Linear Arrangements Questions for CAT

Nine persons — A, B, C, D, E, F, G, H and I — sit in three rows of three. Row 1 (front) faces South and Row 2 (middle) faces North, so Rows 1 and 2 face each other; Row 3 (back) also faces North. Positions 1 to 3 are numbered from the solver's left. 'Directly opposite' means the same position in the facing row; 'directly behind' means the same position in the same-direction row behind. It is known that: (i) A sits at the left end of Row 1 and C sits at the right end of Row 1. (ii) B sits at the centre of Row 1. (iii) D sits directly opposite A and F sits directly opposite C, both in Row 2. (iv) E sits at the centre of Row 2. (v) G sits directly behind D and I sits directly behind F, both in Row 3. (vi) H sits at the centre of Row 3. Refer to the grid in the diagram while answering the questions that follow.

Some persons sit in a single straight row, all facing North (so each person's left is towards lower position numbers). The exact number of persons is not given and must be deduced from the clues. It is known that: (i) P sits 4th from the left end. (ii) P sits 3rd from the right end. (iii) Q sits at the extreme left end. (iv) R sits at the extreme right end. (v) S sits immediately to the left of P. Use the diagram framework to answer the questions that follow.

B, P, K, T, S, N, X and Y sit in a straight line facing north in any order. Exactly one person sits between S and X. N is restricted to sit in either the fifth position or sixth position from left. Two places to the left of T sits K. N and K do not sit beside each other. Both P and S do not agree to sit at the extreme ends. P and S sit beside each other. Four places to the right of B sits N. X is not sitting at either of the extreme ends.

How many people sit between K and X?

10 boxes named from A to J are arranged in a stack. The following clues are given about the arrangement:

1. Though C is below D, it is immediately below J.

2. A is above B and they have only D between them.

3. H is immediately below F. There are two boxes between H and I, where I is below H.

4. There are exactly 5 boxes between F and G, where F is above G.

An apartment has three floors: 1, 2, and 3. Each floor contains three flats named A, B and C. A flat is referred to by its floor number followed by the flat name. E.g., Flat B on the first floor is referred to as Flat 1B. Nine friends - P, Q, S, T, U, V, W, X, and Y bought a flat each in the apartment. All flats named A are situated one above the other. The same holds for B and C as well. Further, the following information is known.1. P bought the flat immediately above the one which X bought.2. The flats of Y and S are on the same floor.3. T bought flat B on the third floor.4. V bought the flat that is immediately below the one which Q bought.5. The flats bought by Q and P are not on the same floor.6. The flat bought by W was immediately below the one bought by U.7. The flat bought by X is not immediately above the flat bought by Y.8. Q did not buy a flat on the third floor.9. S did not buy flat 1C.

Who bought flat 2C?

Amit needs to get his project approved by the Environment Ministry. He knows that Mr Jain, Mr Kulkarni, Mr Mehra, Mr Mukherjee, Mr Sharma and Mr Verma are the head clerks of the different departments within the ministry. The six departments are Accounts, Administration, Archives, Clearance, Main and Technical. The Ministry building is a two floor building with 3 offices on each floor. Amit knows the following information:

a) Mr Mehra’s office is above the Clearance office

b) The Archives dept office is above the Administration dept office

c) The Technical dept office is above the Accounts department

d) The Accounts department is situated between the Administration department on the left and Mr Kulkarni’s office on the right

e) Mr Jain’s office is above Mr Sharma’s office

f) Mr Mukherjee’s office is above the Administration Department

Seven persons — B, C, D, F, G, H and K — sit in a single row of seven seats (positions 1 to 7, numbered from the solver's left). Each faces either North or South. It is known that: (i) C sits at the centre of the row and faces North. (ii) F sits at the extreme right end and faces South. (iii) K sits at the extreme left end and faces North. (iv) H sits immediately to the left of C, from C's perspective, and faces the same direction as F. (v) B sits immediately to the right of C, from C's perspective, and faces North. (vi) D sits between K and H and faces the direction opposite to K. (vii) G sits between B and F and faces the direction opposite to B. Use the diagram framework to answer the questions that follow.