20. Let l = 61 + i. Calculate the remainder when l is divided by 12.
11
Let x = -10 + 21. Suppose u + l - x = 0, 2*u + 0 - 19 = -5*l. Calculate the remainder when u is divided by 8.
4
Suppose 0 = -2*a + 2*k - 12, -5*a = 2*k + 19 + 4. Suppose -3*z + 5*h = -31, 0 = -5*h + 3 + 17. Calculate the remainder when z is divided by (-1)/(-1) - 1*a.
5
Let m(d) be the first derivative of d**3/3 + d**2/2 + 2*d - 3. What is the remainder when 22 is divided by m(2)?
6
Suppose -4*o = -6*o - 3*u + 88, 4*o - 182 = -3*u. What is the remainder when 185 is divided by o?
44
Let j(s) = -s**3 - 2*s**2 - 4*s - 3. Let c be -3 + 6/2 - -3. Suppose -2*u = u + 6, c*v + 2*u = 26. Calculate the remainder when j(-3) is divided by v.
8
Let t(w) = w**2 - 2*w. Let n be t(3). Let p(c) = 4*c - 1. What is the remainder when -1 + (-4 - -21) + 4 is divided by p(n)?
9
Let z(u) = -29*u - 1. Let i be z(-2). Suppose -3*k + 0*k + i = 0. What is the remainder when k is divided by 11?
8
Let u be 3/((-7)/(-2) + -2). Suppose -3*f + 4*f - 6 = 0. What is the remainder when 360/32 + u/(-8) is divided by f?
5
Suppose 234 = 2*c - 0*c. Let l = -71 + c. What is the remainder when l is divided by 16?
14
Let p(n) = 3*n + 2. Let z = 23 - -10. What is the remainder when z is divided by p(5)?
16
Suppose 0 = 3*k - 10 - 2. Let z = k + 8. What is the remainder when 35 is divided by z?
11
Suppose -21 = 2*s + 5*g - 3, -3*s = -2*g + 46. Suppose -l - 3*o - 14 = 0, 5*l + 5*o + 4 + 16 = 0. Let j = l - s. What is the remainder when 43 is divided by j?
13
Let k(n) = -35*n - 1. Calculate the remainder when 134 is divided by k(-1).
32
Let o(i) = -4*i**2 + 12*i - 4. Let g(h) = -9*h**2 + 24*h - 8. Let f(d) = -3*g(d) + 7*o(d). Calculate the remainder when 62 is divided by f(10).
14
Calculate the remainder when 1 is divided by ((-12)/48)/((-1)/4).
0
Suppose -4*l + 1 = z, -z = l - 0 - 1. Let f = z - -18. Calculate the remainder when 54 is divided by f.
16
Suppose 2*p = 4 + 20. Let h(n) = -6*n - 13. What is the remainder when h(-6) is divided by p?
11
Suppose 64 = 6*p - 2*p. Let v = p - 86. Let r = v - -123. What is the remainder when r is divided by 14?
11
Let m = 2 + 58. Suppose -4*j = -3*j - m. What is the remainder when j is divided by 21?
18
Let r be (-2*212/8)/1. Let g = r - -150. What is the remainder when g is divided by 25?
22
Let a be (-1 + 4)*268/12. Suppose a = 5*g - 103. Let t = 25 - 13. What is the remainder when g is divided by t?
10
Suppose 4 = 3*o - 4*o. Let s = 9 - o. What is the remainder when 24 is divided by s?
11
Suppose -3*x - 24 = -u + x, 5*x = -u + 60. Let y be (8/10)/((-1)/(-5)). Suppose -69 = -5*q + n, 0 = y*n - 4. Calculate the remainder when u is divided by q.
12
Let i = 149 - 86. What is the remainder when i is divided by 16?
15
Suppose 5*c = -2*y + 3*y + 33, 0 = -5*y - 15. Let d = -13 + c. Let x = d + 25. Calculate the remainder when 35 is divided by x.
17
Suppose -2*k - 4*r + 3*r + 56 = 0, -2*k + 48 = 5*r. Let m(i) = -i**3 - i - 2. What is the remainder when k is divided by m(-2)?
5
Let d be (-50)/6 - (-2)/(-3). Let u = d + 24. What is the remainder when u is divided by 4?
3
Suppose -5*c + 51 = 4*h - 0*h, 0 = 2*h + c - 21. Let t = h + -5. Suppose -2*g + 14 = -4*j - 0, 4*g = 3*j + 38. What is the remainder when g is divided by t?
3
Let p(a) be the third derivative of -a**4/24 + 5*a**3/3 - a**2. Suppose -6*f = -f - 30. Calculate the remainder when p(0) is divided by f.
4
Let t(r) = 9*r - 12. Calculate the remainder when t(7) is divided by 13.
12
Suppose -57 = -5*a + 4*z - 8*z, 0 = a - 4*z - 21. What is the remainder when a is divided by 8?
5
Suppose -3*u + 4 - 1 = 0. Let r(b) = 86*b**2 - b. Let o be r(u). Suppose w = -2*w + 4*q + o, -5*w + q + 153 = 0. What is the remainder when w is divided by 11?
9
Suppose -4*c = -z + 6 - 3, 2*c = 2. Calculate the remainder when 24 is divided by z.
3
Suppose -3*q + 5 = -16. Calculate the remainder when 19 is divided by q.
5
Suppose -3*a - w = -31, -2*a - 3*w - 7 = -3*a. What is the remainder when 37 is divided by a?
7
Let c(f) = f + 2. Let k be ((-9)/6)/((-3)/4). What is the remainder when c(k) is divided by 3?
