GMAT: Remainders

What is the general Remainder formulas

(1) (Dividend / Divisor) = Quotient + (Remainder / Divisor) D/S = Q + R/S (2) Dividend = Divisor * Quotient + Remainder D = S * Q + R

When positive integer A is divided by positive integer B, the result is 4.35. Which of the following could be the remainder when A is divided by 8? (A) 13 (B) 14 (C) 15 (D) 16 (E) 17

(1) A = 4(B) + 35/100 (2) 7/20 = R/B --> 7B = 20R (R must be multiple of 7) (3) 14 = 7*2 so (B)

You can express the division of 17 by 5 in what three ways?

- 3 with a remainder of 2 - 3 + 2/5 - 3.4

When positive integer n is divided by 7, there is a remainder of 2; what must you think about when generating possible value?

All these values of n is that they are 2 more than a multiple of 7

What are the constraints of the remainder?

Always a NON-NEGATIVE integer less than divisor 0≤r<d

What are the components of remainders?

Dividend Divisor Remainder Quotient

The remainder when m is divided by 5 is 2, and the remainder when m is divided by 3 is 2. If m > 2, what is the least possible value of m? (A) 5 (B) 7 (C) 15 (D) 17 (E) 27

If a number has the same remainder when divided by two different numbers (3 and 5, in this case), it has that remainder when divided by the product of those two numbers 3*5 = 15 5/15 = 0 r 5 7/15 = 0 r 7 15/15 = 1 r 0 17/15 = 1 r 2

When a GMAT question refers to a REMAINDER, it is referring to what?

The INTEGER form of the Remainder i.e., the remainder of 2 in 17 divided by 5

What is the Dividend?

The number being divided

What is the Divisor?

The number dividing the integer Dividend

WHAT STRATEGY DO YOU USE: When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following values CANNOT be the sum x+y? (A) 12 (B) 13 (C)14 (D) 16 (E) 21

To answer these questions accurately and efficiently, you will need to be able to generate possible values for the variables in the question.

What is the first multiple of ANY number?

ZERO

EXPRESS: When positive integer n is divided by 7, there is a remainder of 2

n = 7(Q) + 2 Don't multiply remainder 2 by 7. Already in its correct form Then, GENERATE POSSIBLE VALUES FOR n

SOLVE When positive integer x is divided by 5, the remainder is 2. When positive integer y is divided by 4, the remainder is 1. Which of the following values CANNOT be the sum x+y? (A) 12 (B) 13 (C)14 (D) 16 (E) 21

x = Q(5) + 2 y = Q(4) + 1 Possible values for X: 0(5) + 2 = 2 // 1(5) + 2 = 7 // 12 // 17 Possible values for Y: 0(4) + 1 = 1 // 1(4) + 1 = 5 // 9 // 13 (A) 12 = 7 + 5 (B) 13 = 12 + 1 (C) 14 = ??? (D) 16 = 9 + 7 (E) 21 = 12 + 9 No way for x+y = 14