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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 $(2 * b) - a$ if a>ba > b and bb otherwise. $a # b$ equals (a−b)(a - b) if a+b>0a + b > 0; otherwise, it equals a+ba + b. $a @ b$ equals $a * b$ if 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 $(b + a) * b$ if |a−b|<2|a-b| < 2 and $(a + b) * a$ otherwise. Let A = (((((((((((((((((((((four # -5) @ -8) - 3) ][ five) + eight) @ ten) : 8) @ -8) ][ 6) @ -2) + -2) * -9) + 5) ][ one) - 4) * -5) - -5) # -8) - -10) # one) @ -10) Let B = ((((-3 - 3) * (-8 : 3)) + ((-4 ][ -3) : (1 - -5))) - (((1 * 8) ][ (-6 - three)) @ ((-6 - -3) : (-7 # nine)))) Let C = ((((-2 : -8) - (8 : 6)) ][ ((-10 - -6) : (-6 # four))) : (((4 - 4) - (-7 @ 3)) ][ ((-10 - -3) * (-1 @ two)))). 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 $(2 * b) - a$ if a>b and b otherwise.
$a # b$ equals (a−b) if a+b>0; otherwise,  it equals a+b.
$a @ b$ equals $a * b$ if gcd(a,b)==1 and gcd(a,b) otherwise, where gcd stands for greatest common divisor.
a][b equals $(b + a) * b$ if |a−b|<2 and $(a + b) * a$ otherwise.

Let A = (((((((((((((((((((((four # -5) @ -8) - 3) ][ five) + eight) @ ten) : 8) @ -8) ][ 6) @ -2) + -2) * -9) + 5) ][ one) - 4) * -5) - -5) # -8) - -10) # one) @ -10)
Let B = ((((-3 - 3) * (-8 : 3)) + ((-4 ][ -3) : (1 - -5))) - (((1 * 8) ][ (-6 - three)) @ ((-6 - -3) : (-7 # nine))))
Let C = ((((-2 : -8) - (8 : 6)) ][ ((-10 - -6) : (-6 # four))) : (((4 - 4) - (-7 @ 3)) ][ ((-10 - -3) * (-1 @ two)))).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a : b$ equals $(2 * b) - a$ if $a > b$ and $b$ otherwise.
$a # b$ equals $(a - b)$ if $a + b > 0$; otherwise,  it equals $a + b$.
$a @ b$ equals $a * b$ if $gcd(a, b) == 1$ and $gcd(a, b)$ otherwise, where gcd stands for greatest common divisor.
$a ][ b$ equals $(b + a) * b$ if $|a-b| < 2$ and $(a + b) * a$ otherwise.

Let A = (((((((((((((((((((((four # -5) @ -8) - 3) ][ five) + eight) @ ten) : 8) @ -8) ][ 6) @ -2) + -2) * -9) + 5) ][ one) - 4) * -5) - -5) # -8) - -10) # one) @ -10)
Let B = ((((-3 - 3) * (-8 : 3)) + ((-4 ][ -3) : (1 - -5))) - (((1 * 8) ][ (-6 - three)) @ ((-6 - -3) : (-7 # nine))))
Let C = ((((-2 : -8) - (8 : 6)) ][ ((-10 - -6) : (-6 # four))) : (((4 - 4) - (-7 @ 3)) ][ ((-10 - -3) * (-1 @ two)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
dd682a76-0de3-53c1-8aa1-053c92c3c3e7
task_key
bbeh~5fmultistep~5farithmetic--full--dd682a76-0de3-53c1-8aa1-053c92c3c3e7
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

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