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. 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 ?

(a) 7
(b) 5
(c) 4
(d) 6 ✓ UPSC's answer

Why the answer is (d)

• P is assigned the integer 4.

• The difference between P and T is 5, so T is either 4 + 5 = 9 or 4 - 5 = -1.

• Since the integers are from 1 to 9, T must be 9.

• The difference between N and T is 3, so N is either 9 + 3 = 12 or 9 - 3 = 6.

• Since the integers are from 1 to 9, N must be 6.

• Therefore, the integer assigned to N is 6.

Why the other options are wrong

(a) 7: 7 is incorrect because the difference between 7 and T (9) is 2, not 3.
(b) 5: 5 is incorrect because the difference between 5 and T (9) is 4, not 3.
(c) 4: 4 is incorrect because 4 is already assigned to P, and the difference between 4 and T (9) is 5, not 3.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.