If 2 [3] 4 = 14 and 3 [4] 6 = 60, then 4 [5] 7 = ?
Case 1: 2 [3] 4 = 14. Here a=2, b=3, c=4, R=14.
Case 2: 3 [4] 6 = 60. Here a=3, b=4, c=6, R=60.
We need to find the result for 4 [5] 7 = ?, where a=4, b=5, c=7.
Let’s test the formula R = (a * b + a * c) * (a-1).
For Case 1 (a=2, b=3, c=4): (2*3 + 2*4) * (2-1) = (6 + 8) * 1 = 14 * 1 = 14. This matches the given result.
For Case 2 (a=3, b=4, c=6): (3*4 + 3*6) * (3-1) = (12 + 18) * 2 = 30 * 2 = 60. This matches the given result.
Now apply the formula to the third case (a=4, b=5, c=7):
R = (4*5 + 4*7) * (4-1) = (20 + 28) * 3 = 48 * 3 = 144.
This result (144) is not among the options.
Let’s try another possible pattern based on the values. Consider the formula R = (a*b + a*c) + (a-2)*30.
For Case 1 (a=2, b=3, c=4): (2*3 + 2*4) + (2-2)*30 = (6 + 8) + 0*30 = 14 + 0 = 14. This matches.
For Case 2 (a=3, b=4, c=6): (3*4 + 3*6) + (3-2)*30 = (12 + 18) + 1*30 = 30 + 30 = 60. This matches.
Now apply this formula to the third case (a=4, b=5, c=7):
R = (4*5 + 4*7) + (4-2)*30 = (20 + 28) + 2*30 = 48 + 60 = 108.
This result (108) is present in option D. This pattern appears consistent with the given examples and options.
The rule is a [b] c = (a * b + a * c) + (a – 2) * 30.
– Test the derived pattern with all given examples.
– Apply the confirmed pattern to find the missing value.