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GMAT > Essential Algebra Skills > Flashcards

Essential Algebra Skills Flashcards

1
Q

What are the first 15 Primes?

A

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

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2
Q

What are the divisibility Rules?

  • Do the daily exercises in ChatGPT - Divisibility Rules exercises
A

1) Last Digit rule:

2 - If the number is even, we can divide it by 2.
4 - If the last TWO digits are a multiple of 4, we can divide by 4.
5 - If the last digit is 5 or 0, we can divide by 5
10 - If the last digit is 0, we can divide by 10.

2) Sume Rule:

3 - If the sum of the digits is a multiple of 3, we can divide by 3.
9 - If the sum of the digits is a multiple of 9, we can divide by 9.
* You can eliminate multiples of 3 in large numbers to know they’re divisible.

3) Combo Rules:

6 - If the number is even and has divisibility of 3, we can divide by 6.

8 - If you can divide the number 3 times and the result is an integer, you can divide by 8.

Special Rules:

7 - Double the last digit of the number and subtract it from the rest of the number. If the result is a multiple of 7 or zero, then you can divide by 7.

1 - Odd position minus even position. If the result is a multiple of 11 or zero, then you can divide by 11.

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3
Q

Write Down all the fractions and its variations form 1/2 - 10/11

A

Check ChatGPT Daily Fractions

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4
Q

Give me the squares from 2^2-15^2 and 3 extra variations.

A

Extra Variations:

  • 1^2 = 1
  • (-1)^2 = 1
  • 0^2 = 0

Normal Squares:

  • Powers of 2:

2^2 = 4 , 2^3 = 8 , 2^4 = 16 , 2^5 = 32 , 2^6 = 64

  • Powers of 3:

3^2 = 9 , 3^3 = 27 , 3^4 = 81

  • Powers of 4:

4^2 = 16 , 4^3 = 64, 4^4 = 256

  • Powers of 5:

5^2 = 25 , 5^3 = 125 , 5^4 = 625

  • Powers of 7-25:

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100

11^2 = 121

12^2 = 144

13^2 = 169

14^2 = 196

15^2 = 225

20^2 = 400

25^2 = 625

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5
Q

What are the 4 subtraction rules?

  • Math Trainer
A

Short form

1.-Standard
2.- Break-up
3.- Balancing
4.- Re-Express

1) Rounding up numbers and adjusting

1.- Make the number you’re subtracting a bit bigger so it’s easier to work with.
2.- Do the subtraction.
3.- Add back the extra amount you added to the number you were subtracting.

Example:

- 205-39 = 205-40 = 165 + 1 = 166

2) Breakup:

1.-Separate the number you’re subtracting into parts that are easy to work with.
2.- Subtract each part one at a time.

Example:

  • 143-78 = 143 - 70 - 8 = 73 - 8 = 65

3) Balancing Method:

1.- Add the same amount to both numbers in the subtraction problem to make it easier to subtract.
2.- Perform the subtraction.
3.- The result will be the same as the original problem.

Example:

  • 205 - 39 = 206 - 40 =166

4) Re-expression

1.- Rewrite the larger number to make the subtraction easier.
2.- Perform the subtraction with the rearranged numbers.
3.- Add back any adjustments you made to the original number.

Example:

  • 1,000 - 857 = (999 + 1) - 857 = 142
  • This is easier when performing vertical by hand subtractions.
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6
Q

Which are the 11 Algebra Rules?2

A
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7
Q

What is the specific guideline for handling proper and improper fractions when taking square roots or raising them to the same power?

  • How do we remember, which mnemonic do we use??
  • Solve an example for a proper and improper fraction.
A

Proper Fraction:

X^2 < Proper Fraction < √

Improper Fraction:

X^2 > Improper Fraction > √

*Mnemonic: Square sinks, root rises

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8
Q

How do you use the formula of 3?

GPT example - Rule of three

A
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9
Q

What Does SWIMMER Stand for?

A

Strengthen
Weaken
Inference
Method of reasoning
Mimic the Response
Explain the Paradox
Roles of BoldFace

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10
Q

How do you respond DS questions?

