GMAT Practice Question: For all positive integers m and v, the expression m \Theta v...
Question
For all positive integers m and v, the expression m \Theta v represents the remainder when m is divided by v. What is the value of ((98 \Theta 33) \Theta 17)-(98 \Theta(33 \Theta 17)) ?
- -10
- -2
- 8
- 13
- 17
Topics: remainders, number theory, expression formulas
Solution
Step 1
We first use the definition of remainder in division.
m = v \times q + (m \Theta v)
Step 2
We then find the remainder when 98 is divided by 33.
98 = 33 \times 2 + 32
Step 3
We then find the remainder when 33 is divided by 17.
33 = 17 \times 1 + 16
Step 4
We then find the remainder when 32 is divided by 17.
32 = 17 \times 1 + 15
Step 5
We then find the remainder when 98 is divided by 16.
98 = 16 \times 6 + 2
Step 6
We then subtract the two remainders found above.
15 - 2 = 13
Answer
13
