25-07-2021 Answer

1. If the operation + is defined by the equation 4a + 5b =  20ab , what is the value of  16 + 20 ?

Answer: 320

Solution: 16 + 20 = 4*4 + 5*4 which is similar to 4a + 5b.

Thus, 20ab = 20*4*4 = 320


2. If the operation + is defined by the equation a + b = 3a / 2b, what is the value of 2 + 3 ?

Answer: 1

Solution: The expression becomes

3(2) / 2(3) = 6/6 = 1


3. If the operation - is defined by the equation x - y = x * y + x , what is the value of 4 - 5 ?

Answer: 24

Solution: The expression becomes

4 * 5 + 4 = 20 + 4 = 24


4. If the operation - is defined by the equation a - b = (9a + 12b) % 2, what is the value of 9 - 2 ?
Note: % denotes remainder(modulo) operation

Answer: 1

Solution: The expression becomes

(81 + 24) % 2 = 105 % 2 = 1 


5. If the operation * is defined by the equation a * b = 4a + 3b, what is the value of 5 * 9 ?

Answer: 47

Solution: The expression becomes

4(5)+3(9) = 20 + 27 = 47


6. If the operation * is defined by the equation c * d = (3c / 2d) + 4d , what is the value of 6 * 1  ?

Answer: 13

Solution: The expression becomes

(18 / 2) + 4 = 9 + 4 = 13


7. If the operation ^ is defined by the equation x ^ y = 10y + xy, what is the value of 8 ^ 5 ?

Answer: 90

Solution: The expression becomes

10(5) + 8 * 5 = 50+40 = 90


8. If the operation % is defined by the equation c % d = cd + dc + 12 , what is the value of 9 % 11 ?

Answer: 210

Solution: The expression becomes

99 + 99 + 12 = 210


9. If the operation - is defined by the equation x - y = yx / xy, what is the value of 120 - 2 ?

Answer: 1

Solution: The expression becomes

(240 / 240) = 1


10. If the operation / is defined by the equation x / y = (x * y) % 5, what is the value of 12 / 7 ?


Note: * and % denotes multiplication and remainder(modulo) operations respectively

Answer: 4

Solution: The expression becomes

(12 * 7) % 5 = 84 % 5 = 4


11. If the operation / is defined by the equation a / b = 6a - 4b, what is the value of 3 / 2 ?

Answer: 10

Solution: The expression becomes

6(3) - 4(2) = 18 - 8 = 10


12. If the operation / is defined by the equation x / y = (x ^ y) - (y ^ x), what is the value of 3 / 4 ?

Answer: 17

Solution: The expression becomes

(3 ^ 4) - (4 ^ 3) = 81 - 64 = 17


13. If the operation * is defined by the equation a * b = (a % 5) + b, what is the value of 6 * 15 ?

Answer: 16

Solution: The expression becomes

(6 % 5) + 15 = 1 + 15 = 16


14. If the operation ^ is defined by the equation a ^ b = 2a - 3b, what is the value of 12 ^ 4 ?

Answer: 12

Solution: The expression becomes

24 - 12 = 12


15. If the operation + is defined by the equation a + b = (a ^ b) * a, what is the value of 4 + 2 ?

Answer: 64

Solution: The expression becomes

(4 ^ 2) * 4 = 16 * 4 = 64


16. If the operation ^ is defined by the equation x ^ y = 2x + y, what is the value of a if 2 ^ a = a ^ 3 ?

Answer: 1

Solution: The expression becomes

4 + a = 2a + 3; a = 1


17. If the operation % is defined by the equation x % y = (3y + 2x) * 4x, what is the value of 2 % 3 ?

Answer: 104

Solution: The expression becomes

(9 + 4) * 8 = 13 * 8 = 104


18. If the operation - is defined by the equation c - d = (2d + 2c) * (c + d), what is the value of 6 - 4 ?

Answer: 200

Solution: The expression becomes

(8 + 12) * (6 + 4) = 20 * 10 = 200


19. If the operation - is defined by the equation x - y = 5x + 2y , what is the value of b if 4 - b = b - 2 ?

Answer: 16/3

Solution: The expression becomes

5(4) + 2(b) = 5b + 4

20 + 2b = 5b + 4,

3b = 16

b = 16/3


20. If the operation - is defined by the equation x - y = yx * (x+y), what is the value of 8 - 2 ?

Answer: 160

Solution: The expression becomes

2(8) * (8 + 2) = 16 * 10 = 160


21. If the operation ^ is defined by the equation a ^ b = 9 + ab, what is the value of 4 ^ 3 ?

Answer: 21

Solution: The expression becomes

9 + 4*3 = 9 + 12 = 21


22. If the operation + is defined by the equation c + d = (cd / c) * d, what is the value of 2 + 8 ?

Answer: 64

Solution: The expression becomes

(16 / 2) * 8 = 8 * 8 = 64


23. If the operation % is defined by the equation a % b = 2a * 3b, what is the value of 7 % 3 ?

Answer: 126

Solution: The expression becomes

2(7) * 3(3) = 14 * 9 = 126


24. If the operation + is defined by the equation x + y = (6x/5) * y, what is the value of 5 + 2 ?

Answer: 12

Solution: The expression becomes

6(5)/5 * 2 = 6 * 2 = 12


25. If the operation ^ is defined by the equation a ^ b = 5a + 2b, what is the value of x if 5 ^ x = x ^ 3 ?

Answer: 19/3

Solution: The expression becomes

25 + 2x = 5x + 6 = 19 = 3x; x = 19/3 

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