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BIG-Bench Extra Hard (BBEH) / Consider the following new operations:

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Consider the following new operations: a:ba : b equals (a−b)(a - b) if $a * b > 0$; otherwise, it equals a+ba + b. a<>ba <> b equals (b−a)+b(b - a) + b if |a−b|<2|a-b| < 2 and (a−b)+a(a - b) + a otherwise. $a ~ b$ equals a<>ba <> b if gcd(a,b)==1gcd(a, b) == 1 and gcd(a,b)gcd(a, b) otherwise, where gcd stands for greatest common divisor. a][ba ][ b equals (a−b)(a - b) if a+b>0a + b > 0; otherwise, it equals a+ba + b. For brevity, we use a<op1><op2>ba <op1><op2> b to denote (aop1b)op2b(a op1 b) op2 b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$. Let A = (((((((((((((((((((((two ~ 10) ** two) : -2) +* -4) -*~ -10) ~+ one) +][ -10) ~+ six) ][- one) ][*+ -3) +:][ ten) <>:<> -1) ][ -10) - -7) + ten) ][+ four) ][:: -8) ~-: 5) ~ 8) -<>: -6) ][-~ -3) Let B = ((((-10 ][- 3) - (1 ~ 6)) +<> ((2 * 6) ++* (five ][- 2))) : (((3 ][* -3) *: (10 *: -1)) -<> ((three -<>][ 6) :+~ (-3 : 9)))) Let C = ((((((((((((8 <>-: -4) -:+ -6) <>:: -4) -- 6) ~][ -2) ~*+ four) *:- -7) <>+: 6) - six) ~-- -10) ][<>+ one) ~++ -10). Compute A + B - C. Your final answer must be in number form.
Plain-text mathematical notation (without MathML)
Consider the following new operations:

a:b equals (a−b) if $a * b > 0$; otherwise,  it equals a+b.
a<>b equals (b−a)+b if |a−b|<2 and (a−b)+a otherwise.
$a ~ b$ equals a<>b if gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.
a][b equals (a−b) if a+b>0; otherwise,  it equals a+b.
For brevity, we use a<op1><op2>b to denote (aop1b)op2b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.
Let A = (((((((((((((((((((((two ~ 10) ** two) : -2) +* -4) -*~ -10) ~+ one) +][ -10) ~+ six) ][- one) ][*+ -3) +:][ ten) <>:<> -1) ][ -10) - -7) + ten) ][+ four) ][:: -8) ~-: 5) ~ 8) -<>: -6) ][-~ -3)
Let B = ((((-10 ][- 3) - (1 ~ 6)) +<> ((2 * 6) ++* (five ][- 2))) : (((3 ][* -3) *: (10 *: -1)) -<> ((three -<>][ 6) :+~ (-3 : 9))))
Let C = ((((((((((((8 <>-: -4) -:+ -6) <>:: -4) -- 6) ~][ -2) ~*+ four) *:- -7) <>+: 6) - six) ~-- -10) ][<>+ one) ~++ -10).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a : b$ equals $(a - b)$ if $a * b > 0$; otherwise,  it equals $a + b$.
$a <> b$ equals $(b - a) + b$ if $|a-b| < 2$ and $(a - b) + a$ otherwise.
$a ~ b$ equals $a <> b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a ][ b$ equals $(a - b)$ if $a + b > 0$; otherwise,  it equals $a + b$.
For brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.
Let A = (((((((((((((((((((((two ~ 10) ** two) : -2) +* -4) -*~ -10) ~+ one) +][ -10) ~+ six) ][- one) ][*+ -3) +:][ ten) <>:<> -1) ][ -10) - -7) + ten) ][+ four) ][:: -8) ~-: 5) ~ 8) -<>: -6) ][-~ -3)
Let B = ((((-10 ][- 3) - (1 ~ 6)) +<> ((2 * 6) ++* (five ][- 2))) : (((3 ][* -3) *: (10 *: -1)) -<> ((three -<>][ 6) :+~ (-3 : 9))))
Let C = ((((((((((((8 <>-: -4) -:+ -6) <>:: -4) -- 6) ~][ -2) ~*+ four) *:- -7) <>+: 6) - six) ~-- -10) ][<>+ one) ~++ -10).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
7b4cc333-ad41-54c0-8750-217fb7047f17
task_key
bbeh~5fmultistep~5farithmetic--full--7b4cc333-ad41-54c0-8750-217fb7047f17
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

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