Funny Function

[zagcollins]

For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of ((98Θ33)Θ17) - (98Θ(33Θ17))?

A.-10
B.-2
C.8
D.13
E.17

[Canman]

Easiest to attack this by starting from the inside parantheses and working your way out.

(98*33)*17 - (98*(33*17)

98/33 = 2 32/33 as a mixed fraction, so remainder is 32. Continue to use this logic

32*17 = 1 15/17, remainder is 15

so..

15 - (98*(33*17)

other side...

33/17 = 1 16/17
98/16 = 6 2/16

put it all together...

15 - 2 = 13

Ans D

[sudhir3127]

My answer is 13 as well

[reachac]

IMO D

[zagcollins]

good explanation canman....tried the same logic but wasnt sure....thanks!

[Jeff@TargetTestPrep]

For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of ((98Θ33)Θ17) - (98Θ(33Θ17))?

A.-10
B.-2
C.8
D.13
E.17

Let's start with the first set of parentheses before the minus sign:

98/33 = 2 remainder 32

Next we have:

32 Θ 17

32/17 = 1 remainder 15

So, (( 98 Θ 33 ) Θ 17 ) = 15.

Let's move to the second set of parentheses after the minus sign:

33/17 = 1 remainder 16

Next we have:

98 Θ 16 = 6 remainder 2

Thus, ( 98 Θ (33 Θ 17)) = 2.

So, (( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17)) = 15 - 2 = 13

Answer: D