SAT Math 5.3 Algebra and Functions

Algebra | Factoring Functions |

Elementary Number Theory | Factors, Multiples, and Remainders |

Heart of Algebra | Systems of linear equations in two variables (word problems) |

Math | Algebra |

Polynomials and Rational Expressions | Remainder Theorem |

Product Type | SAT Math |

SAT Math | Algebra and Functions |

All right, so we’ve got some mystery number, and we know the remainder is 1 when you divide it by 11.

Now we want to tack on 10 more and do the same… and we need to determine the new remainder.

We need a quotient… we’ll call that k.

Let’s work in reverse. But be safe – check the rear view mirror first.

Multiplying both sides by 11 and then adding back the remainder gives us n = 11k + 1.

So now we’re looking for the remainder when n + 10 is divided by 11.

Adding 10 to both sides, n + 10 = 11k + 11.

Factoring out the 11, so n + 10 = 11(k + 1).

We want to figure out what the remainder is of (n + 10) divided by 11...

…so dividing both sides of the equation by 11 makes the left side exactly what we’re

looking for. When n + 10 is divided by 11 the quotient

is k + 1 and the remainder is 0. Looks like out answer is (A).

As in, “Auto repair.”