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# GMAT - Algebra

### Key GMAT Algebra

Question | Answer |
---|---|

-1^2= | 1 |

0^2= | 0 |

1^2= | 1 |

2^2= | 4 |

2^3= | 8 |

2^4= | 16 |

2^5= | 32 |

2^6= | 64 |

3^2= | 9 |

3^3= | 27 |

3^4= | 81 |

4^2= | 16 |

4^3= | 64 |

4^4= | 256 |

5^2= | 25 |

6^2= | 36 |

5^3= | 125 |

5^4= | 625 |

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 |

x^0= | 1 if x not equal to 0 |

x^1= | x |

What are the "Order of Operations"? | 1. () -> inner most first 2. ^ 3. x 4. / 5. + 6. - |

(x^5)(x^-4) = | x |

(a/b)+(c/d) = | (ad+bc)/bd |

(2/7)(5/3) = | 10/21 |

(x^a/x^b)= | x^(a-b) |

x^-a= | 1/x^a |

(x^a)^b= | x^ab |

x^a + x^b = | x^(a+b) |

(2/7) / (3/5) = | 10/21 |

1/(y^-b) = | y^b |

(5xyz^2)^2 = | 25(x^2)(y^2)(z^4) |

x^(1/2) = | sqrt(x) |

sqrt(2) = | 2^(1/2) |

sqrt(1) = | 1 |

sqrt(x^2) = | |x| |

sqrt(2^4) = | 2^(4/2) = 4 |

sqrt(72) = | 6sqrt(2) |

sqrt(3) x sqrt(12) = | sqrt(36) = 6 |

sqrt(2) + sqrt(2) + sqrt(2) = | 3sqrt(2) |

sqrt(16) | 4 |

Solve for x x^2 = 16 | 4 or -4 |

What is the coefficient of 3y^2 | 3 |

Solve for x x^2 + 8x + 16 = 0 | -4 |

Solve for x x^2 – 18x +81 = 0 | 9 |

Solve for x x^2 – 64 = 0 | -8 or 8 |

Solve for x (x+8)(x-8)=0 | -8 or 8 |

(x-9)^2 = 0 | 9 |

(x+4)^2 = 0 | -4 |

Percent Difference 5 increased to 8 | 60% |

6,000,000 / 12,000 = | 500 |

Solve for y: 3y-3 < 5y+7 | y > -5 |

Solve for x: |2x-3| = 7 | 5 or -5 |

Solve for x: 2 < x+2 < 4 | 0 < x < 2 |

Solve for y: -2y < 10 | y > -5 |

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