If 'P ! Q' means 'P + Q × 2', 'P @ Q' means 'P – Q ÷ 4' and 'P # Q' means 'P ×…
2023
If 'P ! Q' means 'P + Q × 2', 'P @ Q' means 'P – Q ÷ 4' and 'P # Q' means 'P × Q – 1', what is the value of (18 @ 4) ! (12 # 6) ?
- A.
139
- B.
144
- C.
159
- D.
225
Attempted by 4 students.
Show answer & explanation
Correct answer: C
To find the value of the expression (18 @ 4) ! (12 # 6), we need to apply the given rules for each operator step by step.
Operator Definitions
P ! Q = P + Q * 2
P @ Q = P - Q / 4
P # Q = P * Q - 1
Step-by-Step Calculation
Calculate (18 @ 4):
Using the rule P @ Q = P - Q / 4:
18 - (4 / 4) = 18 - 1 = 17
Calculate (12 # 6):
Using the rule P # Q = P * Q - 1:
(12 * 6) - 1 = 72 - 1 = 71
Calculate the final expression (17 ! 71):
Now, apply the rule P ! Q = P + Q * 2 to the results:
17 + (71 * 2) = 17 + 142 = 159