A

1) BD

2)ACE

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11
Q

How do you distribute Fractions?

  • Do 5 exercises from GPT - Distribute Fractions exercise
A

495/90 = 450/90 + 45/9 = 55

Remember to look at the last number of both numerator and denominator

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12
Q

Which are two exceptional cases with factorials?

A

1) 1! = 1

2) 0! = 1

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13
Q

How do you solve a question where they give you a range and ask for all the primes in that range?

How do you solve a question where they give you a range and ask for all mutiples in that range?

What is a special case for the above question?

  • Solve 3 range questions on GPT - Range Exercise
A
  • The particular case is if it’s Inclusive or not.

1.- Inclusive Range: Include both the starting and ending numbers of the range in your calculations.
2.- Not Inclusive Range: Include only the ending number of the range in your calculations.

Solving ranges prime:

1.- Determine Prime Squares: Identify the square of prime numbers to determine which primes you’ll use for elimination. Use the squares as a mental shortcut if you can’t calculate square roots. For example, if the range is 70-90, find the squares of primes less than 90: 2^2 = 4, 3^2 = 9, 5^2 = 25, 7^2 = 49, 11^2 = 121. Since 121 is greater than 90, you’ll use 2, 3, 5, and 7 for elimination.

2.- Eliminate Even Numbers: Remove all even numbers from the range, except for 2 if it’s in the range and the range is inclusive.

3.- Eliminate Multiples of 3: Remove all multiples of 3 from the remaining numbers, except for 3 if it’s in the range and the range is inclusive.

4.- Eliminate Multiples of 5: Remove all multiples of 5 from the remaining numbers, except for 5 if it’s in the range and the range is inclusive.

5.- Eliminate Multiples of 7: Remove all multiples of 7 from the remaining numbers, except for 7 if it’s in the range, and the range is inclusive

6.- For Ranges Beyond 121: If the range extends beyond 121, continue the elimination process using the next prime (11) and its multiples. Repeat this step for higher primes as needed, using their squares as a guide for when to stop.

Solving ranges multiples:

Subtract the ranges: 114-30 = 84

Divide the result into the multiples = 84/6

Add one if its inclusive = 14 + 1 = 15

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14
Q

What is the Greatest Common Factor (GCF), and what do we use it for?

  • Solve three examples in GPT - GFC exercises
A
  • The GCF is the largest number that can fit into each of the numbers in the set.

How to GCF?

1.- Identify all the prime factors

2.- Take the lowest power of all the common prime factors.

3.- Multiply those factors

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15
Q

How do you find when divisibility ends?

*Do 3 exercises on GPT - Possible Divisor

A

Finding Divisors of N:

  1. Setup: Create two columns on a piece of paper or a digital document. Place the number 1 in the left column and the number (N) in the right column.
  2. Initial Check: Multiply the numbers in the two columns. If they equal (N), then both numbers are divisors of (N).
  3. Increment and Check:
    • Move to the next integer after 1.
    • Place this new integer in the left column.
    • Divide (N) by this new integer.
    • Place the result in the right column.
    • Multiply the numbers in the two columns to confirm they equal N.
    • If they do, both numbers are divisors of N.
  4. Continue the Process: Keep incrementing the number in the left column and adjusting the number in the right column accordingly. Confirm each time that the multiplication equals N.
  5. Stop Condition: Continue this process until the number in the right column is one that has already appeared in the left column. This means you’ve found all unique divisors of N.
  6. List the Divisors At this point, the numbers in both columns collectively represent all the unique divisors of N.
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16
Q

How do you transform a square root into a fraction?

  • Solve 5 exercises in GPT - root exercises
A

Do the exercises

17
Q

If you have 2^4x+2^4x+2^4x+2^4x =?

  • Also, please how formula with letters for the above answer
A
  • The answer is 4 (2^4x)
  • The formula is A + A + A + A = 4A
18
Q

What is the Square root of:

√8
√27
√2
√3
√5

A

√8 = 2 √2

√27 = 3 √3

√2 ≈ 1.4

√3 ≈ 1.7

√5 ≈ 2.2

19
Q

Finish the phrase:

“If I know I’m going to divide something, I stop…?

