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For all positive integers m and v, the expression m Θ v repr
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20 Aug 2020, 09:54
20 Aug 2020, 09:54
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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 (( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17)) ?
A) -10
B) -2
C) 8
D) 13
E) 17
A) -10
B) -2
C) 8
D) 13
E) 17
Re: For all positive integers m and v, the expression m Θ v repr
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20 Aug 2020, 13:07
20 Aug 2020, 13:07
1
So here the parentheses and the order of the numbers in the \(\Theta\) operator matter.
Let's start with the first block of parentheses, that is (( 98 Θ 33 ) Θ 17 )
The first operation to tackle is 98 \(\Theta\) 33.
We have 98 = 33 * 2 + 32 so 98 \(\Theta\) 33 = 32, by definition of the operator given in the instructions.
The first block of parentheses becomes 32 \(\Theta\) 17. But 32 = 17 * 1 + 15 so 32 \(\Theta\) 17 = 15.
Now the first block of parentheses is 15.
Let's turn to the second block, which is ( 98 Θ (33 Θ 17)) . The parentheses rules dictate that the first operation to tackle is now 33 \(\Theta\) 17. 33 = 17 * 1 + 16 so 33 \(\Theta\) 17 = 16
The second block of parentheses becomes 98 \(\Theta\) 16. Now 98 = 16 * 6 + 2 so 98 \(\Theta\) 16 =2
Thus, first block - second block = 15 - 2 = 13
Let's start with the first block of parentheses, that is (( 98 Θ 33 ) Θ 17 )
The first operation to tackle is 98 \(\Theta\) 33.
We have 98 = 33 * 2 + 32 so 98 \(\Theta\) 33 = 32, by definition of the operator given in the instructions.
The first block of parentheses becomes 32 \(\Theta\) 17. But 32 = 17 * 1 + 15 so 32 \(\Theta\) 17 = 15.
Now the first block of parentheses is 15.
Let's turn to the second block, which is ( 98 Θ (33 Θ 17)) . The parentheses rules dictate that the first operation to tackle is now 33 \(\Theta\) 17. 33 = 17 * 1 + 16 so 33 \(\Theta\) 17 = 16
The second block of parentheses becomes 98 \(\Theta\) 16. Now 98 = 16 * 6 + 2 so 98 \(\Theta\) 16 =2
Thus, first block - second block = 15 - 2 = 13
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For all positive integers m and v, the expression m v repr
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09 Jul 2021, 23:01
09 Jul 2021, 23:01
1
This problem is a combination of two concepts. Remainders and Custom Characters.
the expression m Θ v represents the remainder when m is divided by v
(( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17))
Let's solve one by one
98 Θ 33 represents the remainder when 98 is divided by 33
=> 98 Θ 33 = 32
33 Θ 17 represents the remainder when 33 is divided by 17
=> 33 Θ 17 = 16
(( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17)) = (32 Θ 17 ) - ( 98 Θ 16)
= 15 - 2 = 13
So, Answer will be D
Hope it helps!
To learn more about Remainders and Functions and Custom Characters, watch the following video
the expression m Θ v represents the remainder when m is divided by v
(( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17))
Let's solve one by one
98 Θ 33 represents the remainder when 98 is divided by 33
=> 98 Θ 33 = 32
33 Θ 17 represents the remainder when 33 is divided by 17
=> 33 Θ 17 = 16
(( 98 Θ 33 ) Θ 17 ) - ( 98 Θ (33 Θ 17)) = (32 Θ 17 ) - ( 98 Θ 16)
= 15 - 2 = 13
So, Answer will be D
Hope it helps!
To learn more about Remainders and Functions and Custom Characters, watch the following video
