The letters L, M, N, O, P, Q, R, S and T in their order are substituted by nine integers 1 to 9 but not in that order. Integer 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3. What is the integer assigned to N?

Correct Option (D)

The problem provides the following information:

• The integer assigned to P is 4.
• The difference between P and T is 5.
• The difference between N and T is 3.
• The integers assigned to the letters L through T are from 1 to 9.

First, determine the value of T:

• Given P = 4 and |P - T| = 5.
• This implies |4 - T| = 5.
• Therefore, T could be 4 + 5 = 9 or 4 - 5 = -1.
• Since the assigned integers must be within the range 1 to 9, T must be 9.

Next, determine the value of N:

• Given T = 9 and |N - T| = 3.
• This implies |N - 9| = 3.
• Therefore, N could be 9 - 3 = 6 or 9 + 3 = 12.
• Since the assigned integers must be within the range 1 to 9, N must be 6.

Thus, the integer assigned to N is 6.

Incorrect Options:

Options A (7), B (5), and C (4) are incorrect. The sequential application of the given conditions (P=4, |P-T|=5, |N-T|=3) within the specified integer range (1-9) uniquely determines the integer assigned to N as 6. Any other value for N would contradict the problem's constraints.