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