  • Do 5 examples in GPT - Fraction Simplification
A

Multiplying!!

20
Q

What are the 3 Most common Algebraic Equations, with addition and subtraction?

A
  1. (A+B)^2 = A^2 +2AB + B^2
  2. (A-B)^2 = A^2 - 2AB + B^2
  3. Difference of Squares = (A+B)(A-B) = A^2-B^2
21
Q

What is the Formula/Template for inequalities when using Absolute Value?

GPT Exercises - Solving AV Inequalities

What is special case with inequalities?

For example, what is |X-4|>6

A

1) For |X|>Y

  • This inequality is equivalent to X > Y or X < -Y

2) For |X|< Y

  • This inequality is equivalent to -Y < X < Y
22
Q

What happens when you multiply or divide negative numbers when using inequalities?

A

The sign changes

23
Q

What is the quadratic equation?

  • Give an example of the equation and the formula
  • Solve 5 problems in GPT - Quadratic Equation
  • When do you flip the sign, and when you don’t?
A
  • Equation = aX^2 + bX + c = 0
  • Formula:
  • Your flip the sign when factoring, you don’t when using the formula
24
Q

Which are the exponent rules?

*What do we know about both formulas when solving?

  • 5 exercises GPT - Exponent Rules
A

1) Any number raised to an even power = a positive number or zero. Specifically, it will be positive unless the base is zero.

2) A number raised to an odd power = Positive, negative, or zero.

A number raised to an odd power will have the same sign as the original number. If the base is positive, the result is positive, if the base is negative, the result is negative…

  • A priori we know more about even power, a posteriori we know more about odd numbers.
25
Q

What is a function?

  • Solve 5 exercises in GPT - Functions composition & Solutions exercises
A
  • Functions are designed for putting a variable as input, which will give an output.
26
Q

What are the three possibilities for multiplying even and odd numbers?

A

Odd * Odd = Odd

Even * Even = Odd

Odd * Even = Even

27
Q

When is the most precise time that we have to use the difference of squares formula?

Do 5 exercises - Difference of Squares

A

When there are two or more radicals (√) involved

28
Q

How do you find the unit digits of large exponents?

For example 6^14?

Do 3 Exercises GPT - Units Digit

A

There is a table in which you can see unit digits of all numbers have a pattern with exponents.

29
Q

What happens to an equation or inequality when you divide both sides by 1?

A

The equation doesn’t change, it stays the same

30
Q

Adding (+), or multiplying three consecutive numbers will always be divisible by…?

A

Three

Try it?

5+6+7 = 18 and 18/3=6

567= 210 and 210/3=70

31
Q

Three consecutive multiplied numbers always contain at least one _____ number.

What does that mean?

A

Even number.

It means that the result is always going to be even.

Try It?

4+5+6=15 (I believe it is only for multiplication, check GPT or Moi?

456=120

32
Q

Any number that results from multiplying 2 even numbers is divisible by?

A

Its divisible by 4

33
Q

When plugin numbers, what is the order for choosing which ones to plug first?

A

DEA

34
Q

Do 5 exercises factoring equations

A
35
Q

How can you be sure that X^2-Y^2 will be a positive number?

A

If X-Y and X+Y both have positive results, meaning they are more than zero (>0)

X-Y= Positive
X+Y= Positive

36
Q

Fraction, percentage and decimal exercises - Exercises GPT

A
37
Q

Is Zero, negative or positive, and odd or even?

A

Zero is even and is neutral, or not positive or negative

38
Q

What are the 3 possible combinations when you add or subtract and even and an odd number?

How do we remember them?

A

Even +/- Odd = Odd

Odd +/- Odd = Even

Even +/- Even = Even

Shoes exercise or Jero saying Eoooo

39
Q

What are the 3 possible combinations when you multiply or divide a number?

How do we remember them?

A

Odd */ odd = Odd

Odd */ Even = Even

Even */ Even = Even

OOO=Out Of Office

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