakers! Luckily, half the test is given in the universal language… MATH. Even so, I’ve noticed some of the math is taught differently in US schools and some of the questions seem to be more focused on this style of problem. I am talking about percentages specifically. I have seen many students struggle with percentages and they almost always make the same mistakes. I’m hoping the strategy that I lay out below will simplify the problems and help you solve them more quickly, but with most maths there are many different ways to approach the same problem. Some approaches will be easier for some students and the same approach will be more difficult for others. This is the technique with which I’ve had the most success.

Part 1: Increasing by a percentage

Ex: What is 180 increased by 5%?

The quickest way to solve this is to write this 180 * 1.05 = 189.
Hold up.
Why is there a 1.05?
I took a shortcut! 180 increased by 5% can be written as:

180 + 180 * 0.5 which is rewritten 180 * (1+0.5) which simplified is 180 * 1.05

I am using the distributive property of multiplication to get 180 * (1+0.5). An easy way to think of this without the steps is to use this formula when increasing Y by percentage X.

Y*(1+X)

Side note: My thought process for solving this on the exam would go something like this. “180 increased by 5%. Do I know 5% of 180? No. What is 10% of 180? Move the decimal to the left so 18, and 5% is half of 10% so 5% must be 9. 180 plus 9 is 189.”

Part 2: Decreasing by a percentage

Ex: What is 120 decreased by 10%?

The quickest way for solving this would be 120 * 0.9 = 108.
Wait.
Stop.
Where did 0.9 come from?
I took a shortcut again. 120 decreased by 10% can be written as:

120 – 120 * 0.1 which is rewritten 120 * (1-0.1) which is equal to 120 * 0.9

In short, if you have a value Y and are decreasing by percentage X use this formula:

Y*(1-X)

Side note: If you are doing this math in your head, which is necessary for the “no calculator” portion, this is my thought process. “What is 10 percent of 120? Just move the decimal point to the left so 12. Okay, so 120 minus 12 is 108.”

## SAT Math - Percents

Practice: Solve these problems using the technique I described above. Try my thought process as well and see if it helps!

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# Che cos’è l’SAT?

Questo è un esame che viene sostenuto dalla maggior parte degli studenti delle scuole superiori negli Stati Uniti ed è usato per l’ammissione nelle università.Ad ogni modo, anche la Bocconi e altre università in Europa accettano l’esame. Per la Bocconi, se gli studenti ottengono un punteggio adeguato, vengono esonerati dal test d’ingresso dell’università.

Questo esame è composto sia da una parte di matematica che da una parte scritta ed entrambe hanno lo stesso valore per il risultato finale. C’è anche un saggio opzionale che riceverà un punteggio separato.

# Quand’è l’SAT?

L’SAT si svolge internazionalmente soltanto poche volte l’anno. Quando controllate le date, assicuratevi di guardare quelle internazionali e non solo quelle per gli Stati Uniti, perché ci sono alcune discrepanze.

Questo è il sito internazionale dove potete trovare tutte le date: https://collegereadiness.collegeboard.org/sat/register/international

Se non è presente il tasto “Register” sotto la data d’esame, vuol dire che è già passata o che l’esame verrà erogato solo negli Stati Uniti.

# Dove posso registrarmi per l’SAT?

Questo è il sito dove ci si può registrare per l’esame: https://collegereadiness.collegeboard.org/sat/register/international

Basta cliccare il tasto “register” sotto la data d’esame di vostra scelta.

Dovrete creare un nome utente e una password. Assicuratevi di averli segnati da qualche parte, perché probabilmente vi serviranno per accedere al sito più volte.

Il processo di registrazione è molto lungo; possono volerci fino a 40 minuti per completarlo. La cosa importante da ricordare è che si possono saltare tutti I campi senza asterisco (*). Questo vi farà risparmiare un sacco di tempo.

Durante il processo di registrazione, ci sarà l’opzione di aggiungere la spiegazione del punteggio finale tramite una quota aggiuntiva. Non consiglio di pagare per questa aggiunta; non è molto d’aiuto e non dice nulla di davvero utile (scusa College Board!).

Alla fine, dovrete aggiungere una foto formato passaporto (non vi preoccupate, potrete scattarla dal vostro cellulare) e infine pagare per completare la registrazione!

```TARIFFE SAT
SAT senza essay:
\$52 + Tassa Internazionale (\$49) = \$101
SAT con essay:
\$68 + Tassa Internazionale (\$49) = \$118
*I prezzi sono aumentati di recente e potrebbero aumentare nuovamente```

Se avete bisogno di ulteriore aiuto con la registrazione, il nostro team a Scrambled Eggs è sempre pronto ad aiutarvi! Basta chiamarci o inviarci un’e-mail!

Oppure accedi al modulo appuntamenti e prenota un colloquio conoscitivo con un nostro insegnante madrelingua inglese per valutare il tuo livello attuale SAT!