Brilliant Math & Science Wiki. When a system contains a relatively small number of congruences, an efficient process exists to apply the Chinese Remainder Theorem.

Solve the system of congruences: Begin with the congruence with the largest modulus, Rewrite this congruence as an equivalent equation: Substitute this expression for into the congruence with the next largest modulus: Then solve this congruence for Rewrite this congruence as an equivalent equation: Substitute this expression for into the expression for Now substitute this expression for into the final congruence, and solve the congruence for Write this congruence as an equation, then substitute the expression for into the expression for This equation implies the congruence: This happens to be the solution to the system of congruences.

A box contains gold coins. If the coins are equally divided among six friends, four coins are left over. If the coins are equally divided among five friends, three coins are left over. Brahmagupta has a basket full of eggs. Positive integer n leaves a remainder of 4 after division by : GMAT Problem Solving (PS) To elaborate more.

Suppose we are told that:Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 2 after division by 8. What is the remainder that n leaves after division by 12? The statement "positive integer n leaves a remainder of 4 after division by 6" can be expressed as: n=6p+4. SAT Factors, Divisibility, and Remainders. What is the largest integer such that is divisible by and ?

(A) (B) (C) (D) (E) Correct Answer: B Solution 1: Listing the positive numbers divisible by we have: Now, we can evaluate the answers as follows. (A) Since leaves a remainder of upon division by which implies is not divisible by This shows choice (A) may be eliminated. (B) Since is divisible by and is a possible answer. (C) Since leaves a remainder of upon division by which implies is not divisible by This shows choice (C) may be eliminated.

(D) Since is divisible by However, we are asked to find an integer strictly smaller than so choice (D) may be eliminated. Tricky remainder problem. Tricky remainder problem Tue Oct 01, 2013 1:33 pm Quote Elapsed Time: 00:00 Lap #[LAPCOUNT] ([LAPTIME])

A Remainders Shortcut for the GMAT. When positive integer n is divided by 3, the remainder is 2. It's not really a second method.

It's a way to filter through our options a bit more efficiently. If we don't see a pattern, we'll just grind through our list of numbers that give us a remainder of 5 when divided by 7: 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96 Or we can see that the pattern goes like this 5: remainder 2 when divided by 3 12: remainder 0 when divided by 3 19: remainder 1 when divided by 3 26: remainder 2 when divided by 3 33: remainder 0 when divided by 3 40: remainder 1 when divided by 3 For each set of three numbers, starting with 5, 12, 19, only the first term will give us a remainder of 2 when divided by 3. A Remainders Shortcut for the GMAT.

Remainder X - Practice GMAT Data Sufficiency Question. Return to the list of practice GMAT data sufficiency questions.

What is the remainder of a positive integer N when it is divided by 2? N contains odd numbers as factorsN is a multiple of 15 <div class="inline-question-answer-button">Show Answer</div> Correct Answer: E <div class="inline-question-exp-button">Show Explanation</div> Remainder. 2 Tips to Make GMAT Remainder Questions Easy.

Collection of remainder problems in GMAT : GMAT Quantitative Section. I have collected these problems on remainder.

This type of problem is frequently asked in DS.Answers are also given. Please dont mind any typo error. 1.If r is the remainder when the positive integer n is divided by 7, what is the value of r 1. when n is divided by 21, the remainder is an odd number2. when n is divided by 28, the remainder is 3. GMAT Hacks: Working With Remainders. April 18, 2007 While they may sound simple, remainders can be a tricky concept.

The GMAT requires you to understand how they work at a much more abstract level than your teacher did in fourth grade when you first learned what they were. GMAT Number Theory & Properties - Remainders : Wizako Online GMAT classes. The GMAT quant practice question is about finding the remainder of the division of the product of 4 numbers by a divisor.

Question: What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33? Explanatory Answer Video explanation coming soon. Useful result pertaining to remainders You can solve this problem if you know this rule about remainders. Practice Number System Questions: Aptitude, page-5. REMAINDERS : GMAT Quantitative Section. This post is a part of [GMAT MATH BOOK] created by: Bunueledited by: bb, Bunuel Definition If and are positive integers, there exist unique integers and , called the quotient and remainder, respectively, such that and .

When positive integer n is divided by 3, the remainder is 2. GMAT Quant: Thoughts on Remainders - Magoosh GMAT Blog. For a start, give these problems a try. A complete explanation will come at the end of the discussion. 1) When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J? Positive integer n leaves a remainder of 4 after division by : GMAT Problem Solving (PS) When positive integer n is divided by 3, the remainder is 2.