NIMCET 2017 Logical Reasoning Question 51 with Solution

Question 51

Logical Reasoning Data Sufficiency / Interpretation Easy

Two persons S and M have made the following statements among themselves:

S says: "I am certainly not over 40 years."

M says: "I am 38 years and you are at least 5 years older than me."

S says: "You are at least 39 years."

If all the above statements are wrong, what are the ages of M and S?

(A) 36 and 40

(B) 36 and 41

(C) 37 and 40

(D) cannot be determined

View Dynamic Solution & Explanation ▼

Correct Solution: Option D

Step-by-step Solution:

The key is to reverse each of the three "wrong" statements to find out what must be true. Let M's age be M and S's age be S.

Statement 1 Negated: S's claim "I am not over 40" is wrong. Therefore, the truth is: S > 40.

Statement 2 Negated: M's claim "I am 38 AND S is at least 5 years older" is wrong. The logical opposite of "(A and B)" is "(not A) or (not B)". Therefore, the truth is: M ≠ 38 OR S < M + 5.

Statement 3 Negated: S's claim about M, "you are at least 39," is wrong. Therefore, the truth is: M < 39.

We must check if only one pair of ages satisfies these three true conditions.

Test Case 1 (M=37, S=41): This pair satisfies all three true conditions. (S > 40, M < 39, and the "M ≠ 38" part of the OR condition is met).

Test Case 2 (M=36, S=42): This pair also satisfies all three true conditions. (S > 40, M < 39, and the "M ≠ 38" part of the OR condition is met).

Since multiple possible solutions exist, a unique answer cannot be found.

Final Answer: The correct option is D. cannot be determined.