Four consecutive odd numbers form series P with an average of 60, and another four consecutive odd numbers form series Q with an average of 44. Find the difference between the largest number of series P and the second number of series Q.

ATQ, Four consecutive odd numbers differ by 2. For series P, let the numbers be a, a + 2, a + 4 and a + 6. Average of series P = 60 Sum of numbers of P = 60 × 4 = 240 So: a + a + 2 + a + 4 + a + 6 = 240 4a + 12 = 240 4a = 240 − 12 = 228 a = 228/4 a = 57 Series P = 57, 59, 61, 63 Largest number of series P = 63 For series Q, let the numbers be b, b + 2, b + 4 and b + 6. Average of series Q = 44 Sum of numbers of Q = 44 × 4 = 176 So: b + b + 2 + b + 4 + b + 6 = 176 4b + 12 = 176 4b = 176 − 12 = 164 b = 164/4 b = 41 Series Q = 41, 43, 45, 47 Second number of series Q = 43 Required difference = 63 − 43 = 20