Most courses that try to teach content in a classroom only give you the quick headlines of each topic, because they don’t have time for more. Here’s how we are different.

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**Explore topics in more depth**

“Absolute value is the distance of a number from 0 on the number line. 5 and -5 are both 5 away from 0 in different directions, so they both have an absolute value of 5.” We use the || symbol for absolute value, so |-5| means the absolute value of -5. So, |-5|=5 and |5|=5.”

Data sufficiency question:

Does |a-b|=|b-a| ?

(1) Th 5th power of *a* muitplied by the square of *b* is positive

(2) The square of *a* multiplied by the cube of *b* is negative

Now, does that tutorial equip you to answer that question?

Of course it does not. But most courses that try to teach content in the classroom do not have time to go into all the intricacies of topics like absolute value. They teach you the basics then get on to the next topic. Our online learning platform guides you on how to use your basic knowledge to discover more advanced knowledge, so you will be able to use your knowledge of absolute value to answer difficult questions such as this.

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**Micro skills**

Have a look at this question.

Paul buys b books at d dollars each, paying $150. If he had bought 3 fewer books priced at

$3 more each, he would have paid $24 less. How many books did he buy?

- a. 7
- b. 10
- c. 15
- d. 18
- e. 26

SOLUTION

total cost = price * quantity **did you conceptualize it in this way?**

bd=150

(b-3)(d+3) = 126 **Did you generate the two equations?**

d=150/b

**Did you substitute out d because you are solving for b?**

(b-3)((150/b)+3) = 126

150 + 3b - ((150*3)/b) - 9 = 126

**Did you expand the parentheses correctly?**

150b + 3b^2 - (150*3) - 9b = 126b

**Did you recognize that you had to multiply by b to get rid of the fraction?**

3b^2 +15b - (150*3) = 0

**Did you see that this is a quadratic equation that must have zero on one side?**

b^2 + 5b - 150 = 0

**Did you see that it could be divided by 3?**

(b+15)(b-10) = 0

**Did you identify the two numbers that multiply to -150 and sum to +5 as +15 and -10?**

b+15 = 0 b=-15 CAN'T HAPPEN, so b-10=0 means b=10

*Did you identify that the number of books cannot be negative, so -15 is not an option, hence the answer must be 10?*

If you get a question wrong, our online learning platform does not just show you a video on that topic area. It asks a series of leading questions to find out what exact mistake you made, and re-introduces you to that topic area.

While you are learning the topic for the first time, it prompts you for each step one by one

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**Lesser known topics**

Have a look at this question.

If x is an integer, what is the remainder when 3 to the power 16x+5 is divided by 5?

0

1

2

3

4

Did you know that there are some straightforward rules you can use to answer a question like this? You won’t if you take one of the branded courses. They don’t have time to get into it. Our online learning platform will show you lots of helpful and usable rules even on lesser known topics like remainders.