1
Calculate the remainder when 2/(-3) - 290/(-3) is divided by 33.
30
What is the remainder when -2 + 4 + 4 - -1 is divided by 3?
1
Let g = -16 - -8. Let i be 28/6 + g/12. Suppose 0 = -i*h + 59 + 9. What is the remainder when h is divided by 9?
8
Let r = -67 + 120. Let m = 6 + 15. Let s = r - m. Calculate the remainder when s is divided by 11.
10
Calculate the remainder when ((-2)/(-5))/(1/55) is divided by 2/(-4) - (19/(-2) - 3).
10
Let q = 57 + -51. Let l(a) = -a**3 + 5*a**2 - a + 2. Calculate the remainder when l(3) is divided by q.
5
Suppose -4*i + 2*r + 18 = 0, -4*r = -3*i + 19 + 7. Suppose v - w = 37, -v + 4*v - i*w = 112. Calculate the remainder when v is divided by 10/((-3)/(-18)*3).
18
Let l(d) = -d**2 - 23*d - 46. Calculate the remainder when 25 is divided by l(-20).
11
Suppose -11*t + 191 = -73. What is the remainder when 69 is divided by t?
21
Suppose 3*t - 12 = 4*l, 7*l = 2*l. Suppose -j = t*j - 60. Calculate the remainder when j is divided by -7*(-2 + 3)/(-1).
5
Suppose 290 = 4*f + f. Suppose d = -0*d - b + 31, 2*d + b - f = 0. Calculate the remainder when 80 is divided by d.
26
Let n = -11 - -11. Suppose 3*u = n, 2*a + 3*a = -u + 285. What is the remainder when a is divided by 20?
17
Suppose -4*o + 192 = 4*y, 2*o - 92 = -6*y + 3*y. What is the remainder when o is divided by 14?
10
Suppose -c = -2*c. Suppose c = 6*d - d - 65. Calculate the remainder when 38 is divided by d.
12
Suppose 5*o + 50 = 5*v, 0 = 5*v - o + 2*o - 80. Let f = -10 + 37. Calculate the remainder when f is divided by v.
12
Suppose 75 = 5*o + 5*t, 2*t = -2*o - t + 32. What is the remainder when 51 is divided by o?
12
Let h = 46 - 18. Suppose 0 = 2*l - 4*l + h. Calculate the remainder when 41 is divided by l.
13
Let f = -22 - -24. Let a = 6 - 5. Calculate the remainder when f is divided by a.
0
Suppose 9*j = 4*j + 1070. What is the remainder when j is divided by 31?
28
Let v = 0 + 5. Suppose 3*k - 5*t = 49, 6*k - 33 = 3*k - 3*t. Calculate the remainder when k is divided by v.
3
Let z(q) = -q**2 + q - 32. Let l be z(0). Let i = 47 + l. Suppose t - i = -4*t. Calculate the remainder when 5 is divided by t.
2
Let k(d) = -d**2 + 11*d + 7. Let p be k(10). Suppose -4*l = -t - 42 + 8, 3*l - 5*t - p = 0. Suppose 8 = a - 7. Calculate the remainder when a is divided by l.
6
Let u be (-17)/(-2) - (-2)/4. Let k be (-3)/u + 14/6. Let m = k - -7. Calculate the remainder when 25 is divided by m.
7
Suppose -137 = -4*d - 33. Let b(u) = u**3 + 4*u**2 - 7*u - 1. What is the remainder when d is divided by b(-5)?
8
Let p(t) = -t**2 - 10*t - 3. Let b be p(-6). Suppose -2*s - 3 = -b. What is the remainder when 17 is divided by s?
8
Let f(c) = -c**2 - 12*c - 2. Calculate the remainder when f(-5) is divided by 17.
16
Suppose 0 = 2*i + 424 + 24. Suppose -20 - 19 = -3*x. Calculate the remainder when i/(-6) + 2/(-6) is divided by x.
11
What is the remainder when (-3)/(-12) - (-315)/4 is divided by 1199/44 - 2/8?
25
Let r = 57 + -33. Let w(z) = -z**2 + 26*z - 51. Calculate the remainder when w(18) is divided by r.
21
Let f(c) = -c**2 - 15*c - 44. Calculate the remainder when 7 is divided by f(-10).
1
Let t(h) = -h**3 + 6*h**2 + 8*h - 10. Let g be t(7). Let d = 7 + 3. Calculate the remainder when (-1)/g - 332/(-12) is divided by d.
8
Suppose 0*n - 16 = -2*n. Calculate the remainder when n + 4 - (1 + -3) is divided by 5.
4
Let k(x) = 3*x**2 + 5*x - 14. What is the remainder when 70 is divided by k(-5)?
34
Let l(g) = g**3 - 6*g**2 - g + 17. What is the remainder when 117 is divided by l(6)?
7
Let x = 9 + 0. Calculate the remainder when 34 is divided by x.
7
Let k = -18 - -30. Let n = 69 + -62. Calculate the remainder when k is divided by n.
5
Let b(f) = -f**3 + 5*f**2 + 2*f - 3. Let h be b(5). Calculate the remainder when (82/4)/(h/14) is divided by 14.
13
Suppose 0 = -4*l + 227 + 417. Suppose 5*h = -2*z + 67, -l + 45 = -4*z - 4*h. Calculate the remainder when z is divided by 9.
8
Suppose 0 = -u + 5*u - 260. Calculate the remainder when u is divided by 10.
5
Calculate the remainder when 2/(-1) - (-48)/(5 - -1) is divided by 4.
2
Let l(r) = 17*r - 55. What is the remainder when l(7) is divided by 17