Logical Reasoning and Puzzles Flashcards

Statements: 1. All squares are rectangles. 2. Some rectangles are polygons. Based on the statements, which of the following conclusions can be logically drawn?

Answer: Neither Conclusion I nor II follows.

From the statements, we know all squares are a subset of rectangles, and some rectangles overlap with polygons. However, we cannot definitively conclude that any squares are polygons, as the 'some rectangles' that are polygons might be the ones that are not squares. Therefore, 'Some squares are polygons' is not a definite conclusion. Consequently, neither of the potential (but unstated) conclusions that 'Some polygons are squares' (I) or that 'All polygons are squares' (II) can be definitively proven.

A person starts from their house and drives 15 km towards the North. They then turn right and drive 8 km. After this, they turn left and drive 5 km. Finally, they turn left again and drive 8 km to reach their office. How far and in which direction is the office from their house?

Answer: 20 km North

Let the house be at the origin (0,0). 1. Drives 15 km North: Position is (0, 15). 2. Turns right (East) and drives 8 km: Position is (8, 15). 3. Turns left (North) and drives 5 km: Position is (8, 20). 4. Turns left (West) and drives 8 km: Position is (0, 20). The final position is (0, 20), which is 20 km directly North of the starting point (0,0).

Pointing to a boy in a photograph, a woman says, 'His mother's sister is my mother's only daughter.' How is the woman related to the boy in the photograph?

Answer: Aunt

Breaking down the statement: 'My mother's only daughter' refers to the woman herself. Therefore, the statement becomes 'His mother's sister is me'. If the woman is the sister of the boy's mother, she is the boy's aunt.

Six people (A, B, C, D, E, F) are sitting around a circular table facing the center. B is sitting to the immediate right of E. C is sitting opposite to A. D is not an immediate neighbor of A. Who is sitting opposite to B?

Answer: D

Let's arrange the seating. Place E. B is to the immediate right of E. Now place A and C opposite each other. There are two possible spots for them. If we place A to the left of E, then C is opposite. D cannot be next to A, so D must be between C and E. This leaves the last spot for F, which would be between A and B. In this circular arrangement, D is sitting opposite to B.

Which of the following has the same relationship as 'Scalpel : Surgeon'?

Answer: Chisel : Sculptor

The relationship is 'a specific tool used by a professional to perform their craft'. A scalpel is a primary tool for a surgeon. Similarly, a chisel is a primary tool for a sculptor. While a programmer uses a computer, it's a general-purpose machine, not a specific hand tool like a scalpel or chisel. A hammer is used on a nail (object), and a book is a product of an author.

To find out the age of a person 'X', which of the following statements is/are sufficient? I. X is 5 years older than Y. II. The sum of the ages of X and Y is 35.

Answer: Both statements I and II are needed.

Statement I alone gives a relationship (X = Y + 5) but not a specific age. Statement II alone gives a sum (X + Y = 35) but not a specific age for either person. However, if we use both statements together, we can form a system of two linear equations: X = Y + 5 and X + Y = 35. Substituting the first equation into the second gives (Y + 5) + Y = 35, which simplifies to 2Y = 30, so Y = 15. Then X = 20. A unique age for X can be found only by using both statements.