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

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Consider the following new operations: $a # b$ equals min(a,b)min(a, b) if either aa or bb is prime and max(a,b)max(a, b) otherwise. a><ba >< b equals (2+b)−a(2 + b) - a if a>ba > b and bb otherwise. a:ba : b equals $a # b$ if gcd(a,b)==1gcd(a, b) == 1 and gcd(a,b)gcd(a, b) otherwise, where gcd stands for greatest common divisor. $a ~ b$ equals (a−b)(a - b) if a+b>0a + b > 0; otherwise, it equals a+ba + b. $a @ b$ equals $(a ~ b)$ if $a # b > 0$; otherwise, it equals $a * b$. 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 = ((((-1 ** -5) ><~ (-8 ~+ -10)) @ ((-3 +@ 5) +#: (two @+ one))) :+~ (((three # seven) ~ (-9 - ten)) ><* ((-10 ~~ two) ><~- (9 # -6)))) Let B = ((((((((((((-1 #@+ eight) +# ten) ~#~ 3) :#: 5) ~: -9) @:>< -2) * -9) ~~ -4) @ 6) * -8) #~ -6) @## five) Let C = ((((-4 ~ one) ::: (-8 @ -1)) + ((1 @+ -9) # (1 @~+ -7))) ** (((-6 *## -6) ~ (eight +@ -1)) # ((-1 #* -3) @@* (five :>< -2)))). 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 min(a,b) if either a or b is prime and max(a,b) otherwise.
a><b equals (2+b)−a if a>b and b 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.
$a @ b$ 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 = ((((-1 ** -5) ><~ (-8 ~+ -10)) @ ((-3 +@ 5) +#: (two @+ one))) :+~ (((three # seven) ~ (-9 - ten)) ><* ((-10 ~~ two) ><~- (9 # -6))))
Let B = ((((((((((((-1 #@+ eight) +# ten) ~#~ 3) :#: 5) ~: -9) @:>< -2) * -9) ~~ -4) @ 6) * -8) #~ -6) @## five)
Let C = ((((-4 ~ one) ::: (-8 @ -1)) + ((1 @+ -9) # (1 @~+ -7))) ** (((-6 *## -6) ~ (eight +@ -1)) # ((-1 #* -3) @@* (five :>< -2)))).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a # b$ equals $min(a, b)$ if either $a$ or $b$ is prime and $max(a, b)$ otherwise.
$a >< b$ equals $(2 + b) - a$ if $a > b$ and $b$ 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 $a + b$.
$a @ b$ 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 = ((((-1 ** -5) ><~ (-8 ~+ -10)) @ ((-3 +@ 5) +#: (two @+ one))) :+~ (((three # seven) ~ (-9 - ten)) ><* ((-10 ~~ two) ><~- (9 # -6))))
Let B = ((((((((((((-1 #@+ eight) +# ten) ~#~ 3) :#: 5) ~: -9) @:>< -2) * -9) ~~ -4) @ 6) * -8) #~ -6) @## five)
Let C = ((((-4 ~ one) ::: (-8 @ -1)) + ((1 @+ -9) # (1 @~+ -7))) ** (((-6 *## -6) ~ (eight +@ -1)) # ((-1 #* -3) @@* (five :>< -2)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
3d18dae5-aecc-59c5-ae1b-194200448d97
task_key
bbeh~5fmultistep~5farithmetic--full--3d18dae5-aecc-59c5-ae1b-194200448d97
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

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